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Abstracts for Higher Structures in Geometry and Physics 2015

Alternatively have a look at the program.

Derived symplectic geometry. Part 1

Posted in
Speaker: 
Damien Calaque
Affiliation: 
Montpellier
Date: 
Mon, 2015-10-12 09:30 - 10:30
Location: 
MPIM Lecture Hall

Shifted symplectic structures have been introduces by Pantev-Toën-Vaquié-Vezzosi in 2011. They allow to unify various constructions of symplectic structures appearing in mathematical physics and algebraic geometry. I will present the main results from Pantev-Toën-Vaquié-Vezzosi and, if type permits, I will report on recent developments in the field, such as:
- the construction of fully extended TFTs of AKSZ type.
- the recent definition of shifted Poisson structures.

On the relation between $\infty$-categories and model categories

Posted in
Speaker: 
Thomas Nikolaus
Affiliation: 
MPIM
Date: 
Mon, 2015-10-12 11:00 - 12:00
Location: 
MPIM Lecture Hall

We will report on joint work with Steffen Sagave. First we review the notions of model categories and $\infty$-categories which are both frameworks to deal with homotopy coherence and higher structures. The relation between the two is well understood by now thanks to work of Dugger, Lurie and Joyal. We will explain the relation and if time permits some applications. Our main contribution is to give a symmetric monoidal variant of this story: we prove that symmetric monoidal $\infty$-categories and some sort of symmetric monoidal $\infty$-catgories are essentially the same.

Factorization homology. Part 1

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Speaker: 
Hiro Tanaka
Affiliation: 
Harvard
Date: 
Mon, 2015-10-12 15:00 - 16:00
Location: 
MPIM Lecture Hall

Factorization homology provides a bridge between higher algebra and the topology of manifolds. It's a good bridge: Ayala and Francis have recently proven the cobordism hypothesis using it. In this lecture series we'll explain how to build this bridge, prove results indicating the utility of the bridge, and, time willing, walk across it a few times.
 

Geometric quantization as deformation quantization

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Speaker: 
Pavel Safronov
Affiliation: 
Oxford
Date: 
Mon, 2015-10-12 16:30 - 17:30
Location: 
MPIM Lecture Hall

I will describe an approach to geometric quantization in terms of deformation quantization in the setting of algebraic symplectic structures. I will explain why it recovers the expected answer for cotangent bundles. One can also modify this approach to understand geometric quantization of (-1) and 1-shifted symplectic structures which I will describe for the case of a derived critical locus.

Derived symplectic geometry. Part 2

Posted in
Speaker: 
Damien Calaque
Affiliation: 
Montpellier
Date: 
Tue, 2015-10-13 09:30 - 10:30
Location: 
MPIM Lecture Hall

Spin-net formalism for 3-dimensional topological quantum field theories

Posted in
Speaker: 
Bruce Bartlett
Affiliation: 
Oxford
Date: 
Tue, 2015-10-13 11:00 - 12:00
Location: 
MPIM Lecture Hall

The graphical formalism of string nets, due to Levin, Wen and Kirillov, is an elegant way to describe the vector spaces assigned to oriented surfaces in the Turaev-Viro model. It takes as input a spherical fusion category. What happens if one starts with just a "bare" fusion category? I will describe a "spin net" formalism for this case, which applies to surfaces equipped with a spin structure. In this way one obtains representations of the spin mapping class groups of surfaces.

Factorization homology. Part 2

Posted in
Speaker: 
Hiro Tanaka
Affiliation: 
Harvard
Date: 
Tue, 2015-10-13 15:00 - 16:00
Location: 
MPIM Lecture Hall

Derived symplectic geometry. Part 3

Posted in
Speaker: 
Damien Calaque
Affiliation: 
Montpellier
Date: 
Wed, 2015-10-14 09:30 - 10:30
Location: 
MPIM Lecture Hall

Quantum BV theories on manifolds with boundary. Part 1

Posted in
Speaker: 
Pavel Mnev
Affiliation: 
MPIM
Date: 
Wed, 2015-10-14 11:00 - 12:00
Location: 
MPIM Lecture Hall

I plan to give an introduction to the programme of perturbative quantization of gauge theories (and in particular, topological field theories of AKSZ type) on manifolds with boundary.

Factorization homology. Part 3

Posted in
Speaker: 
Hiro Tanaka
Affiliation: 
Harvard
Date: 
Wed, 2015-10-14 15:00 - 16:00
Location: 
MPIM Lecture Hall
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