Geometry/Topology Seminar
Fall 2015
Thursdays (and sometimes Tuesdays) 34pm, in
Eckhart 308

 Tuesday October 13 at 34pm in Eck 308
 Igor Belegradek, Georgia Tech
 Spaces of nonnegatively curved metrics

Abstract: I will explain how to determine
homeomorphism type of the space of complete nonnegatively
curved metrics on the plane and the 2sphere in the smooth
and in the Holder topologies. If time allows I will also
survey what is known about the space of complete
nonnegatively curved metrics on higher dimensional
manifolds.

 Tuesday October 20 at 4:30pm (pretalk at 3:00pm) in Eck 203
 Alexander Kupers, Stanford
 E_{n} cells and homological stability (joint seminar with algebraic topology)

Abstract: When studying objects with additional
algebraic structure, e.g. algebras over an operad, it can be
helpful to consider cell decompositions adapted to these
algebraic structures. I will talk about joint work with
Jeremy Miller on the relationship between Encells and
homological stability. Using this theory, we prove a
localtoglobal principle for homological stability, as well
as give a new perspective on homological stability for
various spaces including symmetric products and spaces of
holomorphic maps.

 Thursday October 22 at 34pm in Eck 308
 Andrew Sanders, UIC
 Complex deformations of Anosov representations

Abstract: An Anosov representation of a hyperbolic
surface group is a homomorphism from the surface group into
a semisimple Lie group which satisfies a certain dynamical
property: from this property one deduces that Anosov
representations are discrete, faithful and the set of all
Anosov representations is an open subset of the space of all
homomorphisms. In recent years, GuichardWeinhard produced
examples of cocompact domains of discontinuity for Anosov
representations, which lie in various homogeneous spaces,
thus giving an answer to the question of whether or not
Anosov representations appear as monodromies of locally
homogeneous geometric structures on manifolds. In this talk,
which comprises joint work with David Dumas, I will discuss
some of the complex analytic features of these locally
homogeneous geometric manifolds in the case the relevant
homogeneous space is a generalized flag variety. In
particular, we will give sufficient conditions to compute
the space of all infinitesimal deformations of the complex
manifold underlying these manifolds. Time permitting, we
will discuss the problem of deforming a pair (M,Z) where M
is a holomorphic locally homogeneous manifold and Z is a
complex submanifold and indicate an application to the
study of Anosov representations.

 Tuesday November 03 at 4:30 PM (pretalk at 3:00) in Eck 203
 Ben Knudsen, Northwestern
 Rational homology of configuration spaces via factorization homology

Abstract: The study of configuration spaces is
particularly tractable over a field of characteristic zero,
and there has been great success over the years in producing
complexes simple enough for explicit computations, formulas
for Betti numbers, and descriptive results. I will discuss
recent work identifying the rational homology of the
configuration spaces of an arbitrary manifold with the
homology of a Lie algebra constructed from its cohomology.
The aforementioned results follow immediately from this
identification, albeit with hypotheses removed; in
particular, one obtains a new, elementary proof of
homological stability for configuration spaces.

 Tuesday November 03 at 34PM in Eck 206
 Tullia Dymarz, Univ. Wisconsin
 Nonrectifiable Delone sets in amenable groups

Abstract: In 1998 BuragoKleiner and McMullen
constructed the first examples of coarsely dense and
uniformly discrete subsets of R^{n} that are not
biLipschitz equivalent to the standard lattice
Z^{n}. We will show how to find such sets inside
certain other solvable Lie groups. The techniques involve
combining ideas from BuragoKleiner with quasiisometric
rigidity results from geometric group theory.

 Tuesday November 17 at 34PM in Eck 206
 John WiltshireGordon, University of Michigan
 Algebraic invariants of configuration space via representation theory of finite sets

Abstract: The space of ntuples of distinct points
in a smooth manifold M is called the nth configuration space
of M. As n grows, what happens to configuration space? This
attractive question continues to receive plenty of
attention. Recently, ChurchEllenbergFarb obtained strong
results on the eventual behavior of the cohomology of
configuration space using the representation theory of
finite sets. I will use recent advances in this theory to
prove a theorem about configuration space when M admits a
nowherevanishing vector field. Finally, I will use
Goodwillie calculus to prove a similar result for
configurations of smoothly embedded circles if M has
almostcomplex structure. This talk is based on joint work
with Jordan Ellenberg.

 Tuesday February 9 at 34PM in Eck 206
 Craig Westerland, University of Minnesota
 TBA

Abstract: TBA
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