Nathan Broaddus
Honglin Min

Hotel Information

University Plaza Hotel
3110 Olentangy River Rd.
Columbus, OH 43202

Travel Information

Math Building
Visitor Parking
Campus Map


Related workshops at OSU
OSU Math Department


Mladen Bestvina
Joan Birman
Dan Boros
Tara Brendle
Martin Bridson
Nathan Broaddus
Indira Chatterji
Thomas Church
Mike Davis
Matt Day
Benson Farb
Ian Leary
Dan Margalit
Silvia Onofrei
Piotr Przytycki
Andy Putman
Masatoshi Sato
Stefan Witzel

Rob Ackermann
Hadi Bigdely
James Cooper
Matthew Durham
Pritam Ghosh
Funda Gultepe
Hao Liang
Dawid Kielak
Alexandre Martin
Andrew Nicol
Patrick Papadopulos
Catherine Pfaff
Rita Jimenez Rolland
Richard Wade
Rebecca Winarski


The conference will consist of 3 days of introductory talks for nonexperts (May 2-4) followed by two days of research talks (May 5-6).

Registering for the conference

There is no formal registration for this conference. However, if you are interested in attending, please send an e-mail Nathan Broaddus. This will allow us to add you to the mailing list, and keep you informed of any activities during the week of the conference.

Contacting the organizers

If you have any questions or concerns, please feel free to contact the organizers:

  • Nathan Broaddus (Ohio State University),


Sunday, May 1, 2011

Barbecue at Nate's

63 Warren St., Columbus OH

Monday, May 2, 2011
1:30pm-2:30pm in CH 240

Tara Brendle, University of Glasgow

Mapping Class Group I

3:00pm-4:00pm in CH 240

Tara Brendle, University of Glasgow

Mapping Class Group II

4:10pm-4:30pm in CH 240

Dawid Kielak, University of Oxford

Linear and free representations of Out(Fn)


We will discuss low-dimensional linear representations of Out(Fn) and use this knowledge to obtain a rigidity-like result about possible homomorphisms between groups Out(Fn) for varying parameter n.

Tuesday, May 3, 2011

11am University Plaza Hotel Shuttle to OSU

11:30am-12:30pm in CH 240

Tom Church, University of Chicago

Stability I


I will introduce homological stability and explain how it is proved in each of the major cases where homological stability is known: braid groups Bn, special linear groups SLn(Z), moduli spaces of Riemann surfaces Mg, symmetric groups Sn, automorphism groups of free groups Aut(Fn), and configuration spaces Confn(M).

2:00pm-2:20pm in CH 240

Catherine Pfaff, Rutgers University

Constructing and Classifying Fully Irreducible Outer Automorphisms of Free Groups


The main goal of my research is to prove a fully irreducible outer automorphisms analogue of the Howard Masur and John Smillie theorem which precisely records the lists of foliation singularity indices which arise from pseudo-Anosov elements of Mapping Class Groups. The more appropriate conjectured theorem in the Out(Fr) setting actually records possibilities for an even finer outer automorphism invariant, an ideal Whitehead graph. I have developed methods for constructing and identifying fully irreducible outer automorphisms that have thus far been used to completely determine which connected graphs with 5 vertices occur as ideal Whitehead graphs for ageometric fully irreducible outer automorphisms of free groups.

2:25pm-3:25pm in CH 240

Tom Church, University of Chicago

Stability II


See Stability I above.

4:30pm-4:50pm in CH 240

Funda Gultepe, University of Oklahoma

Normal tori in #n(S2 × S1)


The fundamental group of M = #n(S2 × S1) is Fn, the free group with n generators. There is a one-to-one correspondence between the Z-splittings of Fn and embedded essential tori in M. We define and prove a local notion of minimal intersection for tori with respect to a maximal sphere system in M which generalizes Hatcher’s work [Hat95] on 2-spheres in the same manifold.

Wednesday, May 4, 2011

10am University Plaza Hotel Shuttle to OSU

10:30am-11:15am in CH 240

Martin Bridson, University of Oxford

Outer automorphisms of free groups

11:30am-12:30am in CH 240

Dan Margalit, Georgia Tech

Torelli Group I

2:30pm-3:30pm in CH 240

Dan Margalit, Georgia Tech

Torelli Group II

3:40pm-4:00pm in CH 240

Richard Wade, University of Oxford

4:05pm-4:25pm in CH 240

Masatoshi Sato, Osaka University

MMM classes

4:30pm-5:30pm in CH 240

Andrew Putman, Rice University

Teichmüller space

Thursday May 5, 2011

8am University Plaza Hotel Shuttle to OSU

8:30am-9:20am in CH 240

Tara Brendle, University of Glasgow

Hyperelliptic Birman Exact Sequences


Motivated by a conjecture of Hain and Morifuji that the hyperelliptic Torelli group SI is generated by Dehn twists about symmetric separating curves, we will give Birman exact sequences for hyperelliptic mapping class groups. We will also describe various aspects of the structure of SI, including some relations in the Torelli group which allow us to write certain examples of elements of SI in terms of Hain's generators. (Joint work with Dan Margalit.)

9:30am-10:20am in CH 240

Mladen Bestvina, University of Utah

10:30am-11:20am in CH 240

Dan Margalit, Georgia Tech

The Torelli group is generated by bounding pair maps


We give a new proof of that the Torelli group is generated by pair maps that is analogous to the proof that the mapping class group is generated by Dehn twists. This is joint work with Allen Hatcher.

11:30am-12:20pm in CH 240

Joan Birman, Columbia University

Invariants of pseudo-Anosov maps


Let F be a pA map acting on a surface S. Extending the Bestvina-Handel algorithm, Brinkmann, Kawamuro and I investigated the structure of the characteristic polynomial det(xI-T) of a transition matrix T associated to F. We learned that certain polynomial divisors of det(xI-T) are invariants of F. We give examples of pA maps having the same dilatation which can be shown to be non-conjugate by our invariants.

2:30pm-3:20pm in CH 240

Justin Malestein, Temple University

On genericity of pseudo-Anosovs in the Torelli group


We will show that, for any (symmetric) finite generating set of the Torelli group of a closed surface, the probability that a random word is not pseudo-Anosov decays exponentially in the length of the word. As a consequence of our methods, we will prove the same statement for some other finitely generated subgroups of the mapping class group. (Joint work with Juan Souto)

3:30pm-4:20pm in CH 240

Benson Farb, University of Chicago

Representation Theory and Homological Stability


In this talk I will explain some recent work with Tom Church. The story begins when we were working out some cohomology computations for a problem in geometric topology. Hints of a pattern emerged, but we struggled to find a way to describe it. We finally developed a language to do this, and called the phenomenon "representation stability".

As we began to look more broadly we started to see representation stability in many different areas of mathematics: from group cohomology to the topology of configuration spaces to classical representation theory to flag varieties to Lie algebras to algebraic combinatorics. We have been able to apply representation stability to prove theorems and make new predictions in these directions (some since proved by others). Many conjectures remain.

My goal in this talk will be to explain representation stability through examples and applications. I will also explain how Church, Jordan Ellenberg and I are applying this theory in order to compute and explain various combinatorial statistics in number theory. I will try to make this talk accessible to first-year graduate students.

4:30pm-5:20pm in CH 240

Masatoshi Sato, Osaka University

On the third cohomology group of the Torelli group


This is a joint work with Nariya Kawazumi. We have been trying to determine whether the even Morita-Mumford-Miller classes are trivial or not in the Torelli group. If a third cohomology class m2,1 called the (2,1)-twisted MMM class in the Torelli group is trivial, the second MMM class e2 is also trivial. In this talk, I will talk about some results about the class m2,1.

Friday May 6, 2011

8am University Plaza Hotel Shuttle to OSU

8:30am-9:20am in CH 240

Martin Bridson, University of Oxford

Abelian covers of graphs and maps between outer automorphism groups of free groups


This is joint work with Karen Vogtmann. It is part of a programme whereby I'd like to understand all maps between outer automorphism groups of free groups. The main result here is that if m=rn(n-1)+1, where r is coprime to (n-1), then there is an embedding of Out(Fn) into Out(Fm). This is proved by determining for which abelian covers of finite graphs one can lift the action of the group of homotopy equivalences of the base to the cover.

9:30am-10:20am in CH 240

Andrew Putman, Rice University

Small generating sets for the Torelli group


Proving a conjecture of Johnson, we show that for g at least 3, the genus g Torelli group has a finite generating set Sg with |Sg| = O(g3). The main tool is a new space (the "handle graph") on which the Torelli group acts cocompactly.

11:00am-11:50am in CH 240

Matthew Day, Caltech

Generalized Johnson homomorphisms and non-finitely presentable subgroups of Aut(Fn)


We investigate a subgroup K of Aut(Fn) that is an analogue of the kernel of the Birman exact sequence in mapping class groups. We produce homomorphisms on K and its subgroups that are restrictions of crossed homomorphisms, in a way that is formally parallel to the classic higher Johnson homomorphisms in mapping class groups. Our homomorphisms suffice to compute the abelianization of K, and are a key ingredient in building infinitely many independent classes in the second rational cohomology groups of K. This is joint with Andrew Putman.

12:00pm-12:50pm in CH 240

Piotr Przytycki

The ending lamination space for the five-punctured sphere


Joint with Sebastian Hensel. We prove that the ending lamination space (i.e. the boundary of the curve complex) for the 5-punctured sphere is the so called Noebeling curve. This is the space obtained from R3 by removing all points with at least 2 rational coordinates.

This conference is supported by the National Science Foundation (NSF) under Grant Nos. 0752826 and 1007059, and by the OSU Mathematics Research Institute (MRI).
Any opinions, findings and conclusions or recomendations expressed in this material are those of the organizers and do not necessarily reflect the views of the NSF.