Geometry/Topology Seminar
Fall 2016
Thursdays (and sometimes Tuesdays) 3-4pm, in
Eckhart 308
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- Thursday September 22 at 3-4pm in Eck 308
- Sebastian Hensel, Bonn
- Rigidity and Flexibility for the Handlebody Group
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Abstract: The handlebody group Hg is the
subgroup of the mapping class group Modg of a
surface formed by all those elements which extend to a given
handlebody. In this talk we will first show that finite
index subgroups of this group are rigid: any inclusion into
Modg is conjugate to the standard inclusion. We
then discuss flexible behaviour: the existence of inclusion
of Hg into Modh whose image is not
conjugate into any handlebody subgroup of Modh.
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- Thursday September 29 at 3-4pm in Eck 308
- Jesse Wolfson, University of Chicago
- Coincidences of homological densities, predicted by arithmetic
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Abstract: Basic questions in analytic number theory
concern the density of one set (e.g. square-free integers)
in another (e.g. all integers). Motivated by Weil's number
field/function field dictionary, we introduce several
topological analogues, measuring the “homological
density” of one space in another. In arithmetic, Euler
products can be used to show that many seemingly different
densities coincide in the limit. By combining methods from
manifold topology and algebraic combinatorics, we discover
analogous coincidences for limiting homological densities
arising from spaces of 0-cycles (e.g. configuration spaces
of points) on smooth manifolds and complex varieties. We do
not yet understand why these topological coincidences occur.
This is joint work with Benson Farb and Melanie Wood.
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- Thursday October 6 at 3-4pm in Eck 308
- Arie Levit, Hebrew University of Jerusalem
- Local rigidity of uniform lattices
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Abstract: A lattice is topologically locally rigid
(t.l.r) if small deformations of it are isomorphic lattices.
Uniform lattices in Lie groups were shown to be t.l.r by
Weil [60']. We show that uniform lattices are t.l.r in any
compactly generated topological group. A lattice is locally
rigid (l.r) is small deformations arise from conjugation. It
is a classical fact due to Weil [62'] that lattices in
semi-simple Lie groups are l.r. Relying on our t.l.r results
and on recent work by Caprace-Monod we prove l.r for uniform
lattices in the isometry groups of proper geodesically
complete CAT(0) spaces, with the exception of SL2(R) factors
which occurs already in the classical case. Moreover we are
able to extend certain finiteness results due to Wang to
this more general context of CAT(0) groups. In the talk I
will explain the above notions and results, and present some
ideas from the proofs. This is a joint work with Tsachik
Gelander.
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- Thursday October 13 at 3-4pm in Eck 308
- Rita Gitik, University of Michigan
- ON INTERSECTIONS OF CONJUGATE SUBGROUPS
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Abstract: We define a new invariant of a conjugacy
class of subgroups which we call the weak width and prove
that a quasiconvex subgroup of a negatively curved group has
finite weak width in the ambient group. Utilizing the coset
graph and the geodesic core of a subgroup we give an
explicit algorithm for constructing a finite generating set
for an intersection of a quasiconvex sub- group of a
negatively curved group with a conjugate. Using that
algorithm we construct algorithms for computing the weak
width, the width and the height of a quasiconvex subgroup of
a negatively curved group. These algorithms decide if a
quasiconvex subgroup of a negatively curved group is almost
mal- normal in the ambient group.
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- Thursday November 10 at 3-4pm in Eck 308
- Priyam Patel, University of California, Santa Barbara
- TBA
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Abstract: TBA
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- Thursday December 01 at 3-4pm in Eck 308
- Jeremy Miller, Purdue
- TBA
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Abstract: TBA
Due to the high number of requests, we are no longer accepting speakers via self-invitations.
For questions, contact