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Abstracts for MPIM Topology Seminar

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Stein fillings and SU(2) representations

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Speaker: 
Steven Sivek
Affiliation: 
Princeton University/MPI
Date: 
Mon, 24/10/2016 - 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

Instanton Floer homology is a powerful gauge theoretic invariant of 3-manifolds which
by construction contains useful information about their fundamental groups.  I will outline
its construction, review some facts about Stein manifolds, and then explain a surprising
new connection between the two, proved in joint work with John Baldwin: if a homology
3-sphere bounds a Stein surface which is not a homology 4-ball, then its instanton Floer
homology is nontrivial and hence its fundamental group admits a nontrivial representation
to SU(2).

Classical upper bounds for slice genera

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Speaker: 
Peter Feller
Affiliation: 
Boston College / MPIM
Date: 
Mon, 31/10/2016 - 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

Using elementary 3-dimensional invariants for knots in 3-space, we
will provide surprising upper bounds on the topological slice
genus---a 4-dimensional measure of complexity based on Fox's
sliceness. These upper bounds are established by crucially invoking
Freedman's Disk Theorem. As an application, strong
differences to the smooth notion of sliceness for knots are
established.
This talk is based on ongoing work with Lukas Lewark with a special

Artin induction, nilpotence, and algebraic K-theory

Posted in
Speaker: 
Akhil Mathew
Affiliation: 
Harvard University
Date: 
Mon, 14/11/2016 - 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

Let R be a ring. A classical result of Mitchell states that the algebraic K-theory of R has
no chromatic information at heights at least 2. We give a new approach to Mitchell's
theorem and analogs for some ring spectra as predicted by the redshift philosophy
of Rognes. Our methods are based on Hopkins-Kuhn-Ravenel character theory, a
nilpotence conjecture of J.P. May, and a version of Swan K-theory.
This is joint work with Dustin Clausen, Niko Naumann, and Justin Noel.

Configuration categories and spaces of embeddings

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Speaker: 
Pedro Boavida
Affiliation: 
Instituto Superior Técnico, Lisboa
Date: 
Mon, 21/11/2016 - 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

I will describe some connections between spaces of embeddings, both smooth and
topological, and operad theory. A central notion here is that of a configuration category
of a manifold, an entity which aggregates the configuration space data of the manifold,
and which has good homotopical properties. This is joint work with M. Weiss.

Supersymmetric Path Integrals, the Localization principle and the Atiyah-Singer Index Theorem

Posted in
Speaker: 
Matthias Ludewig
Affiliation: 
MPIM
Date: 
Mon, 28/11/2016 - 16:30 - 18:00
Location: 
MPIM Lecture Hall
Parent event: 
MPIM Topology Seminar

We give an overview of the (non-rigorous) path integral proof of the Atiyah-Singer theorem, based
on the work of Witten, Atiyah Alvarez-Gaumé and others. The approach postulates the validity of
the localization principle of equivariant cohomology for (purely formal) differential form integrals
over the loop space of a compact manifold, in analogy to the finite-dimensional case. In the second
part of the talk, we show how to rigorously construct an integral map on differential forms on the

 

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