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 . 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  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 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