Geometry/Topology Seminar
Fall 2018
Thursdays (and sometimes Tuesdays) 2:30-3:30pm, in
Ryerson 358
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- Thursday October 11 at 3-4pm in Ry 358
- Rita Gitik, University of Michigan
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On Tame Subgroups of Finitely Presented Groups
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Abstract: We describe several examples of tame
subgroups of finitely presented groups and prove that the
fundamental groups of certain finite graphs of groups are
locally tame.
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- Thursday October 18 at 3-4pm in Ry 358
- Daniel Ramras, IUPUI
- Homological stability for spaces of representations
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Abstract: I will discuss recent work with Mentor
Stafa on homological stability for various spaces built from
commuting elements in Lie groups. These results depend on
rational models for these spaces due to T. Baird, and
utilize J. Wilson's theory of FIW-modules. A key
aspect of this work is the relationship between stability in
ordinary and in equivariant (co)homology. Time permitting,
I'll also discuss what is known regarding stability for
character varieties of free groups and surface groups.
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- Thursday October 25 at 3-4pm in Ry 358
- Daniel Studenmund, Notre Dame
- Commensurability growth of nilpotent groups
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Abstract: A classical area of study in geometric
group theory is subgroup growth, which counts the number of
subgroups of a given group Gamma as a function their index.
We will study a richer function, the commensurability
growth, associated to a subgroup Gamma in an ambient group
G. The main result of this talk concerns the case that Gamma
is an arithmetic subgroup of a unipotent group G, starting
with the simplest example of the integers in the real line.
This is joint work with Khalid Bou-Rabee.
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- Thursday November 01 at 3-4pm in Ry 358
- Yulan Qing, University of Toronto
- Loops with Large Twist Get Short Along Quasi-geodesics in Out(Fn)
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Abstract: We study the behaviour of quasi-geodesics
in Out(Fn) equipped with word metric. Given an element
\phi of Out(Fn), there are several natural paths
connecting the origin to \phi in Out(Fn). We show
that these paths are, in general, not quasi-geodesics in
Out(Fn). In fact, we clear up the current misunderstanding
about distance estimating in Out(Fn) by showing that there
exists points in Out(Fn) where all quasi-geodesics between
them backtracks in all of the current Out(Fn) complexes .
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- Thursday November 08 at 3-4pm in Ry 358
- Kevin Schreve, University of Chicago
- Action Dimension of Simple Complexes of Groups
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Abstract: The action dimension of a discrete group G
is the minimal dimension of contractible manifold that
admits a properly discontinuous G action. I will compute the
action dimension of several examples,including Artin groups,
graph products, and hyperplane arrangements.
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- Thursday November 15 at 3-4pm in Ry 358
- Trevor Hyde, University of Michigan
- Moduli of multivariate irreducible polynomials and liminal reciprocity
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Abstract: I will share some recent results on the
moduli space of multivariate polynomials which are
irreducible over a field K, including a surprising
connection between univariate polynomials and the limiting
space of irreducibles in infinitely many variables.
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- Thursday November 29 at 3-4pm in Ry 358
- Fedor Manin, Ohio State University
- Geometric shadows of rational homotopy theory
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Abstract: Given compact simplicial complexes or
Riemannian manifolds X and Y, what is
the least Lipschitz constant of a nullhomotopy of an
L-Lipschitz map X \to Y, as a function
of L? If X is the circle, then this is
certainly bounded below by the square root of the Dehn
function of \pi1(Y), which for certain
Y grows faster than any computable function. On
the other hand, if Y is simply connected, then
for any X whatsoever the answer is
O(L2) (this is almost sharp in some
cases.) This, among other results, follows from a geometric
upgrade to a fundamental correspondence in algebraic
topology due to Sullivan, which I will attempt to describe.
Due to the high number of requests, we are no longer accepting speakers via self-invitations.
For questions, contact