BEGIN:VCALENDAR
PRODID;X-RICAL-TZSOURCE=TZINFO:-//com.denhaven2/NONSGML ri_cal gem//EN
CALSCALE:GREGORIAN
VERSION:2.0
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20101005T203000Z
DTSTART;VALUE=DATE-TIME:20101005T193000Z
DESCRIPTION:Jim Fowler (The Ohio State University): A first talk on surge
ry. Some graduate students have asked me about surgery theory and what
it can do\; this talk is an extraordinarily brief\, high-level introduct
ion.
SUMMARY:Jim Fowler: A first talk on surgery
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20101012T203000Z
DTSTART;VALUE=DATE-TIME:20101012T193000Z
DESCRIPTION:Dan Burghelea (The Ohio State University): Persistence\, an i
nvitation to ``Topology for Data Analysis''. Persistence is an importan
t new topic in Computational Topology. In this talk I will explain what
``Persistence'' is\, what is this good for\, how can it be calculated a
nd what are the new invariants involved in the measuring of persistence.
This is a summary of work of Edelsbrunner\, Letcher\, Zomorodian\, Carl
sson. To the extent the time permits\, or in a follow up lecture\, a mo
re refined version of persistence\, whose calculation has the same degre
e of complexity but carry considerably more information will be describe
d (joint work with Tamal Dey). The exposition is elementary and needs o
nly basic concepts of simplicial complexes and homology.
SUMMARY:Dan Burghelea: Persistence\, an invitation to ``Topology for Data
Analysis''
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20101019T203000Z
DTSTART;VALUE=DATE-TIME:20101019T193000Z
DESCRIPTION:Rob Kirby (University of California\, Berkeley): Wrinkled fib
rations for 4-manifolds. (This is joint work with David Gay) I will dis
cuss the existence and uniqueness theorems for wrinkled fibrations of ar
bitrary orientable\, smooth $n$-manifolds ($n=4$ is the most interesting
case) over orientable surfaces. Existence sometimes holds\, and there
is a natural set of moves relating different wrinkled fibrations for a g
iven $n$-manifold. A wrinkled fibration is one in which the rank of the
differential is 2 or is a curve of points of rank 1 which look locally
like an arc cross an indefinite $k$-handle (and the curve is the arc cro
ss the critical point of the k-handle). Furthermore\, fibers are always
connected.
SUMMARY:Rob Kirby: Wrinkled fibrations for 4-manifolds
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20101026T203000Z
DTSTART;VALUE=DATE-TIME:20101026T193000Z
DESCRIPTION:Bruce Williams (University of Notre Dame): Family Hirzebruch
Signature Theorem with Converse. Let $X$ be a space which satisfied $4k
$-dimensional Poincar\\'e Duality\, and let $\\sigma(X)$ be the signatur
e of $X$. If $X$ is a manifold\, then $\\sigma(X)$ can be ``disassembled
''\, i.e. $\\sigma(X)$ is determined by a local invariant\, the Hirzebru
ch $L$-polynomial. In this talk I'll give an enriched version of $\\sigm
a(X)$ which is defined in all dimensions\, and for dim >4\, the enriched
version can be disassembled if and only if $X$ admits manifold structur
e. There is also a family version of this for fibrations
SUMMARY:Bruce Williams: Family Hirzebruch Signature Theorem with Converse
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20101102T203000Z
DTSTART;VALUE=DATE-TIME:20101102T193000Z
DESCRIPTION:Ian Leary (The Ohio State University): Infinite Smith groups
and Kropholler's hierarchy I. This talk concerns actions of (discrete)
groups on finite-dimensional contractible simplicial complexes. I call
a group G a `Smith group' if every action of G on a finite-dimensional c
ontractible simplicial complex has a fixed point. (The P A Smith theore
m tells us that every finite p-group is a Smith group\; there are no oth
er finite Smith groups.)\\nKropholler's hierarchy assigns an ordinal to
a group\, describing how simply it can be made to act on a finite-dimens
ional contractible simplicial complex. Finite groups are at stage 0 of
the hierarchy and stage 1 contains all groups that act on a finite-dimen
sional contractible simplicial complex without a fixed point. Until our
work\, no group was known to lie in the hierarchy beyond stage 3.\\nWe
construct an infinite Smith group\, and construct groups that show that
for countable groups\, Kropholler's hierarchy is as long as it possibly
could be.\\nIn the talks\, I will describe some fixed-point theorems and
explain some aspects of our group constructions. The first talk will f
ocus on Smith groups and the second on Kropholler's hierarchy.\\nJoint w
ith G Arzhantseva\, M Bridson\, T Januszkiewicz\, P Kropholler\, A Minas
yan and J Swiatkowski.
SUMMARY:Ian Leary: Infinite Smith groups and Kropholler's hierarchy I
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20101109T213000Z
DTSTART;VALUE=DATE-TIME:20101109T203000Z
DESCRIPTION:Ian Leary (The Ohio State University): Infinite Smith groups
and Kropholler's hierarchy II.
SUMMARY:Ian Leary: Infinite Smith groups and Kropholler's hierarchy II
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20101116T213000Z
DTSTART;VALUE=DATE-TIME:20101116T203000Z
DESCRIPTION:Igor Kriz (University of Michigan): Homotopy and Reality. Th
e Galois action of $\\mathbb{Z}/2$ on the field of complex numbers plays
prominent role in algebraic topology. Its significance in various conte
xts was discovered by Atiyah (in $K$-theory)\, Karoubi (Hermitian $K$-th
eory) and Landweber (real cobordism MR). It also played an important rol
e in the development of equivariant stable homotopy theory by Araki\, Ad
ams\, May and others. In 1998\, Po Hu and I did extensive work on MR\, i
ncluding a complete calculation of its coefficients\, and development of
what we called Real homotopy theory. Our work was discovered 10 years l
ater by Hill\, Hopkins and Ravenel\, and played a central role in their
recent solution of the Kervaire invariant 1 problem. Meanwhile\, there i
s a baffling parallel between Real and motivic homotopy theory which was
used by Morel and Voevodsky\, Levine and others in their investigation
of algebraic cobordism. Recently\, Hu\,Ormsby and myself combined Real a
nd algebraic techniques in a solution of the homotopy completion problem
for Hermitian K-theory for fields of characteristic 0. I hope to touch
on the different aspects of this amazing story in my talk.
SUMMARY:Igor Kriz: Homotopy and Reality
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20101130T213000Z
DTSTART;VALUE=DATE-TIME:20101130T203000Z
DESCRIPTION:Sergei Chmutov (The Ohio State University): Polynomials of gr
aphs on surfaces. The Jones polynomial of links in 3-space is a special
ization of the Tutte polynomial of corresponding plane graphs. There are
several generalizations of the Tutte polynomial to graphs embedded into
a surface. Some of them are related to the theory of virtual links. Alt
hough virtual link theory predicts some relations between these generali
zations. I will report about the results obtained in this direction duri
ng my summer program "Knots and Graphs".\\nIn particular I will compare
three polynomials of graphs on surfaces and a relative version of the Tu
tte polynomial of planar graphs. The first polynomial\, defined by M.Las
Vergnas\, uses a strong map of the bond matroid of the dual graph to th
e circuit matroid of the original graph. The second polynomial is the Bo
llobas-Riordan polynomial of a ribbon graph\, a straightforward generali
zation of the Tutte polynomial. The third polynomial\, due V.Krushkal\,
is defined using the symplectic structure in the first homology group of
the surface.
SUMMARY:Sergei Chmutov: Polynomials of graphs on surfaces
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110104T213000Z
DTSTART;VALUE=DATE-TIME:20110104T203000Z
DESCRIPTION:Zbigniew Fiedorowicz (The Ohio State University): Interchange
of monoidal structures in homotopy theory.
SUMMARY:Zbigniew Fiedorowicz: Interchange of monoidal structures in homot
opy theory
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110111T213000Z
DTSTART;VALUE=DATE-TIME:20110111T203000Z
DESCRIPTION:Guido Mislin (The Ohio State University): Borel cohomology an
d large-scale geometry in Lie groups. The Borel cohomology groups $H_B^
\\star(G\, \\mathbb{Z})$ of a Lie group $G$ are based on cocycles\, whic
h are Borel maps. These Borel cohomology groups are known to be naturall
y isomorphic to the singular cohomology groups $H^\\star(BG\,\\mathbb{Z}
)$ of the classifying space $BG$ of $G$\, the domain of primary characte
ristic classes. We discuss the relationship between boundedness properti
es of cocycles in $H_B^\\star(G\, \\mathbb{Z})$ and subgroup distortion
in $G$ (joint work with Indira Chatterji\, Yves de Cornulier and Christo
phe Pittet).
SUMMARY:Guido Mislin: Borel cohomology and large-scale geometry in Lie gr
oups
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110118T213000Z
DTSTART;VALUE=DATE-TIME:20110118T203000Z
DESCRIPTION:Louis Kauffman (University of Illinois at Chicago): Virtual K
not Theory. Virtual knot theory studies knots in thickened surfaces and
has a combinatorial representation that is similar to the diagrams for
classical knot theory. This talk is an introduction to virtual knot theo
ry and an exposition of new ideas and constructions\, including the pari
ty bracket polynomial\, the arrow polynomial and categorifications of th
e arrow polynomial. The arrow polynomial (of Dye and Kauffman) is a natu
ral generalization of the Jones polynomial\, obtained by using the orien
ted structure of diagrams in the state sum. We will discuss a categorifi
cation of the arrow polynomial due to Dye\, Kauffman and Manturov and wi
ll give an example (from many found by Aaron Kaestner) of a pair of virt
ual knots that are not distinguished by Khovanov homology (mod 2)\, or b
y the arrow polynomial\, but are distinguished by a categorification of
the arrow polynomial.
SUMMARY:Louis Kauffman: Virtual Knot Theory
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110125T213000Z
DTSTART;VALUE=DATE-TIME:20110125T203000Z
DESCRIPTION:Brian Munson (Wellesley College): Linking numbers\, generaliz
ations\, and homotopy theory. The linking number was first defined by G
auss in 1833\, who wrote it as an integral which is supposed to compute
the number of times one circle wraps around another in space. I will beg
in by discussing the classical linking number using a much simpler defin
ition by taking a planar projection of the link and counting the number
of times one component lies over the other. From this we will see exactl
y what it is the linking number counts\, and this leads to two things. T
he first is the realization that the linking number is really a "relativ
e" invariant. The second is a generalization\, due to the speaker\, of a
linking "number" for arbitrary manifolds in an arbitrary manifold. I wi
ll also discuss Milnor's higher-order linking numbers\, which detect\, f
or example\, that classical links such as the Borromean rings are linked
(despite being pairwise unlinked). This was generalized by Koschorke to
higher-order linking of arbitrary spheres in Euclidean space\, and the
speaker generalized this to arbitrary manifolds. These higher-order inva
riants are also relative invariants in the same way the linking number i
s\, and they admit a number of interesting geometric interpretations. Al
ong the way\, we will observe that the classical linking number is relat
ed to the stable homotopy groups of spheres\, whereas the higher-order g
eneralizations are related to a certain filtration of the unstable homot
opy groups of spheres.
SUMMARY:Brian Munson: Linking numbers\, generalizations\, and homotopy th
eory
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110201T213000Z
DTSTART;VALUE=DATE-TIME:20110201T203000Z
DESCRIPTION:Niles Johnson (University of Georgia): Complex Orientations a
nd p-typicality. This talk will describe computational results related
to the structure of power operations on complex oriented cohomology theo
ries (localized at a prime $p$)\, making use of the amazing connection b
etween complex orientations and the theory of formal group laws. After i
ntroducing the relevant concepts\, we will describe results from joint w
ork with Justin Noel showing that\, for primes $p$ less than or equal to
13\, orientations factoring non-trivially through the Brown-Peterson sp
ectrum cannot carry power operations\, and thus cannot provide $MU_{(p)}
$-algebra structure. This implies\, for example\, that if E is a Landweb
er exact $MU_{(p)}$-ring whose associated formal group law is $p$-typica
l of positive height\, then the canonical map $\\mathrm{MU}_{(p)} \\to E
$ is not a map of $H_\\infty$ ring spectra. It immediately follows that
the standard $p$-typical orientations on $\\mathrm{BP}$\, $E(n)$\, and $
E_n$ do not rigidify to maps of $E_\\infty$ ring spectra. We conjecture
that similar results hold for all primes.
SUMMARY:Niles Johnson: Complex Orientations and p-typicality
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110204T193000Z
DTSTART;VALUE=DATE-TIME:20110204T183000Z
DESCRIPTION:Martin Frankland (University of Illinois at Urbana-Champaign)
: Moduli spaces of 2-stage Postnikov systems. It is a classic fact that
any graded group (abelian above dimension 1) can be realized as the hom
otopy groups of a space. However\, the question becomes difficult if one
includes the data of primary homotopy operations\, known as a Pi-algebr
a. When a Pi-algebra is realizable\, we would also like to classify all
homotopy types that realize it.\\nUsing an obstruction theory of Blanc-D
wyer-Goerss\, we will describe the moduli space of realizations of certa
in 2-stage Pi-algebras. This is better than a classification: The moduli
space provides information about realizations as well as their higher a
utomorphisms.
SUMMARY:Martin Frankland: Moduli spaces of 2-stage Postnikov systems
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110208T213000Z
DTSTART;VALUE=DATE-TIME:20110208T203000Z
DESCRIPTION:Howard Marcum (The Ohio State University): Hopf invariants in
$W$-topology. Let ${\\mathcal{T}\\hspace{-0.3ex}op}_{\\ast}$ denote
the 2-category of based topological spaces\, base point preserving conti
nuous maps\, and based track classes of based homotopies. Let $W$ be a f
ixed space or spectrum and consider the 2-functor on ${\\mathcal{T}\\hsp
ace{-0.3ex}op}_{\\ast}$ obtained by taking the smash product with $W$. T
he categorical full image of this functor is a 2-category denoted $W{\\m
athcal{T}\\hspace{-0.3ex}op}_{\\ast}$ and called the *$W$-topology c
ategory*. For $W$ a space the study of $W$-topology was initiated by
Hardie\, Marcum and Oda [1]. Of course $W$-topology and stable homotopy
theory\, while related\, are distinct.\\nIn the associated $W$-homotopy
category the $W$-homotopy groups $\\pi_{r}^W (X)$ have long been recogn
ized as rather significant (but in other notation of course). For exampl
e\, Barratt (1955) studied $\\pi_{n}^W (S^{n})$ for $W=S^1 \\cup_p e^2$
Toda (1963) considered the *suspension order* of a complex $Y
_k$ having the same homology as the $(n-1)$-fold suspension $\\Sigma^{n-
1} P^{2k}$ of the real projective $2k$-space $P^{2k}$\, namely the order
of the identity class of $\\pi_{1}^W (S^{1})$ when $W=Y_k$. \\nIn [1] s
ome non-trivial elements in $W$-homotopy groups were detected by making
use of $W$-Hopf invariants. This talk focuses on a general proceedure fo
r introducing Hopf invariants into $W$-topology. As an application\, whe
n $W$ is a mod $p$ Moore space\, namely $W=S^1 \\cup_p e^2$\, we show
that it is possible to detect elements in $\\pi_{r+1}^W (\\Omega S^{m+1}
)$ which have connection with known stable periodic families of the hom
otopy groups of spheres. In particular we prove nontriviality in $\\pi_
{r+1}^W (\\Omega S^{m+1})$ of elements related to families discovered by
Gray (1984) (for $p$ an odd prime) and by Oda (1976) (for $p=2$). This
represents joint work with K. \;Hardie and N. \;Oda. \\n[1] K. H
ardie\, H. Marcum and N. Oda\, *The Whitehead products and powers in
$W$-topology*\, Proc. Amer. Math. Soc. **131** (2003)\, 941&ndash
\;951.
SUMMARY:Howard Marcum: Hopf invariants in $W$-topology
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110215T213000Z
DTSTART;VALUE=DATE-TIME:20110215T203000Z
DESCRIPTION:Jim Fowler (The Ohio State University): $\\mathcal B$-bounded
finiteness. Given a bounding class $B$\, we construct a bounded refine
ment $BK(-)$ of Quillen's $K$-theory functor from rings to spaces. $BK(
-)$ is a functor from weighted rings to spaces\, and is equipped with a
comparison map $BK \\to K$ induced by "forgetting control". In contrast
to the situation with $B$-bounded cohomology\, there is a functorial spl
itting $BK(-) \\simeq K(-) \\times BK^{rel}(-)$ where $BK^{rel}(-)$ is t
he homotopy fiber of the comparison map. For the bounding class $P$ of p
olynomial functions\, we exhibit an element of infinite order in $PK^{re
l}_0(Z[G])$ for $G$ the fundamental group of a certain 3-dimensional sol
vmanifold.
SUMMARY:Jim Fowler: $\\mathcal B$-bounded finiteness
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110222T213000Z
DTSTART;VALUE=DATE-TIME:20110222T203000Z
DESCRIPTION:Dan Burghelea (The Ohio State University): New topological in
variants in Morse Novikov theory (bar codes and Jordan cells). Inspired
by the idea of ``persistence'' (persistent homology) we introduce a new
class of topological invariants for (tame) circle valued maps $f: X \\t
o S^1$. They are Bar Codes and Jordan Cells. If $X$ is compact and $f$ i
s topologically tame (in particular a Morse circle valued function)\, th
ey are algorithmically computable\; moreover all topological invariants
of interest in Novikov-Morse theory can be recovered from them\; (for ex
ample the Novikov-Betti numbers of $(M\, \\xi)$\, $\\xi \\in H^1(M\;\\ma
thbb{Z})$ representing the homotopy class of $f$\, can be recovered from
the bar codes while the usual Betti numbers of $M$ from bar codes and J
ordan cells. A more subtle invariant like Reidemeister torsion is relate
d to the Jordan cells. The definition of these invariants is based on re
presentation theory of quivers ($=$oriented graphs). The above theory ex
tends Novikov-Morse theory from Morse circle valued maps to tame maps $f
:X \\to S^1$ and even further to 1-cocycle which is the topological vers
ion of closed one form for smooth manifolds. This last extension is more
elaborate and will be discussed later.
SUMMARY:Dan Burghelea: New topological invariants in Morse Novikov theory
(bar codes and Jordan cells)
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110301T213000Z
DTSTART;VALUE=DATE-TIME:20110301T203000Z
DESCRIPTION:Crichton Ogle (The Ohio State University): Finitely presented
groups and the $\\ell^1$ $K$-theory Novikov Conjecture. Using techniqu
es developed for studying polynomially bounded cohomology\, we show that
the assembly map for $K_*^t(\\ell^1(G))$ is rationally injective for al
l finitely presented discrete groups $G$. This verifies the $\\ell^1$-an
alogue of the Strong Novikov Conjecture for such groups. The same method
s show that the Strong Novikov Conjecture for all finitely presented gro
ups can be reduced to proving a certain (conjectural) rigidity of the cy
clic homology group $HC_1^t(H^{CM}_m(F))$ where $F$ is a finitely-genera
ted free group and $H^{CM}_m(F)$ is the ``maximal'' Connes-Moscovici alg
ebra associated to $F$.
SUMMARY:Crichton Ogle: Finitely presented groups and the $\\ell^1$ $K$-th
eory Novikov Conjecture
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110308T213000Z
DTSTART;VALUE=DATE-TIME:20110308T203000Z
DESCRIPTION:Crichton Ogle (The Ohio State University): Hermitian K-theory
of Spaces . A fundamental question (still unanswered) is whether certa
in ``periodic'' functors on the category of discrete groups\, such as th
e topological $K$-theory of $C^*(\\pi)$ or the Witt theory of $\\mathbb
Z[\\pi]$\, can be extended to a functors on the category of basepointed
topological spaces which depend (rationally) on more than just the funda
mental group. Following earlier work of Burghelea-Fiedorowicz\, Fiedorow
icz-Vogt\, and Vogell\, I will propose a model for a functor $X\\mapsto
AH(X)$\, which may be thought of as an Hermitian analogue of Waldhausen'
s functor $X\\mapsto A(X)$\, and occurs as the $\\mathbb Z/2$ fixed-poin
t set of an involution defined on a certain model of $A(X)$. I will also
explain how a suitable $\\mathbb Z/2$-equivariant version of Waldhausen
's splitting $Q(X_+)\\to A(X)\\to Q(X_+)$ verifies the Novikov conjectur
e for $\\pi_1(X)$.
SUMMARY:Crichton Ogle: Hermitian K-theory of Spaces
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110315T203000Z
DTSTART;VALUE=DATE-TIME:20110315T193000Z
DESCRIPTION:Frank Connolly (University of Notre Dame): Involutions on Tor
i and Topological Rigidity. How many involutions on the $n$ torus have
an isolated fixed point?\\nThis is a report of joint work with Jim Davis
and Qayum Khan.\\nWe prove that there is only one involution on the $n
$-torus\, $T^n$\, up to conjugacy\, for which the fixed set contains an
isolated point. But here\, $n$ must be of the form $4k$ or $4k+1$ (or
else\, n must be $\\leq 3$). In the other dimensions\, we classify all
such involutions\, using surgery theory and the calculation of the grou
ps $UNil_n(Z\,Z\,Z).$\\nWe also introduce a Topological Rigidity Conjec
ture and we show that the above result is a consequence of it.
SUMMARY:Frank Connolly: Involutions on Tori and Topological Rigidity
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110405T203000Z
DTSTART;VALUE=DATE-TIME:20110405T193000Z
DESCRIPTION:Indira Chatterji (The Ohio State University): Discrete linear
groups containing arithmetic groups. We discuss a question by Nori\, w
hich is to determine when a discrete Zariski dense subgroup in a semisim
ple Lie group containing a lattice has to be itself a lattice. This is j
oint work with Venkataramana.
SUMMARY:Indira Chatterji: Discrete linear groups containing arithmetic gr
oups
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110419T203000Z
DTSTART;VALUE=DATE-TIME:20110419T193000Z
DESCRIPTION:Michael Davis (The Ohio State University): Random graph produ
cts of groups. There is a theory of random graphs due to Erdos and Ren
yi. Associated to any group and a graph there is a notion of its graph p
roduct. So\, there also is a notion of a random graph products of group
s. For example\, by letting the group be Z/2\, the graph product can be
any right-angled Coxeter group. We compute the cohomological invariant
s of random graph products. This is joint work with Matt Kahle.
SUMMARY:Michael Davis: Random graph products of groups
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110426T193000Z
DTSTART;VALUE=DATE-TIME:20110426T183000Z
DESCRIPTION:Paul Goerss (Northwestern University): Picard groups in stabl
e homotopy theory. In any symmetric monoidal category $C$\, the Picard
group is the group of isomorphism classes of invertible objects. For the
usual stable homotopy category\, the only invertible objects are the sp
here spectra $S^n$\, with $n$ an integer. However\, if $E_\\star$ is a g
ood (i.e.\, complex-orientable) homology theory\, Mike Hopkins noticed t
hat the $E$-local stable homotopy category could have a rich and curious
Picard group---and that this group could give information about how hom
otopy theory of spectra reassembles from localizations. I'll review this
theory\, revisit some of the curious examples\, and report on recent ca
lculations. This is joint work with Hans-Werner Henn\, Mark Mahowald\, a
nd Charles Rezk.
SUMMARY:Paul Goerss: Picard groups in stable homotopy theory
LOCATION:EA295
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110504T213000Z
DTSTART;VALUE=DATE-TIME:20110504T203000Z
DESCRIPTION:Andy Putman (Rice University): Teichmüller space.
SUMMARY:Andy Putman: Teichmüller space
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110510T180000Z
DTSTART;VALUE=DATE-TIME:20110510T170000Z
DESCRIPTION:Boris Tsygan (Northwestern University): Algebraic structures
on Hochschild and cyclic complexes. The Hochschild chain and cochain co
mplexes and the cyclic complex of an associative algebra serve as noncom
mutative analogs of classical geometric objects on a manifold\, such as
differential forms and multivector fields. These complexes are known to
possess a very nontrivial and rich algebraic structure that is analogous
to\, and goes well beyond\, the classical algebraic structures known in
geometry. In this talk\, I will give a review of the subject and outlin
e an approach that is based on an observation that differential graded c
ategories form a two-category up to homotopy.
SUMMARY:Boris Tsygan: Algebraic structures on Hochschild and cyclic compl
exes
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110517T180000Z
DTSTART;VALUE=DATE-TIME:20110517T170000Z
DESCRIPTION:Stacy Hoehn (Vanderbilt University): Obstructions to Fiberin
g Maps. Given a fibration p\, we can ask when p is fiber homotopy equi
valent to a topological fiber bundle with compact manifold fibers\; assu
ming that the fibration p does admit a compact bundle structure\, we can
also ask to classify all such bundle structures on p. Similarly\, give
n a map f between compact manifolds\, we can ask when f is homotopic to
a topological fiber bundle with compact manifold fibers\, and assuming t
hat the map f does fiber\, we can ask to classify all of the different w
ays to fiber f. In this talk\, we will begin by describing the space
of all compact bundle structures on a fibration\, which is nonempty if a
nd only if p admits a compact bundle structure. We will then show that
\, as long as we are willing to stabilize by crossing with a disk\, the
obstructions to stably fibering a map f are related to the space of bund
le structures on the fibration p associated to f.
SUMMARY:Stacy Hoehn: Obstructions to Fibering Maps
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110524T203000Z
DTSTART;VALUE=DATE-TIME:20110524T193000Z
DESCRIPTION:John Klein (Wayne State University): Bundle structures and Al
gebraic $K$-theory. This talk will describe (Waldhausen type) algebraic
$K$-theoretic obstructions to lifting fibrations to fiber bundles havin
g compact smooth/topological manifold fibers. The surprise will be that
a lift can often be found in the topological case. Examples will be give
n realizing the obstructions.
SUMMARY:John Klein: Bundle structures and Algebraic $K$-theory
LOCATION:EA295
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110531T203000Z
DTSTART;VALUE=DATE-TIME:20110531T193000Z
DESCRIPTION:Dan Burghelea (The Ohio State University): TBA.
SUMMARY:Dan Burghelea: TBA
LOCATION:EA295
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110607T203000Z
DTSTART;VALUE=DATE-TIME:20110607T193000Z
DESCRIPTION:Courtney Thatcher (Penn State Altoona): On free $Z/p$ actions
on products of spheres. We consider free actions of large prime order
cyclic groups on products of spheres. The equivariant homotopy type wil
l be determined and the simple structure set discussed. Similar to lens
spaces\, the first $k$-invariant generally determines the homotopy type
\, however for homotopy equivalences between products of an even number
of spheres the Whitehead torsion vanishes and the quotients are also sim
ple homotopy equivalent. Unlike lens spaces which are determined by the
ir Reidemeister torsion and $\\rho$-invariant\, the $\\rho$-invariant va
nishes for products of an even number of spheres and the Pontrjagin clas
ses become p-localized homeomorphism invariants for a given dimension.
The cohomology classes\, Pontrjagin classes\, and the set of normal inva
riants will also be discussed.
SUMMARY:Courtney Thatcher: On free $Z/p$ actions on products of spheres
LOCATION:CH240faceb
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110715T193000Z
DTSTART;VALUE=DATE-TIME:20110715T183000Z
DESCRIPTION:Bobby Ramsey (University of Hawaii at Manoa): TBA. TBA
SUMMARY:Bobby Ramsey: TBA
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110825T203000Z
DTSTART;VALUE=DATE-TIME:20110825T193000Z
DESCRIPTION:Zhixu Su (Rose-Hulman Institute of Technology): Non-simply-co
nnected rational surgery. We will generalize Sullivan's rational surger
y realization theorem to the case when the fundamental group is finite\;
given a finite group action on a rational Poincar\\'e duality algebra\,
does there exist a closed manifold realizing the algebra as its cohomol
ogy ring with the group acting freely on it?
SUMMARY:Zhixu Su: Non-simply-connected rational surgery
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20110921T203000Z
DTSTART;VALUE=DATE-TIME:20110921T193000Z
DESCRIPTION:Stefan Haller (University of Vienna): The cohomology of sympl
ectic fiber bundles. The deRham cohomology of a Poisson manifold comes
equipped with a canonical filtration. For symplectic manifolds this filt
ration is well understood and can be computed from the cup product actio
n of the cohomology class represented by the symplectic form. In this ta
lk we will discuss said filtration for the total space of sympletic fibe
r bundles. The latter constitute a class of Poisson manifolds closely re
lated to the topology of the sympletic group of the typical fiber.
SUMMARY:Stefan Haller: The cohomology of symplectic fiber bundles
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20111007T213000Z
DTSTART;VALUE=DATE-TIME:20111007T203000Z
DESCRIPTION:Dan Burghelea (The Ohio State University): New topological in
variants (bar codes and Jordan cell) at work (part I). Bar codes and Jo
rdan cells provide a new type of linear algebra invariants which can be
used in topology. In joint work with Tamal Dey we have associated with a
ny angle valued generic map $f : X \\to S^1$\, $X$ a compact nice space
(ANR)\, $\\kappa$ any field and any integer $r$\, $0 \\leq r \\leq \\dim
X$\, a collection of such bar codes and Jordan cells. They can be effec
tively computed in case $\\kappa = \\mathbb{C}$ or $\\mathbb{Z}_2$\, $X$
is a simplicial complex and f a simplicial map by algorithms implementa
ble by familiar software (Matematica\, Mapple or Matlab). In this lectur
e I will describe some joint work with S Haller.\\n1. We prove that the
Jordan cells defined using $f$ are homotopy invariants of the pair $(X\,
\\xi)$\, $\\xi ∈ H^1(X\;\\mathbb{Z})$ representing $f$. \\n2. We calcula
te the homology $H_∗(\\tilde{X}\;\\kappa)$ as a $\\kappa[t^{−1}\,t]$ mod
ule\, $\\tilde{X}$ the infinite cyclic cover of $X$ induced by $\\xi$\,
as well as and the Novikov homology and Milnor-Turaev torsion of $(X\;\\
xi)$ in terms of bar codes and Jordan cells. \\n3. As a consequence we i
ntroduce Lefchetz zeta function of a pair $(X\;\\xi)$ which generalizes
the familiar Lefschetz zeta function of a self map of a compact manifold
and the Alexander polynomial of a knot\, and relate this function to dy
namics.
SUMMARY:Dan Burghelea: New topological invariants (bar codes and Jordan c
ell) at work (part I)
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20111014T213000Z
DTSTART;VALUE=DATE-TIME:20111014T203000Z
DESCRIPTION:Dan Burghelea (The Ohio State University): New topological in
variants (bar codes and Jordan cell) at work (part II). Bar codes and J
ordan cells provide a new type of linear algebra invariants which can be
used in topology. In joint work with Tamal Dey we have associated with
any angle valued generic map $f : X \\to S^1$\, $X$ a compact nice space
(ANR)\, $\\kappa$ any field and any integer $r$\, $0 \\leq r \\leq \\di
m X$\, a collection of such bar codes and Jordan cells. They can be effe
ctively computed in case $\\kappa = \\mathbb{C}$ or $\\mathbb{Z}_2$\, $X
$ is a simplicial complex and f a simplicial map by algorithms implement
able by familiar software (Matematica\, Mapple or Matlab). In this lectu
re I will describe some joint work with S Haller.\\n1. We prove that the
Jordan cells defined using $f$ are homotopy invariants of the pair $(X\
,\\xi)$\, $\\xi ∈ H^1(X\;\\mathbb{Z})$ representing $f$. \\n2. We calcul
ate the homology $H_∗(\\tilde{X}\;\\kappa)$ as a $\\kappa[t^{−1}\,t]$ mo
dule\, $\\tilde{X}$ the infinite cyclic cover of $X$ induced by $\\xi$\,
as well as and the Novikov homology and Milnor-Turaev torsion of $(X\;\
\xi)$ in terms of bar codes and Jordan cells. \\n3. As a consequence we
introduce Lefchetz zeta function of a pair $(X\;\\xi)$ which generalizes
the familiar Lefschetz zeta function of a self map of a compact manifol
d and the Alexander polynomial of a knot\, and relate this function to d
ynamics.
SUMMARY:Dan Burghelea: New topological invariants (bar codes and Jordan c
ell) at work (part II)
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20111021T213000Z
DTSTART;VALUE=DATE-TIME:20111021T203000Z
DESCRIPTION:Matt Sequin (The Ohio State University): An Algebraic Proof o
f the Equivalence of Two Quantum 3-Manifold Invariants. We will compare
two different quantum 3-manifold invariants\, both of which are given u
sing a finite dimensional Hopf Algebra $H$. One is the Hennings invarian
t\, given by an algorithm involving the link surgery presentation of a 3
-manifold and the Drinfeld double $D(H)$\; the other is the Kuperberg in
variant\, which is computed using a Heegaard diagram of the 3-manifold a
nd the same $H$. We have shown that when $H$ has the property of being
involutory\, these two invariants are actually equivalent. The proof is
totally algebraic and does not rely on general results involving catego
rical invariants. We will also briefly discuss some results in the case
where $H$ is not involutory.
SUMMARY:Matt Sequin: An Algebraic Proof of the Equivalence of Two Quantum
3-Manifold Invariants
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20111028T213000Z
DTSTART;VALUE=DATE-TIME:20111028T203000Z
DESCRIPTION:John Oprea (Cleveland State University): LS category\, the fu
ndamental group and Bochner-type estimates. The LS category of a space
X is a numerical invariant that measures the complexity of a space. Whil
e it is usually very hard to compute explicitly\, there are estimates an
d approximating invariants that help us to understand category better. A
big problem is to understand the effect of the fundamental group on cat
egory. Recently\, extending work of Dranishnikov\, Jeff Strom and the sp
eaker have given an upper bound for category using Ralph Fox's 1-categor
y (and another approximating invariant). Using an interpretation of this
1-category given by Svarc\, we have also been able to refine Bochner's
bound on the first Betti number in the presence of non-negative Ricci cu
rvature. Finally\, the 1-category forms a bridge between the theorems of
Yamaguchi and Kapovitch-Petrunin-Tuschmann on manifolds with almost non
-negative sectional curvature.
SUMMARY:John Oprea: LS category\, the fundamental group and Bochner-type
estimates
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20111101T153000Z
DTSTART;VALUE=DATE-TIME:20111101T143000Z
DESCRIPTION:Ron Fintushel (Michigan State University): Surgery on nullhom
ologous tori and smooth structures on 4-manifolds. By studying the exam
ple of smooth structures on $CP^2 \\# 3(-CP^2)$\, I will illustrate how
surgery on a single embedded nullhomologous torus can be utilized to cha
nge the symplectic structure\, the Seiberg-Witten invariant\, and hence
the smooth structure on a 4-manifold.
SUMMARY:Ron Fintushel: Surgery on nullhomologous tori and smooth structur
es on 4-manifolds
LOCATION:Scott Laboratory N0056
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20111109T223000Z
DTSTART;VALUE=DATE-TIME:20111109T213000Z
DESCRIPTION:Grigori Avramidi (University of Chicago): Isometries of asphe
rical manifolds. I will describe some recent results on isometry groups
of aspherical Riemannian manifolds and their universal covers. The gene
ral theme is that topological properties of an aspherical manifold often
restrict the isometries of an arbitrary complete Riemannian metric on t
hat manifold. These topological properties tend to be established by us
ing a specific "nice" metric on the manifold.\\nI will illustrate this b
y explaining why on an irreducible locally symmetric manifold\, no metri
c has more symmetry than the locally symmetric metric. I will also discu
ss why moduli space is a minimal orbifold and relate this phenomenon to
symmetries of arbitrary metrics on moduli space.
SUMMARY:Grigori Avramidi: Isometries of aspherical manifolds
LOCATION:Derby Hall 0047
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20111118T223000Z
DTSTART;VALUE=DATE-TIME:20111118T213000Z
DESCRIPTION:Max Forester (University of Oklahoma): Higher Dehn functions
of some abelian-by-cyclic groups. I will discuss the geometry of certai
n abelian-by-cyclic groups and show how to establish the optimal top-dim
ensional isoperimetric inequality that holds in these groups. This is jo
int work with Noel Brady.
SUMMARY:Max Forester: Higher Dehn functions of some abelian-by-cyclic gro
ups
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20111122T211000Z
DTSTART;VALUE=DATE-TIME:20111122T201000Z
DESCRIPTION:Steve Ferry (Rutgers University): Volume Growth\, DeRham Coho
mology\, and the Higson Compactification. We construct a variant of DeR
ham cohomology and use it to prove that the Higson compactification of $
R^n$ has uncountably generated $n^{\\mbox{th}}$ integral cohmology. We a
lso explain that there is\, nevertheless\, a way of using the Higson com
pactification to prove the Novikov conjecture for a large class of group
s.
SUMMARY:Steve Ferry: Volume Growth\, DeRham Cohomology\, and the Higson C
ompactification
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20111202T203000Z
DTSTART;VALUE=DATE-TIME:20111202T193000Z
DESCRIPTION:Dave Constantine (University of Chicago): Group actions and c
ompact Clifford-Klein forms of homogeneous spaces. A compact Clifford-
Klein form of the homogeneous space $J\\backslash H$ is a compact manifo
ld $J\\backslash H/\\Gamma$ constructed using a discrete subgroup $\\Gam
ma$ of $H$. I will survey the existence problem for compact forms\, with
particular attention to the case when there is an action by a large gro
up on $J\\backslash H/\\Gamma$. I will also make some remarks on a conje
cture of Kobayashi on the scarcity of compact forms.
SUMMARY:Dave Constantine: Group actions and compact Clifford-Klein forms
of homogeneous spaces
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120110T213000Z
DTSTART;VALUE=DATE-TIME:20120110T203000Z
DESCRIPTION:Pablo Su\\'arez-Serrato (Universidad Nacional Aut\\'onoma de
M\\'exico): Using 4-manifolds to describe groups. We will describe deco
mpositions of finitely presented groups\, using descriptions of smooth a
nd of symplectic four-manifolds. Every finitely presented group admits a
decomposition into a triple consisting of the fundamental groups of two
compact complex Kähler surfaces with boundary and the fundamental group
of a three manifold. We will exhibit various ways of obtaining similar
decompositions of finitely presented groups into graphs\, via descriptio
ns of smooth 4-manifolds into Lefschetz fibrations. We distill this data
into invariants\, by considering the minimal number of edges these grap
hs may have. These ideas are related to the minimal euler characteristic
of symplectic four-manifolds and the minimal genus of a Lefschetz fibra
tion\, seen as group invariants.
SUMMARY:Pablo Su\\'arez-Serrato: Using 4-manifolds to describe groups
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120112T213000Z
DTSTART;VALUE=DATE-TIME:20120112T203000Z
DESCRIPTION:Eric Babson (Univeristy of California\, Davis): Random simpli
cial complexes. The study of fundamental groups of random two dimension
al simplicial complexes calls attention to the small subcomplexes of suc
h objects. Such subcomplexes have fewer triangles than some multiple of
the number of their vertices. One gets that this condition with constant
less than two on a connected complex (and all of its subcomplexes) impl
ies that it is homotopy equivalent to a wedge of circles\, spheres and p
rojective planes. This analysis yields parameter regimes for vanishing\
, hyperbolicity and Kazhdanness of these groups. For clique complexes of
random graphs there is a similar problem involving complexes with fewer
edges than thrice the number of their vertices resulting in similar res
ults on the fundamental groups of their clique complexes. This is based
on joint work with Hoffman and Kahle.
SUMMARY:Eric Babson: Random simplicial complexes
LOCATION:MW154
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120117T213000Z
DTSTART;VALUE=DATE-TIME:20120117T203000Z
DESCRIPTION:Graham Denham (The University of Western Ontario): Duality pr
operties for abelian covers. In parallel with a classical definition du
e to Bieri and Eckmann\, say an FP group G is an abelian duality group i
f H^p(G\,Z[G^{ab}]) is zero except for a single integer p=n\, in which c
ase the cohomology group is torsion-free. We make an analogous definiti
on for spaces. In contrast to the classical notion\, the abelian dualit
y property imposes some obvious constraints on the Betti numbers of abel
ian covers.\\nWhile related\, the two notions are inequivalent: for exam
ple\, surface groups of genus at least 2 are (Poincaré) duality groups\,
yet they are not abelian duality groups. On the other hand\, using a re
sult of Brady and Meier\, we find that right-angled Artin groups are abe
lian duality groups if and only if they are duality groups: both propert
ies are equivalent to the Cohen-Macaulay property for the presentation g
raph. Building on work of Davis\, Januszkiewicz\, Leary and Okun\, hype
rplane arrangement complements are both duality and abelian duality spac
es. These results follow from a slightly more general\, cohomological v
anishing theorem\, part of work in progress with Alex Suciu and Sergey Y
uzvinsky.
SUMMARY:Graham Denham: Duality properties for abelian covers
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120124T213000Z
DTSTART;VALUE=DATE-TIME:20120124T203000Z
DESCRIPTION:Jean Lafont (The Ohio State University): Riemannian vs. metri
c non-positive curvature on 4-manifolds. I'll outline the construction
of smooth 4-manifolds which support locally CAT(0)-metrics (the metric
version of non-positive curvature)\, but do not support any Riemannian m
etric of non-positive sectional curvature. This is joint work with Mike
Davis and Tadeusz Januszkiewicz.
SUMMARY:Jean Lafont: Riemannian vs. metric non-positive curvature on 4-ma
nifolds
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120131T213000Z
DTSTART;VALUE=DATE-TIME:20120131T203000Z
DESCRIPTION:Thomas Kerler (The Ohio State University): Faithful Represent
ations of the Braid Groups via Quantum Groups. In the last couple of de
cades the study of representations of braid groups $B_n$ attracted atte
ntion from two rather different motivations. One deals with the linearit
y of the braid groups\, that is\, whether the $B_n$ can be faithfully re
presented.\\nThis question was answered in the positive for the Lawrence
-Krammer-Bigelow (LKB) representation independently by Krammer and Bigel
ow around 2001. The LKB representation is given by the natural action of
$B_n$ in the second homology of a rank two free abelian cover of the tw
o-point configuration space on the $n$-punctured disc. It is thus natura
lly a module over the ring of Laurent polynomials in two variables.\\nTh
e other development is the construction of braid representations from qu
antum groups. One such class of $B_n$-representations of is constructed
using quantum-$sl_2$\, which is a one-parameter Hopf algebra deformation
of the universal enveloping algebra of $sl_2$. The algebra admits a qua
si-triangular R-matrix which can be used to represent $B_n$ on the $n$-f
old tensor product of a Verma module with generic highest weight.\\nWe p
rove that the latter representation\, with some refinement of the ground
ring\, is isomorphic to the LKB representation where the two parameters
corresponding to the generators of the Deck transformation group are id
entified with the deformation parameter of quantum-$sl_2$ and the gener
ic highest weight of the Verma module respectively. We also show irredu
cibility of this representation over the fraction field of the ring of L
aurent polynomials.\\n Time permitting we will discuss relations to othe
r types of braid group representations that may shed light on this curio
us connection\, as well as reducibility issues at certain choices of par
ameters.\\nJoint work with Craig Jackson.
SUMMARY:Thomas Kerler: Faithful Representations of the Braid Groups via Q
uantum Groups
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120207T213000Z
DTSTART;VALUE=DATE-TIME:20120207T203000Z
DESCRIPTION:Niles Johnson (University of Georgia): Obstruction theory for
homotopical algebra maps. We take an obstruction-theoretic approach to
the question of algebraic structure in homotopical settings. At its he
art\, this is an application of the Bousfield-Kan spectral sequence adap
ted for the action of a monad T on a topological model category.\\nThis
talk will focus on the special case where T is a monad encoding E_infty
structure in spectra and H_infty structure in the derived category of sp
ectra. We will present examples from rational homotopy theory illustrat
ing the obstructions to rigidifying homotopy algebra maps to strict alge
bra maps\, and explain in a precise way how the edge homomorphism of thi
s obstruction spectral sequence measures the difference between up-to-ho
motopy and on-the-nose T-algebra maps.
SUMMARY:Niles Johnson: Obstruction theory for homotopical algebra maps
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120214T203000Z
DTSTART;VALUE=DATE-TIME:20120214T193000Z
DESCRIPTION:Dan Burghelea (The Ohio State University): New topological in
variants for a continuous nonzero complex valued function. Given a comp
act ANR $X$ and $f : X \\to \\mathbb{C} \\setminus 0$ a continuous map\,
for any $0 \\leq r \\leq \\dim X$\, one proposes three monic complex va
lued polynomials $P_{r\,s}(z)$\, $P_{r\,a}(z)$ and $P_{r\,m}(z)$\, with
$\\deg(P_{r\,s}(z) = \\beta_r(X)$ where $\\beta_r(X)$ is the r−th Betti
number\, $\\deg(P_{r\,a}(z) = \\beta_r^N(X\,f)$\, where $\\beta_r^{N}(X\
,f)$ is the $r$−th Novikov Betti number\, $P_{r\,m}(z)$ a homotopy invar
iant of $f$. The first two are continuous assignments with respect to co
mpact open topology\, the last is locally constant (on the space of cont
inuous functions with compact open topology).
SUMMARY:Dan Burghelea: New topological invariants for a continuous nonzer
o complex valued function
LOCATION:MW154
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120221T213000Z
DTSTART;VALUE=DATE-TIME:20120221T203000Z
DESCRIPTION:Ian Hambleton (McMaster University): Co-compact discrete grou
p actions and the assembly map. A discrete group $\\Gamma$ can act free
ly and properly on $S^n \\times R^m$\, for some $n\, m >0$ if and only i
f $\\Gamma$ is a countable group with periodic Farrell cohomology: Conno
lly-Prassidis (1989) assuming $vcd(\\Gamma)$ finite\, Adem-Smith (2001).
For free co-compact actions there are additional restrictions\, but no
general sufficient conditions are known. The talk will survey this probl
em and its connection to the Farrell-Jones assembly maps in K-theory and
L-theory.
SUMMARY:Ian Hambleton: Co-compact discrete group actions and the assembly
map
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120228T213000Z
DTSTART;VALUE=DATE-TIME:20120228T203000Z
DESCRIPTION:James Davis (Indiana University): Smith Theory. P.A. Smith\
, in the first half of the 20th century\, developed homological tools to
study actions of finite p-groups on topological spaces. The standard a
pplications of Smith theory are that if a p-group acts on a {disk\, sphe
re\, manifold\, finite-dimensional space} then the fixed set of the acti
on is a {mod p homology disk\, mod p homology sphere\, mod p homology ma
nifold\, finite dimensional space}.\\nThis talk will review the classica
l theory\, give applications to actions on aspherical manifolds\, and ex
tend the theory to give restrictions on periodic knots.
SUMMARY:James Davis: Smith Theory
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120306T213000Z
DTSTART;VALUE=DATE-TIME:20120306T203000Z
DESCRIPTION:Bobby Ramsey (The Ohio State University): Amenability and Pro
perty A. We discuss Yu's property A as a generalization of amenability
for countable groups. A few characterizations of amenability and prope
rty A are given\, including Johnson's cohomological characterization of
amenability and the recent work of Brodzki\, Nowak\, Niblo\, and Wright
which characterizes property A in a similar manner. These characterizati
ons play a major role in the relative versions of these properties.
SUMMARY:Bobby Ramsey: Amenability and Property A
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120313T203000Z
DTSTART;VALUE=DATE-TIME:20120313T193000Z
DESCRIPTION:Bobby Ramsey (The Ohio State University): Relative Property A
and Relative Amenability. We define the notion of a group having rela
tive property A with respect to a finite family of subgroups. Many chara
cterizations for relative property A are given. In particular a cohomo
logical characterization shows that if $G$ has property A relative to a
family of subgroups $\\mathcal{H}$\, and if each $H \\in \\mathcal{H}$
has property A\, then $G$ has property A. This result leads to new cla
sses of groups that have property A. Specializing the definition of re
lative property A\, an analogue definition of relative amenability for
discrete groups are introduced and similar results are obtained.
SUMMARY:Bobby Ramsey: Relative Property A and Relative Amenability
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120403T203000Z
DTSTART;VALUE=DATE-TIME:20120403T193000Z
DESCRIPTION:Randy McCarthy (University of Illinois at Urbana-Champaign):
On the Algebraic K-theory of Brave New Tensor Algebras. Waldhausen's A-
theory of a space $X$ is sometimes described as the ``universal Euler cl
ass''. Along these lines\, the ``universal generalized Lefschetz class''
of an endomorphism would be the reduced algebraic K-theory of an associ
ated ``brave new'' tensor algebra. Recent joint work with Ayelet Lindens
trauss describing this spectrum\, when one is working in an analytic ran
ge (in the sense of Goodwillie's calculus of functors) will be discussed
.\\nFor $\\pi_0$\, these results go back to Almkvist\, Rincki and L\\"uc
k. More generally these results are related to the theses of Lydakis and
Iwachita which built upon the computation of the $A$-theory of the sus
pension of a space by Carlsson\, Cohen\, Goodwillie and Hsiang.
SUMMARY:Randy McCarthy: On the Algebraic K-theory of Brave New Tensor Alg
ebras
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120410T203000Z
DTSTART;VALUE=DATE-TIME:20120410T193000Z
DESCRIPTION:Matt Kahle (The Ohio State University): Sharp vanishing thres
holds for cohomology of random flag complexes. The random flag complex
is a natural combinatorial model of random topological space. In this
talk I will survey some results about the expected topology of these obj
ects\, focusing on recent work which gives a sharp vanishing threshold f
or kth cohomology with rational coefficients.\\n This recent work provid
es a generalization of the Erdos-Renyi theorem which characterizes how m
any random edges one must add to an empty set of n vertices before it be
comes connected. As a corollary\, almost all d-dimensional flag complex
es have rational homology only in middle degree (d/2).\\n This is topolo
gy seminar\, so I will assume that people know what homology and cohomol
ogy are\, but I will strive to make the talk self contained and define a
ll the necessary probability as we go.
SUMMARY:Matt Kahle: Sharp vanishing thresholds for cohomology of random f
lag complexes
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120424T203000Z
DTSTART;VALUE=DATE-TIME:20120424T193000Z
DESCRIPTION:Ruben Sanchez-Garcia (University of Southampton ): Classifyin
g spaces and the Isomorphism Conjectures. For each discrete group G one
can find a universal G-space with stabilizers in a prescribed family of
subgroups of G. These spaces play a prominent role in the so-called Iso
morphism Conjectures\, namely the Baum-Connes and the Farrell-Jones conj
ectures. We will discuss the former conjecture in more detail and descri
be its topological side: the equivariant K-homology of the universal spa
ce for proper actions. Finally\, we will report on joint work with Jean-
François Lafont and Ivonne Ortiz on the rationalized topological side fo
r some low dimensional groups.
SUMMARY:Ruben Sanchez-Garcia: Classifying spaces and the Isomorphism Conj
ectures
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120426T203000Z
DTSTART;VALUE=DATE-TIME:20120426T193000Z
DESCRIPTION:Ivonne Ortiz (Miami University): The lower algebraic $K$-theo
ry of three-dimensional crystallographic groups. In this joint work wit
h Daniel Farley\, we compute the lower algebraic $K$-groups of all split
three-dimensional crystallographic groups $G$. These groups account for
73 isomorphism types of three-dimensional crystallographic groups\, out
of 219 types in all. Alves and Ontaneda in 2006\, gave a simple formul
a for the Whitehead group of a 3-dimensional crystallographic group $G$
in terms of the Whitehead groups of the virtually infinite cyclic subgro
ups of $G$. The main goal in this work in progress is to obtain explicit
computations for $K_0(ZG)$ and $K_{-1}(ZG)$ for these groups.
SUMMARY:Ivonne Ortiz: The lower algebraic $K$-theory of three-dimensional
crystallographic groups
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120515T203000Z
DTSTART;VALUE=DATE-TIME:20120515T193000Z
DESCRIPTION:Dan Isaksen (Wayne State University): Sums-of-squares formula
s and motivic cohomology. A sums-of-squares formula over a field $k$ is
a polynomial identity of the form $\\left( x_1^2 + \\cdots + x_r^2 \\ri
ght) \\left( y_1^2 + \\cdots + y_s^2 \\right) = z_1^2 + \\cdots z_t^2\,$
where the $z$'s are bilinear in the $x$'s and $y$'s over $k$. If a sums
-of-squares formula exists over $\\mathbb{R}$\, then a theorem of Hopf f
rom 1940 gives numerical restrictions on $r$\, $s$\, and $t$. This resul
t was one of the earliest uses of the cup product in singular cohomology
.\\nI will describe some joint work with D. Dugger on generalizing Hopf'
s result to arbitrary fields of characteristic not $2$. The basic idea
is to use motivic cohomology instead of singular cohomology.\\nThis lead
s into the broader subject of computations in motivic homotopy theory.\\
nThis is a joint talk with algebraic geometry seminar.
SUMMARY:Dan Isaksen: Sums-of-squares formulas and motivic cohomology
LOCATION:Journalism Building 353
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120522T203000Z
DTSTART;VALUE=DATE-TIME:20120522T193000Z
DESCRIPTION:Andrew Salch (Wayne State University): Algebraic G-theory via
twisted deformation theory. We review some old problems in algebraic t
opology--namely\, the classification of finite-dimensional modules over
subalgebras of the Steenrod algebra\, and related classification problem
s in representation theory and finite CW complexes--and some old techniq
ues in deformation theory--namely\, the use of Hochschild 1- and 2-cocyc
les with appropriate coefficients to classify first-order deformations o
f modules and algebras\, respectively. Then we work out how one has to a
dapt these old methods to solve these old problems\, ultimately using so
me modern technology: a deformation-theoretic interpretation of twisted
nonabelian higher-order Hochschild cohomology.
SUMMARY:Andrew Salch: Algebraic G-theory via twisted deformation theory
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120828T200000Z
DTSTART;VALUE=DATE-TIME:20120828T190000Z
DESCRIPTION:Grigori Avramidi (University of Chicago): Flat tori in the ho
mology of some locally symmetric spaces. I'll show that many finite cov
ers of $\\mathrm{SL}(m\,Z)\\backslash \\mathrm{SL}(m\,R)/\\mathrm{SO}(m)
$ have non-trivial homology classes generated by totally geodesic flat $
(m-1)$-tori. This is joint work with Tam Nguyen Phan.
SUMMARY:Grigori Avramidi: Flat tori in the homology of some locally symme
tric spaces
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120904T200000Z
DTSTART;VALUE=DATE-TIME:20120904T190000Z
DESCRIPTION:Stefan Haller (University of Vienna): Commutators of diffeomo
rphisms. Suppose $M$ is a smooth manifold and let $G$ denote the connec
ted component of the identity in the group of all compactly supported di
ffeomorphisms of $M$. It has been known for quite some time that the gro
up $G$ is simple\, i.e. has no non-trivial normal subgroups. Consequentl
y\, $G$ is a perfect group\, i.e. each element $g$ of $G$ can be written
as a product of commutators\, $$g=[h_1\,k_1]\\circ\\cdots\\circ[h_N\,k_
N].$$ Actually\, all available proofs (Herman\, Mather\, Epstein\, Thurs
ton) for the simplicity of $G$ first establish perfectness\; it is then
rather easy to conclude that $G$ has to be simple.\\nIn the talk I will
discuss a new\, more elementary\, proof for the perfectness of the group
$G$. This approach also shows that the factors $h_i$ and $k_i$ in the p
resentation above can be chosen to depend smoothly on $g$. Moreover\, it
leads to new estimates for the number of commutators necessary. If $g$
is sufficiently close to the identity\, then $N=4$ commutators are suffi
cient\; for certain manifolds (e.g. mapping tori) even $N=3$ will do.\\n
This talk is based on joint work with T. Rybicki and J. Teichmann.
SUMMARY:Stefan Haller: Commutators of diffeomorphisms
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20120918T200000Z
DTSTART;VALUE=DATE-TIME:20120918T190000Z
DESCRIPTION:Christopher Davis (The Ohio State University): Computing Abel
ian rho-invariants of links via the Cimasoni-Florens signature. The sol
vable filtration of the knot concordance group has been studied closely
since its definition by Cochran\, Orr and Teichner in 2003. Recently Coc
hran\, Harvey and Leidy have shown that the successive quotients in this
filtration contain infinite rank free abelian groups and even exhibit a
kind of primary decomposition. Unfortunately\, their construction relie
s on an assumption of non-vanishing of certain rho-invariants. By relati
ng these rho-invariants to the signature function defined by Cimasoni an
d Florens in 2007\, we remove this ambiguity from the construction of Co
chran-Harvey-Leidy.
SUMMARY:Christopher Davis: Computing Abelian rho-invariants of links via
the Cimasoni-Florens signature
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20121002T200000Z
DTSTART;VALUE=DATE-TIME:20121002T190000Z
DESCRIPTION:Duane Randall (Loyola University\, New Orleans): On Homotopy
Spheres. We present results concerning the existence of nontrivial homo
topy spheres and also discuss the determination of the smallest dimensio
nal Euclidean spaces in which they smoothly embed.
SUMMARY:Duane Randall: On Homotopy Spheres
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20121009T200000Z
DTSTART;VALUE=DATE-TIME:20121009T190000Z
DESCRIPTION:Niles Johnson (The Ohio State University\, Newark): Ecologica
l Niche Topology. The ecological niche of a species is the set of envir
onmental conditions under which a population of that species persists.
This is often thought of as a subset of "environment space" -- a Euclide
an space with axes labeled by environmental parameters. This talk will e
xplore mathematical models for the niche concept\, focusing on the relat
ionship between topological and ecological ideas. We also describe appl
ications of machine learning to develop empirical models from data in th
e field. These lead to novel questions in computational topology\, and
we will discuss recent progress in that direction. This is joint with Jo
hn Drake in ecology and Edward Azoff in mathematics.
SUMMARY:Niles Johnson: Ecological Niche Topology
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20121016T200000Z
DTSTART;VALUE=DATE-TIME:20121016T190000Z
DESCRIPTION:Paul Arne Østvær (University of Oslo): Motivic slices and the
graded Witt ring. We compute the motivic slices of hermitian K-theory
and higher Witt-theory. The corresponding slice spectral sequences relat
e motivic cohomology to Hermitian K-groups and Witt groups\, respectivel
y. Using this we compute the Hermitian K-groups of number fields\, and (
re)prove Milnor's conjecture on quadratic forms for fields of characteri
stic different from 2. Joint work with Oliver Röndigs.
SUMMARY:Paul Arne Østvær: Motivic slices and the graded Witt ring
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20121030T200000Z
DTSTART;VALUE=DATE-TIME:20121030T190000Z
DESCRIPTION:Pierre-Emmanuel Caprace (Université catholique de Louvain): R
ank one elements in Coxeter groups and CAT(0) cube complexes. This talk
centers around the Rank Rigidity Conjecture for groups acting properly
and cocompactly on CAT(0) spaces. After discussing some generalities on
the conjecture and some of its consequences\, I will focus on the two sp
ecial cases alluded to in the title.
SUMMARY:Pierre-Emmanuel Caprace: Rank one elements in Coxeter groups and
CAT(0) cube complexes
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20121106T210000Z
DTSTART;VALUE=DATE-TIME:20121106T200000Z
DESCRIPTION:Jean Lafont (The Ohio State University): Comparing semi-norms
on 3rd homology. It follows from work of Crowley-Loeh (d>3) and Barge
-Ghys (d=2) that in all degrees distinct from d=3\, the l^1-seminorm and
the manifold semi-norm coincide on homology of degree d. We show that w
hen d=3\, the two semi-norms are bi-Lipschitz to each other\, with an ex
plicitly computable constant. This was joint work with Christophe Pittet
(Univ. Marseille).
SUMMARY:Jean Lafont: Comparing semi-norms on 3rd homology
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20121113T210000Z
DTSTART;VALUE=DATE-TIME:20121113T200000Z
DESCRIPTION:Jim Fowler (The Ohio State University): Numeric methods in to
pology. Often the answer to a topological question is\, by its own admi
ssion\, nonconstructive\, but even when the answer is constructive\, ser
ious difficulties can arise in carrying out that construction. We will
consider a couple cases like this. As an approachable\, low-dimensional
example\, we decompose surfaces as a square complex with a fixed number
of squares meeting at a vertex. As a high-dimensional example\, we con
sider the possible Pontrjagin numbers of highly connected 32-manifolds.
To address this latter case\, we will be confronted with needing to com
pute the coefficients of the Hirzebruch $L$-polynomial\; some topology p
rovides a recursive method faster than naive symmetric reduction.
SUMMARY:Jim Fowler: Numeric methods in topology
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20121127T210000Z
DTSTART;VALUE=DATE-TIME:20121127T200000Z
DESCRIPTION:Neal Stoltzfus (Louisiana State University): Knots with Cycli
c Symmetries and Recursion in Knot Polynomial of Link families. For kno
ts invariant under a finite order cyclic symmetry\, Seifert\, Murasugi a
nd others developed relations constraining the Alexander polynomial of
such knots.\\nWe develop similar constraints using the transfer method o
f generating functions is applied to the ribbon graph rank polynomial. T
his polynomial\, denoted $R(D\;X\,Y\,Z)$\, is due to Bollob\\'as\, Rior
dan\, Whitney and Tutte. Given a sequence of ribbon graphs\, $D_n$\, con
structed by successive amalgamation of a fixed pattern ribbon graph\, we
prove by the transfer method that the associated sequence of rank polyn
omials is recursive: that is\, the polynomials $R(D_n\;X\,Y\,Z)$ satisf
y a linear recurrence relation with coefficients in $Z[X\,Y\,Z]$.\\nWe d
evelop conditions for the Jones polynomial of links which admit a period
ic homeomorphism\, by applying the above result and the work of Dasbach
et al showing that the Jones polynomial is a specialization of the ribbo
n graph rank polynomial.\\nThis is joint work with Jordan Keller and Mur
phy-Kate Montee)
SUMMARY:Neal Stoltzfus: Knots with Cyclic Symmetries and Recursion in Kno
t Polynomial of Link families
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20121204T210000Z
DTSTART;VALUE=DATE-TIME:20121204T200000Z
DESCRIPTION:Jenny George (The Ohio State University): TQFTs from Quasi-Ho
pf Algebras and Group Cocycles. The original Hennings TQFT is defined f
or quasitriangular Hopf algebras satisfying various nondegeneracy requir
ements. We extend this construction to quasitriangular quasi-Hopf algeb
ras with related nondegeneracy conditions and prove that this new ``quas
i-Hennings'' algorithm is well-defined and gives rise to TQFTs. The ult
imate goal is to apply this construction to the Dijkgraaf-Pasquier-Roche
twisted double of the group algebra\, and then show that the resulting
TQFT is equivalent to a more geometric one\, described by Freed and Quin
n.
SUMMARY:Jenny George: TQFTs from Quasi-Hopf Algebras and Group Cocycles
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20130108T223000Z
DTSTART;VALUE=DATE-TIME:20130108T213000Z
DESCRIPTION:Tam Nguyen Phan (The Ohio State University): Aspherical manif
olds obtained by gluing locally symmetric manifolds. Aspherical manifo
lds are manifolds that have contractible universal covers. I will explai
n how to construct closed aspherical manifolds by gluing the Borel-Serre
compactifications of locally symmetric spaces using the reflection grou
p trick. I will also discuss rigidity aspects of these manifolds\, such
as whether a homotopy equivalence of such a manifold is homotopic to a h
omeomorphism.
SUMMARY:Tam Nguyen Phan: Aspherical manifolds obtained by gluing locally
symmetric manifolds
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20130115T210000Z
DTSTART;VALUE=DATE-TIME:20130115T200000Z
DESCRIPTION:Anh T. Tran (The Ohio State University): On the AJ conjecture
for knots. We consider the AJ conjecture that relates the A-polynomial
and the colored Jones polynomial of a knot. Using skein theory\, we sho
w that the conjecture holds true for some classes of two-bridge knots an
d pretzel knots.
SUMMARY:Anh T. Tran: On the AJ conjecture for knots
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20130122T210000Z
DTSTART;VALUE=DATE-TIME:20130122T200000Z
DESCRIPTION:Moshe Cohen (The Emmy Noether Mathematical Institute): Kauffm
an's clock lattice as a graph of perfect matchings: a formula for its he
ight.. Kauffman gives a state sum formula for the Alexander polynomial
of a knot using states in a lattice that are connected by his clock mov
es. We show that this lattice is more familiarly the graph of perfect m
atchings of a bipartite graph obtained from the knot diagram by overlayi
ng the two dual Tait graphs of the knot diagram.\\nUsing a partition of
the vertices of the bipartite graph\, we give a direct computation for t
he height of Kauffman's clock lattice obtained from a knot diagram with
two adjacent regions starred and without crossing information specified.
\\nWe prove structural properties of the bipartite graph in general and
mention applications to Chebyshev or harmonic knots (obtaining the popul
ar grid graph) and to discrete Morse functions.\\nThis talk is accessibl
e to those without a background in knot theory. Basic graph theory is a
ssumed.
SUMMARY:Moshe Cohen: Kauffman's clock lattice as a graph of perfect match
ings: a formula for its height.
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20130212T210000Z
DTSTART;VALUE=DATE-TIME:20130212T200000Z
DESCRIPTION:John Harper (Purdue University): Completions in topology and
homotopy theory. I will give a historical overview of completions in to
pology and homotopy theory starting with the work of D. Sullivan\, toget
her with motivation and applications of these constructions\, including
H.R. Miller's proof of the Sullivan conjecture and Mandell's "homotopica
l double dual" result for algebraically characterizing p-adic homotopy t
ypes. I will then describe a variation of these completion ideas for the
enriched algebraic-topological context of homotopy theoretic commutativ
e rings that arises naturally in algebraic K-theory\, derived algebraic
geometry\, and algebraic topology. I will finish by describing some rece
nt results on completion in this new context\, which are joint with M. C
hing.
SUMMARY:John Harper: Completions in topology and homotopy theory
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20130226T210000Z
DTSTART;VALUE=DATE-TIME:20130226T200000Z
DESCRIPTION:Nathan Dunfield (University of Illinois at Urbana-Champaign):
Integer homology 3-spheres with large injectivity radius. Conjecturall
y\, the amount of torsion in the first homology group of a hyperbolic 3-
manifold must grow rapidly in any exhaustive tower of covers (see Berger
on-Venkatesh and F. Calegari-Venkatesh). In contrast\, the first betti n
umber can stay constant (and zero) in such covers. Here "exhaustive" mea
ns that the injectivity radius of the covers goes to infinity. In this t
alk\, I will explain how to construct hyperbolic 3-manifolds with trivia
l first homology where the injectivity radius is big almost everywhere b
y using ideas from Kleinian groups. I will then relate this to the recen
t work of Abert\, Bergeron\, Biringer\, et. al. In particular\, these ex
amples show a differing approximation behavior for L^2 torsion as compar
ed to L^2 betti numbers. This is joint work with Jeff Brock.
SUMMARY:Nathan Dunfield: Integer homology 3-spheres with large injectivit
y radius
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20130305T210000Z
DTSTART;VALUE=DATE-TIME:20130305T200000Z
DESCRIPTION:Martin Frankland (University of Illinois at Urbana-Champaign
): The homotopy of p-complete K-algebras. Morava E-theory is an importa
nt cohomology theory in chromatic homotopy theory. Rezk described the al
gebraic structure found in the homotopy of $K(n)$-local commutative E-al
gebras\, via a monad on $E_\\ast$-modules that encodes all power operati
ons. However\, the construction does not see that the homotopy of a $K(n
)$-local spectrum is L-complete (in the sense of Greenlees-May and Hovey
-Strickland). We show that the construction can be improved to a monad o
n $L$-complete $E_\\ast$-modules\, and discuss some applications. Joint
with Tobias Barthel.
SUMMARY:Martin Frankland : The homotopy of p-complete K-algebras
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20130319T200000Z
DTSTART;VALUE=DATE-TIME:20130319T190000Z
DESCRIPTION:Nobuyuki Oda (Fukuoka University): Brown-Booth-Tillotson prod
ucts and exponentiable spaces. To study the exponential law for functio
n spaces with the compact-open topology\, R. Brown introduced a topology
for product set\, which is finer than the product topology\, and showed
the exponential law for any Hausdorff spaces. The method was improved b
y P. Booth and J. Tillotson\, making use of test maps\, and they removed
the Hausdorff condition for spaces. The product space they used is call
ed the BBT-product. If we use any class of exponentiable spaces\, then w
e can define a topology for function spaces which enables us to prove th
e exponential law with the BBT-product for any spaces. We can apply the
result to based spaces and we get various good results for homotopy the
ory. For example\, we can prove a theorem of pairings of function spaces
without imposing conditions on spaces and base points. If we look at th
e techniques carefully\, we find that the results can also be applied to
study group actions on function spaces.\\nThe BBT-product is asymmetric
in general and we can define the `centralizer' of the BBT-product\, whi
ch contains the class of k-spaces defined by the class. The centralizer
of the BBT-product has good properties for homotopy theory.\\nThis talk
is based on joint work with Yasumasa Hirashima.
SUMMARY:Nobuyuki Oda: Brown-Booth-Tillotson products and exponentiable sp
aces
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20130326T200000Z
DTSTART;VALUE=DATE-TIME:20130326T190000Z
DESCRIPTION:Charles Estill (The Ohio State University): Matroid Connectio
n: Matroids for Algebraic Topology. In our paper "Polynomial Invariants
of Graphs on Surfaces" we found a relationship between two polynomials
cellularly embedded in a surface\, the Krushkal polynomial\, based on th
e Tutte polynomial of a graph and using data from the algebraic topology
of the graph and the surface\, and the Las Vergnas polynomial for the m
atroid perspective from the bond matroid of the dual graph to the circui
t matroid of the graph\, $\\mathcal{B}(G^\\ast) \\to \\mathcal{C}(G)$.\\
nWith Vyacheslav Krushkal having (with D. Renardy) expanded his polynomi
al to the $n$th dimension of a simplicial or CW decomposition of a $2n$-
dimensional manifold\, a matroid perspective was found whose Las Vergnas
polynomial would play a similar role to that in the 2-dimensional case.
\\nWe hope that these matroids and the perspective will prove useful in
the study of complexes.
SUMMARY:Charles Estill: Matroid Connection: Matroids for Algebraic Topolo
gy
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20130402T200000Z
DTSTART;VALUE=DATE-TIME:20130402T190000Z
DESCRIPTION:Ian Leary (University of Southampton): Platonic triangle comp
lexes. I will discuss work arising from Raciel Valle's thesis concernin
g complexes built from triangles that are highly symmetrical and have ve
rtex links the join of $n$ pairs of points (equivalently the $1$-skeleto
n of the $n$-dimensional analogue of the octahedron).
SUMMARY:Ian Leary: Platonic triangle complexes
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20130409T200000Z
DTSTART;VALUE=DATE-TIME:20130409T190000Z
DESCRIPTION:Michael A. Mandell (Indiana University\, Bloomington): The ho
motopy theory of cyclotomic spectra. In joint work with Andrew Blumberg
\, we construct a category of cyclotomic spectra that is (something like
) a closed model category and which has well-behaved mapping spectra. W
e show that topological cyclic homology (TC) is the corepresentable func
tor on this category given by maps out of the sphere spectrum\, verifyin
g a conjecture of Kaledin.
SUMMARY:Michael A. Mandell: The homotopy theory of cyclotomic spectra
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20130416T200000Z
DTSTART;VALUE=DATE-TIME:20130416T190000Z
DESCRIPTION:Mark Meilstrup (Southern Utah University): Reduced forms for
one-dimensional Peano continua. We will discuss a few reduced forms for
homotopy types of 1-dim Peano continua. "Deforested" continua contain n
o attached strongly contractile subsets (dendrites). For 1-dim continua
this always gives a minimal deformation retract\, or core. In a core 1-d
im continuum\, the points which are not homotopically fixed form a graph
. Furthermore\, this can be homotoped to an "arc reduced" continuum\, wh
ere the non-homotopically fixed points are in fact a union of arcs.
SUMMARY:Mark Meilstrup: Reduced forms for one-dimensional Peano continua
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20130423T200000Z
DTSTART;VALUE=DATE-TIME:20130423T190000Z
DESCRIPTION:Christopher Davis (The Ohio State University): Satellite oper
ators as a group action. Let $P$ be a knot in a solid torus\, $K$ be a
knot in $3$-space and $P(K)$ be the satellite knot of $K$ with pattern $
P$. This correspondence defines an operator\, the satellite operator\,
on the set of knot types and induces a satellite operator $P:C\\to C$ o
n the set of smooth concordance classes of knots. In a recent paper wit
h Tim Cochran and Arunima Ray\, we show that for many patterns this map
is injective. I will approach this result from a different perspective\
, namely by showing that satellite operators really come from a group ac
tion. In 2001\, Levine studied homology cylinders over a surface modul
o the relation of homology cobordism as a group containing the mapping c
lass group. We show that this group also contains satellite operators a
nd acts on an enlargement of knot concordance. In doing so we recover t
he injectivity result. I will also present some preliminary results on
the surjectivity of satellite operators on knot concordance.
SUMMARY:Christopher Davis: Satellite operators as a group action
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20130430T200000Z
DTSTART;VALUE=DATE-TIME:20130430T190000Z
DESCRIPTION:Andrew Salch (Wayne State University): Chromatic convergence
and its discontents. The chromatic convergence theorem of Ravenel and
Hopkins asserts that\, if $X$ is a $p$-local finite spectrum\, then the
homotopy limit $\\text{holim}_n L_{E(n)}(X)$ of the localizations of $X$
at each of the Johnson-Wilson $E$-theories $E(n)$ is homotopy-equivalen
t to $X$ itself. One way of seeing the chromatic convergence theorem is
by regarding the functor sending a spectrum $X$ to $\\text{holim}_n L_{E
(n)}(X)$ as a kind of completion\, "chromatic completion\," which has th
e agreeable property that $p$-local finite spectra are all already chrom
atic complete. Then there are two natural questions:\\n1. Given a (not n
ecessarily finite) spectrum $X$\, is there a criterion that lets us deci
de easily whether $X$ is chromatically complete or not?\\n2. Given a non
classical setting for homotopy theory\, such as equivariant spectra or m
otivic spectra\, what analogue of the chromatic convergence theorem migh
t hold?\\nWe give an answers to each of these two questions. For a symme
tric monoidal stable model category $C$ satisfying some reasonable hypot
heses\, we produce a natural notion of "chromatic completion\," as well
as the notion of a "chromatic cover\," a commutative monoid object which
shares important properties with the complex cobordism spectrum $MU$ fr
om classical stable homotopy theory. We show that\, if a chromatic cover
exists in $C$\, then any object $X$ satisfying Serre's condition $S_n$
for any $n$ is chromatically complete if and only if the microlocal coho
mology of $X$ vanishes. (Of course we have to define Serre's condition $
S_n$ as well as microlocal cohomology in this context!)\\nWe get two imp
ortant corollaries: first\, by computing some microlocal cohomology grou
ps\, we find that large classes of non-finite classical spectra are not
chromatically complete\, such as the connective spectra $ku$ and $BP\\la
ngle n \\rangle$ for all finite $n$. We also get some non-chromatic-comp
leteness results for $\\text{ko}$\, $\\text{tmf}$\, and $\\text{taf}$. S
econd\, we get conditions under which a chromatic completion theorem can
hold for motivic and equivariant spectra: one needs a chromatic cover t
o exist in those categories of spectra. We identify a candidate for such
a chromatic cover for motivic spectra over $\\text{Spec}\\\, C$\, assum
ing the Dugger-Isaksen nilpotence conjecture.
SUMMARY:Andrew Salch: Chromatic convergence and its discontents
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20130501T200000Z
DTSTART;VALUE=DATE-TIME:20130501T190000Z
DESCRIPTION:Andrew Salch (Wayne State University): Explicit class field t
heory and stable homotopy groups of spheres. One knows from Artin reci
procity that\, for any abelian Galois extension $L/K$ of $p$-adic number
fields\, there is an isomorphism $K^{\\times} / N_{L/K} L^{\\times} \\t
o Gal(L/K)$ from the units in $K$ modulo the norms of units in $L$ to t
he Galois group of $L/K$\; this isomorphism is called the "norm residue
symbol." Computing the norm residue symbol explicitly on specific elemen
ts of its domain is quite difficult and is an open area of research in a
lgebraic number theory.\\nGiven an abelian Galois extension $L$ of $Q_p$
and a finite CW-complex $X$\, we use Lubin-Tate theory and the Goerss-H
opkins-Miller theorem to produce a particular subgroup of the $K(1)$-loc
al stable homotopy groups of $X$. We show that this construction provide
s a filtration\, indexed by the abelian extensions of $Q_p$\, of the $K(
1)$-local stable homotopy groups of finite CW-complexes\, and we use Dwo
rk's computation of the norm residue symbol on the maximal abelian exten
sion of $Q_p$ to compute this filtration explicitly on some interesting
finite CW-complexes\, such as mod $p$ Moore spaces. We then use the nilp
otence and localization theorems of Ravenel-Devinatz-Hopkins-Smith to pr
oduce a "dictionary" that lets us pass between norm residue symbols comp
utations from explicit class field theory\, and families of nilpotent el
ements in the $K(1)$-local stable homotopy groups of finite ring spectra
.\\nTime allowing\, we will discuss what versions of a (so far only conj
ectural) $p$-adic Langlands correspondence would permit these methods to
be extended to higher heights\, i.e.\, $K(n)$-local stable homotopy gro
ups and nonabelian Galois extensions of $Q_p$.
SUMMARY:Andrew Salch: Explicit class field theory and stable homotopy gro
ups of spheres
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20130910T200000Z
DTSTART;VALUE=DATE-TIME:20130910T190000Z
DESCRIPTION:Dan Burghelea (The Ohio State University): A (computer friend
ly) alternative to Morse-Novikov theory. We present an alternative to M
orse-Novikov theory which works for a considerably larger class of spac
es and maps rather than smooth manifolds and Morse maps. One explains
what Morse-Novikov theory does for dynamics and topology and indicates
how our theory does almost the same for a considerably larger class of
situations as well as its additional features.
SUMMARY:Dan Burghelea: A (computer friendly) alternative to Morse-Novikov
theory
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20130924T200000Z
DTSTART;VALUE=DATE-TIME:20130924T190000Z
DESCRIPTION:Taehee Kim (Konkuk University): Concordance of knots and Seif
ert forms. Two knots in the 3-sphere are said to be concordant if they
cobound a locally flat\, properly embedded annulus in the product of the
3-sphere and the unit interval. The notion of concordance originates fr
om Fox and Milnor\, and it is related with other 3- and 4-dimensional to
pological properties such as homology cobordism and topological surgery
theory. In this talk\, I will discuss various relationships between conc
ordance and Seifert forms (or the Alexander polynomial) of knots. In par
ticular\, I will explain Cha-Orr's extension of Cochran-Orr-Teichner's c
oncordance invariants\, which are von Neumann rho-invariants\, and show
its application to this subject.
SUMMARY:Taehee Kim: Concordance of knots and Seifert forms
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20131003T185000Z
DTSTART;VALUE=DATE-TIME:20131003T175000Z
DESCRIPTION:Kun Wang (The Ohio State University): On group actions on $\\
mathrm{CAT}(0)$-spaces and the Farrell-Jones Isomorphism Conjecture.. T
he Farrell-Jones isomorphism conjecture (FJIC) plays an important role i
n manifold topology as well as computations in algebraic $K$- and $L$-th
eory. It implies\, for example\, the Borel conjecture of topological rig
idity of closed aspherical manifolds and the Novikov conjecture of homot
opy invariance of higher signatures. By the work of A. Bartels\, W. Lue
ck and C. Wegner\, it's now known that FJIC holds for $\\mathrm{CAT}(0)$
-groups\, i.e. groups admitting proper\, cocompact actions on finite dim
ensional proper $\\mathrm{CAT}(0)$-spaces. This includes for example fun
damental groups of nonpositively curved closed Riemannian manifolds. It
's a natural question that if a group admits a "nice" but not necessary
proper action on a $\\mathrm{CAT}(0)$-space and if the point stabilizers
satisfy FJIC\, whether the original group satisfies FJIC. In this talk\
, after outlining the general strategy for proving FJIC\, I will talk a
bout the progress that I have made concerning the above question.
SUMMARY:Kun Wang: On group actions on $\\mathrm{CAT}(0)$-spaces and the F
arrell-Jones Isomorphism Conjecture.
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20131015T200000Z
DTSTART;VALUE=DATE-TIME:20131015T190000Z
DESCRIPTION:Ryan Kowalick (The Ohio State University): Discrete Systolic
Inequalities and Applications. We investigate a discrete analogue of Gr
omov's systolic estimate and use it to prove facts about triangulations
of surfaces. We also discribe a procedure for obtaining Gromov's result
from the discrete version.
SUMMARY:Ryan Kowalick: Discrete Systolic Inequalities and Applications
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20131022T200000Z
DTSTART;VALUE=DATE-TIME:20131022T190000Z
DESCRIPTION:Wouter van Limbeek (University of Chicago): Riemannian manifo
lds with local symmetry. In this talk I will discuss the problem of cla
ssifying all closed Riemannian manifolds whose universal cover has nondi
screte isometry group. Farb and Weinberger solved this under the assumpt
ion that $M$ is aspherical. Roughly\, they proved that any such $M$ is a
fiber bundle with locally homogeneous fibers. However\, if $M$ is not a
spherical\, many new examples and phenomena appear. I will exhibit some
of these\, and discuss progress towards a classification. As an applicat
ion\, I will characterize simply-connected manifolds with both a compact
and a noncompact finite volume quotient.
SUMMARY:Wouter van Limbeek: Riemannian manifolds with local symmetry
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20131112T210000Z
DTSTART;VALUE=DATE-TIME:20131112T200000Z
DESCRIPTION:Xiaolei Wu (Binghamton University): Farrell-Jones conjecture
for Baumslag-Solitar groups. The Baumslag-Solitar groups are a particul
ar class of two-generator one-relation groups which have played a surpri
singly useful role in combinatorial and geometric group theory. They hav
e provided examples which mark boundaries between different classes of g
roups and they often provide a test-cases for theories and techniques. I
n this talk\, I will illustrate the proof of the Farrell-Jones conjectur
e for them. This is a joint work with my advisor Tom Farrell.
SUMMARY:Xiaolei Wu: Farrell-Jones conjecture for Baumslag-Solitar groups
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20131119T195000Z
DTSTART;VALUE=DATE-TIME:20131119T185000Z
DESCRIPTION:Somnath Basu (Binghamton University): The closed geodesic pr
oblem for four manifolds. We will explain why a generic metric on a smo
oth four manifold (with second Betti number at least three) has the expo
nential growth property\, i.e.\, the number of geometrically distinct pe
riodic geodesics of length at most l grow exponentially as a function of
l. Time permitting\, we shall explain related topological consequences.
SUMMARY:Somnath Basu : The closed geodesic problem for four manifolds
LOCATION:Central Classroom Building 306
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20131126T210000Z
DTSTART;VALUE=DATE-TIME:20131126T200000Z
DESCRIPTION:Dan Burghelea (The Ohio State University): Alexander Polynomi
al revisited. I will provide alternative definitions and methods of cal
culations for the Alexander Polynomial of a knot and ultimately a gener
alization of this invariant to all odd dimensional manifolds with large
fundamental group. The generalization is a "rational function" on the va
riety of complex rank K representations of the fundamental group.
SUMMARY:Dan Burghelea: Alexander Polynomial revisited
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20131203T210000Z
DTSTART;VALUE=DATE-TIME:20131203T200000Z
DESCRIPTION:Crichton Ogle (The Ohio State University): Fundamental Theore
ms for the $K$-theory of $S$-algebras. We show how recent results of D
undas-Goodwillie-McCarthy can be used to give efficient proofs of i) a F
undamental Theorem for the K-theory of connective S-algebras\, ii) an in
tegral localization theorem for the relative K-theory of a 1-connected m
ap of connective S-algebras\, iii) a generalized localization theorem f
or the p-complete relative K-theory of a 1-connected map of connective S
-algebras. Following Weibel\, we define homotopy K-theory for general S-
algebras\, and prove that the corresponding NK-groups of the sphere spec
trum are non-trivial.\\nMuch of this work arose in an attempt to apply r
ecent results and methods from topological cyclic homology to update Wal
dhausen's original program for studying the effect of Ravenel's chromati
c tower on the algebraic K-theory of the sphere spectrum. We will give a
brief summary of this program\, along with recent results of Blumberg-M
andell and how they fit into some deep conjectures of Rognes. As time pe
rmits\, we will add some conjectures to the list.
SUMMARY:Crichton Ogle: Fundamental Theorems for the $K$-theory of $S$-alg
ebras
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20131210T210000Z
DTSTART;VALUE=DATE-TIME:20131210T200000Z
DESCRIPTION:Stratos Prassidis (University of the Aegean): Equivariant Rig
idity of Quasi-toric Manifolds. We show that quasi-toric manifolds are
topologically equivariant rigid with the natural torus action. The proof
of the rigidity is done in three steps. First we show that for the mani
fold equivariantly homotopy equivalent to the quasi-toric manifold the a
ction of the torus is locally standard (it resembles the standard action
of the torus on the complex space). The second step is that the manifol
d is equivariantly homeomorphic to the standard model of such actions. T
he final step is based on the topological rigidity of the quotient space
which is a manifold with corners. This is joint work with Vassilis Meta
ftsis.
SUMMARY:Stratos Prassidis: Equivariant Rigidity of Quasi-toric Manifolds
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20140114T210000Z
DTSTART;VALUE=DATE-TIME:20140114T200000Z
DESCRIPTION:Dave Constantine (University of Chicago): On volumes of compa
ct anti-de Sitter 3-manifolds. Anti de-Sitter manifolds are Lorentzian
manifolds with constant curvature $-1$. In a loose analogy with Teichmu
ller space\, there is a moduli space of AdS 3-manifolds with a given fun
damental group. This space is not entirely understood---for instance\,
we do not know how many connected components it has---but we do know a f
air amount. We know much less about how the geometry of the manifolds v
aries across the moduli space. I'll present the some preliminary result
s on how volume varies across the moduli space and state a few questions
the results so far raise.
SUMMARY:Dave Constantine: On volumes of compact anti-de Sitter 3-manifold
s
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20140211T210000Z
DTSTART;VALUE=DATE-TIME:20140211T200000Z
DESCRIPTION:Michael Davis (The Ohio State University): When are two Coxet
er orbifolds diffeomorphic?. One can define what it means for a compact
manifold with corners to be a ``contractible manifold with contractible
faces.'' Two combinatorially equivalent\, contractible manifolds with c
ontractible faces are diffeomorphic if and only if their $4$-dimensional
faces are diffeomorphic. It follows that two simple convex polytopes a
re combinatorially equivalent if and only if they are diffeomorphic as m
anifolds with corners. On the other hand\, by a result of Akbulut\, fo
r each n greater than 3\, there are smooth\, contractible n-manifolds wi
th contractible faces which are combinatorially equivalent but not diffe
omorphic. Applications are given to rigidity questions for reflection g
roups and smooth torus actions.
SUMMARY:Michael Davis: When are two Coxeter orbifolds diffeomorphic?
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20140225T210000Z
DTSTART;VALUE=DATE-TIME:20140225T200000Z
DESCRIPTION:Allan Edmonds (Indiana University Bloomington): Introduction
to Haken $n$-manifolds. Haken $n$-manifolds have recently been defined
and studied by B. Foozwell and H. Rubinstein in analogy with the classic
al Haken manifolds of dimension 3\, using the the theory of boundary pat
terns developed by K. Johannson. They can be systematically cut apart al
ong essential codimension-one hypersurfaces until one obtains a system o
f $n$-cells with a boundary pattern recording some of the information ca
rried by the original manifold and the cutting hypersurfaces. Haken manf
olds in all dimensions are aspherical and\, in general are amenable to p
roofs by induction on the length of a hierarchy (and on dimension). As s
uch they provide a a context to explore the classical Euler characterist
ic conjecture for closed aspherical manifolds\, which we are doing in so
me joint work with M. Davis.
SUMMARY:Allan Edmonds: Introduction to Haken $n$-manifolds
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20140325T200000Z
DTSTART;VALUE=DATE-TIME:20140325T190000Z
DESCRIPTION:Effie Kalfagianni (Michigan State University): Geometric stru
ctures and stable coefficients of Jones knot polynomials. We will discu
ss a way to ``re-package" the colored Jones polynomial knot invariants t
hat allows to read some of the geometric properties of knot complements
they detect.
SUMMARY:Effie Kalfagianni: Geometric structures and stable coefficients o
f Jones knot polynomials
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20140422T200000Z
DTSTART;VALUE=DATE-TIME:20140422T190000Z
DESCRIPTION:Andy Nicol (The Ohio State University): Quasi-isometries of g
raph manifolds do not preserve non-positive curvature. In this talk\,
we will see the definition of high dimensional graph manifolds and see t
hat there are examples of graph manifolds with quasi-isometric fundament
al groups\, but where one supports a locally CAT(0) metric while the oth
er cannot. We will use properties of the Euler class as well as various
results on bounded cohomology.
SUMMARY:Andy Nicol: Quasi-isometries of graph manifolds do not preserve n
on-positive curvature
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20140610T200000Z
DTSTART;VALUE=DATE-TIME:20140610T190000Z
DESCRIPTION:Andr\\'as N\\'emethi (Alfr\\'ed R\\'enyi Institute of Mathema
tics): Lattice and Heegaard-Floer homologies of algebraic links. We com
pute the Heegaard-Floer link homology of algebraic links in terms of the
multivariate Hilbert function of the corresponding plane curve singular
ities. A new version of lattice homology is defined: the lattice corresp
onds to the normalization of the singular germ\, and the Hilbert functio
n serves as the weight function. The main result of the paper identifie
s four homologies: (a) the lattice homology associated with the Hilbert
function\, (b) the homologies of the projectivized complements of local
hyperplane arrangements cut out from the local algebra by valuations gi
ven by the normalizations of irreducible components\, (c) a certain var
iant of the Orlik--Solomon algebra of these local arrangements\, and (d)
the Heegaard--Floer link homology of the local embedded link of the ge
rm. In particular\, the Poincar\\'e polynomials of all these homology
groups are the same\, and we also show that they agree with the coeffici
ents of the motivic Poincar\\'e series of the singularity.
SUMMARY:Andr\\'as N\\'emethi: Lattice and Heegaard-Floer homologies of al
gebraic links
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20141007T200000Z
DTSTART;VALUE=DATE-TIME:20141007T190000Z
DESCRIPTION:Dan Burghelea (The Ohio State University): Refinements of Bet
ti numbers. In this talk I will propose a refinement of the Betti numbe
rs provided by a continuous real valued map. These refinements consist o
f monic polynomials in one variable with complex coefficients\, of degre
e the Betti numbers. A number of remarkable properties of these polynomi
als will be discussed.\\nIn case X is a Riemannian manifold these refine
ments can be even "more refined"\; One can assign to the map and each no
nnegative integer a collection of mutually orthogonal subspaces of the H
armonic forms = deRham cohomology in degree labelled by the zeros of the
above mentioned polynomials and of dimension the multiplicity of the co
rresponding zero.\\nIf the map is a Morse function the polynomials can b
e calculated in terms of critical values of the map and the number of tr
ajectories of the gradient of the Morse function between critical points
.
SUMMARY:Dan Burghelea: Refinements of Betti numbers
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20141014T200000Z
DTSTART;VALUE=DATE-TIME:20141014T190000Z
DESCRIPTION:Michael Donovan (MIT): TBA. TBA
SUMMARY:Michael Donovan: TBA
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20141016T200000Z
DTSTART;VALUE=DATE-TIME:20141016T190000Z
DESCRIPTION:Kun Wang (Vanderbilt University): Some structural results for
Farrell's twisted Nil-groups. Farrell Nil-groups are generalizations o
f Bass Nil-groups to the twisted case. They mainly play role in (1) The
twisted version of the Fundamental theorem of algebraic K-Theory (2) Alg
ebraic K-theory of group rings of virtually cyclic groups (3) as the obs
truction to reduce the family of virtually cyclic groups used in the Far
rell-Jones conjecture to the family of finite groups. These groups are q
uite mysterious. Farrell proved in 1977 that Bass Nil-groups are either
trivial or infinitely generated in lower dimensions. Recently\, we exten
ded Farrell’s result to the twisted case in all dimensions. We indeed de
rived some structural results for general Farrell Nil-groups. As a conse
quence\, a structure theorem for an important class of Farrell Nil-group
s is obtained. This is a joint work with Jean Lafont and Stratos Prassid
is.
SUMMARY:Kun Wang: Some structural results for Farrell's twisted Nil-group
s
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20141021T200000Z
DTSTART;VALUE=DATE-TIME:20141021T190000Z
DESCRIPTION:Nick Gurski (University of Sheffield): TBA. TBA
SUMMARY:Nick Gurski: TBA
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20141028T200000Z
DTSTART;VALUE=DATE-TIME:20141028T190000Z
DESCRIPTION:Michael Ching (Amherst College): TBA. TBA
SUMMARY:Michael Ching: TBA
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20141104T210000Z
DTSTART;VALUE=DATE-TIME:20141104T200000Z
DESCRIPTION:Michael Andrews (MIT): TBA. TBA
SUMMARY:Michael Andrews: TBA
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20141118T210000Z
DTSTART;VALUE=DATE-TIME:20141118T200000Z
DESCRIPTION:Luis A. Pereira (University of Virginia): TBA. TBA
SUMMARY:Luis A. Pereira: TBA
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20141125T210000Z
DTSTART;VALUE=DATE-TIME:20141125T200000Z
DESCRIPTION:Jon Beardsley (Johns Hopkins University): Ravenel's $X(n)$ Sp
ectra as Iterated Hopf-Galois Extensions. We prove that the X(n) spectr
a\, used in the proof of Ravenel's Nilpotence Conjecture\, can be constr
ucted as iterated Hopf-Galois extensions of the sphere spectrum by loop
spaces of odd dimensional spheres. We hope to leverage this structure to
obtain a better understanding of the Nilpotence Theorem as well as deve
lop an obstruction theory for the construction of complex orientations o
f homotopy commutative ring spectra. The method of proof is easily gener
alized to show that other Thom spectra can be considered intermediate Ho
pf-Galois extensions\, for instance the fact that MU is a Hopf-Galois ex
tension of MSU by infinite dimensional complex projective space.
SUMMARY:Jon Beardsley: Ravenel's $X(n)$ Spectra as Iterated Hopf-Galois E
xtensions
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20141202T210000Z
DTSTART;VALUE=DATE-TIME:20141202T200000Z
DESCRIPTION:Yilong Wang (The Ohio State University): TBA. TBA
SUMMARY:Yilong Wang: TBA
LOCATION:CH240
END:VEVENT
BEGIN:VEVENT
DTEND;VALUE=DATE-TIME:20141209T210000Z
DTSTART;VALUE=DATE-TIME:20141209T200000Z
DESCRIPTION:Gabriel Valenzuela (Wesleyan University): TBA. TBA
SUMMARY:Gabriel Valenzuela: TBA
LOCATION:CH240
END:VEVENT
END:VCALENDAR