MONDAY
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9:40 - 10:40 Ian Agol: The virtual Haken conjecture, Part I
Abstract: We prove a conjecture of Wise that cubulated hyperbolic
groups are virtually special. The proof relies on results of Haglund
and Wise which also imply that they are linear groups, and
quasi-convex subgroups are separable. A consequence is that closed
hyperbolic 3-manifolds have finite-sheeted Haken covers, which
resolves the virtual Haken question of Waldhausen and Thurston's
virtual fibering question. Part of the result depends on joint work
with Groves and Manning on filling hyperbolic groups.
4:30 - 5: 30 Martin Bridson: Recognition problems, profinite completions of groups, and cube
complexes
Abstract: In this talk I shall discuss ways in which geometric ideas
can be used to explore recognition problems in group theory: given a
finite group-presentation, can one determine if the group presented
has a non-trivial finite quotient; under what circumstances is a
residually finite group determined by its finite quotients; which
properties of discrete groups are invariants of their profinite and
pro-nilpotent completions; and can one determine when two finitely
presented subgroups of a mapping class group are conjugate or
isomorphic? (I shall explain all of these terms.)
I shall place particular emphasis on the role played by CAT(0) cube
complexes.
TUESDAY
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9:40 - 10:40 Ian Agol: The virtual Haken conjecture, Part II
4:30 - 5:30 Benson Farb: Permutations and polynomiality in algebra and topology
Abstract: Tom Church, Jordan Ellenberg and I recently discovered that each Betti number
of the space of configurations on n points on any manifold is a polynomial in n. Similarly
for the moduli space of n-pointed genus g curves. Similarly for the dimensions of various spaces
of homogeneous polynomials arising in algebraic combinatorics. Why? What do these
disparate examples have in common? The goal of this talk will be to answer this question by
explaining a simple underlying structure shared by these (and many other) examples in algebra and topology.
THURSDAY
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9:40-10:40 Chris Leininger: Mapping class groups, Kleinian groups, and convex cocompactness.
Abstract: For mapping class groups there is a notion of convex
cocompactness, due to Farb and Mosher, defined by way of analogy with
the concept of the same name in Kleinian groups. On the other hand,
there are certain Kleinian groups which can themselves naturally be
thought of as subgroups of mapping class groups. After describing
some of the background, I will discuss a direct relationship between
convex cocompactness in the two settings for this special class of
groups. This is joint work with Spencer Dowdall and Richard Kent.
4:30-5:30 Alessandra Iozzi: Rigidity of actions on CAT(0) cube complexes
Abstract: Let G be a group acting non-elementarily by automorphisms on
a finite dimensional CAT(0) cube complex. We prove the non-vanishing
of second bounded cohomology of G with geometrically defined
coefficients and we apply this result to establish a super-rigidity
result. This is joint work with Indira Chatterji and Talia Fernos.
FRIDAY
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9:40-10:40 Piotr Przytycki: Mixed 3-manifolds are virtually special
Abstract: This is joint work with Dani Wise. Let M be a compact oriented
irreducible 3-manifold which is neither a graph manifold nor a
hyperbolic manifold. We prove that the fundamental group of M is virtually
special, in particular linear. Combined with works of Wise and Agol on
hyperbolic manifolds and of Liu on graph manifolds, this confirms Liu's
conjecture that compact aspherical 3-manifolds have virtually special
fundamental groups if and only if they admit a npc Riemannian metric.
4:30-5:30 Kevin Wortman: Cohomology of arithmetic groups
Abstract: Let F be a finite field. There is a finite index subgroup G
of SL(n,F[t]) such that H^(n-1)(G,F) is infinite. I'll talk about this
result.