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Abstracts for Workshop on Homotopy theory, manifolds, and field theories

Alternatively have a look at the program.

Elliptic cohomology and elliptic curves

Posted in
Speaker: 
Charles Rezk
Affiliation: 
University of Illinois at Urbana-Champaign
Date: 
Mon, 2015-06-15 10:15 - 11:00
Location: 
MPIM Lecture Hall

The abstract for the entire Felix Klein lecture series can be found here. The talks during the workshop will start over with a new topic.

 

Elliptic cohomology and elliptic curves

Posted in
Speaker: 
Charles Rezk
Affiliation: 
University of Illinois at Urbana-Champaign
Date: 
Mon, 2015-06-15 11:15 - 12:00
Location: 
MPIM Lecture Hall

The abstract for the entire Felix Klein lecture series can be found here. The talks during the workshop will start over with a new topic.

Three points of view on string topology

Posted in
Speaker: 
Nathalie Wahl
Affiliation: 
University of Copenhagen
Date: 
Mon, 2015-06-15 15:00 - 16:00
Location: 
MPIM Lecture Hall
String topology is concerned with a certain multiplicative structure existing on the chains on the free loop space of a manifold. I'll explain how approaching this structure from three rather different points of view, one algebraic, one geometric and one inspired by physics, all lead to considering the same compactification of the moduli space of Riemann surfaces.

A Universal description of global homotopy theory

Posted in
Speaker: 
Thomas Nikolaus
Affiliation: 
University of Bonn
Date: 
Mon, 2015-06-15 16:30 - 17:30
Location: 
MPIM Lecture Hall
The passage from the category of spaces to the category of spectra can be desribed by universally `inverting' spheres or equivalently imposing stability. This turns out to be technically very usefuly and philosopically explains why spectra play such an important role. A similar description can be given in equivariant homotopy theory for a fixed Lie group G. We will explain in this talk how such a description can be given for the category of global spectra (which are in some sense equivariant for all Lie groups at the same time) recently studied by Schwede.

Factorizing the index

Posted in
Speaker: 
Owen Gwilliam
Affiliation: 
MPIM
Date: 
Tue, 2015-06-16 10:00 - 11:00
Location: 
MPIM Lecture Hall
The Batalin-Vilkovisky procedure for quantization of field theories naturally produces factorization algebras. In this talk, I will discuss issues that arise in studying families of BV theories, focusing on a natural class of holomorphic BV theories that bears a natural relationship with the Grothendieck-Riemann-Roch theorem. This joint work with Brian Williams should provide a higher-dimensional generalization of aspects of the relationship between the Virasoro algebra and the moduli of curves.

(Op)lax natural transformations for higher categories and two applications

Posted in
Speaker: 
Claudia Scheimbauer
Affiliation: 
MPIM
Date: 
Tue, 2015-06-16 11:30 - 12:30
Location: 
MPIM Lecture Hall

A relative (also called twisted) quantum field theory should be some transformation between quantum field theories, which themselves are symmetric monoidal functors out of a space-time category. In examples, the notion of natural transformation turns out to be too strong, making it necessary to relax it. In joint work with Theo Johson-Freyd we provide a framework for both lax and oplax transformations and their higher analogs called transfors between strong $(\infty, n)$-functors.

Descent in algebraic K-theory via May's nilpotence conjecture

Posted in
Speaker: 
Akhil Mathew
Affiliation: 
University of California at Berkeley
Date: 
Tue, 2015-06-16 15:00 - 16:00
Location: 
MPIM Lecture Hall
A general Galois descent question in algebraic K-theory asks when the K-theory of stable infinity-categories commutes (after some localization) with homotopy fixed points for finite group actions. In joint work with Niko Naumann and Justin Noel, we approach this question using "derived induction and restriction theory" in the category of equivariant spectra. A key ingredient is a (proved) conjecture of J.P. May which states that the nilpotence of elements in H-infinity-ring spectra can be detected using integral homology.

Extended 3-dimensional topological field theories

Posted in
Speaker: 
Chris Schommer-Pries
Affiliation: 
MPIM
Date: 
Tue, 2015-06-16 16:30 - 17:30
Location: 
MPIM Lecture Hall
I will survey recent advances in our understanding of extended 3-dimensional topological field theories. I will describe recent work (joint with B. Bartlett, C. Douglas, and J. Vicary) which gives an explicit ”generators and relations” classification of partially extended 3D TFTS (assigning values only to 3-manifolds, surfaces, and 1-manifolds). This will be compared to the fully-local case (which has been considered in joint work with C. Douglas and N. Snyder).

Elliptic cohomology and elliptic curves

Posted in
Speaker: 
Charles Rezk
Affiliation: 
University of Illinois at Urbana-Champaign
Date: 
Wed, 2015-06-17 10:15 - 11:00
Location: 
MPIM Lecture Hall

The abstract for the entire Felix Klein lecture series can be found here. The talks during the workshop will start over with a new topic.

Elliptic cohomology and elliptic curves

Posted in
Speaker: 
Charles Rezk
Affiliation: 
University of Illinois at Urbana-Champaign
Date: 
Wed, 2015-06-17 11:15 - 12:00
Location: 
MPIM Lecture Hall

The abstract for the entire Felix Klein lecture series can be found here. The talks during the workshop will start over with a new topic.

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