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Minicourse "Free loop spaces in topology and physics"

April 22 - 24, 2013

in Münster

 

For registration please send an Email to angela.loew@uni-muenster.de with the following information:

Your name, private address, date of birth, bank details including IBAN and BIC, date of arrival and departure, estimatet travel costs, accommodation requirements and if you are German: zuständiges Finanzamt

To ensure accommodation we ask you to register as soon as possible but not later than 7th April 2013



Speaker:

Kathryn Hess (Lausanne, Switzerland)

Abstract:

In this mini-course Kathryn Hess will outline a few of the important roles that free loop spaces play in topology and mathematical physics. In particular, she will talk about enumeration of geodesics on manifolds, as well as about the relationship between Hochschild homology and free loop spaces. Moreover, Kathryn Hess will sketch how a free loop space gives rise to a homological conformal field theory, via string topology.

The schedule and a more detailed program can be found below.

 
General directions to the Department of Mathematics can be found here. The next bus stop is named 'Coesfelder Kreuz'. From the train station you may take the buses 5 or 11 in direction "Gievenbeck". Here is a map centered at the math building.


The workshop is financially supported by SFB 878 - Groups, Geometry & Actions


Schedule:

All lectures will take place at room N2.

Monday

9 am  Welcome (room SR0, ground floor of math building)

9.30 am - 10.30 am Lecture 1: Introduction

Coffee and Tea break

11.30 am - 12.30 pm Lecture 2: The closed geodesic problem

Lunch break

3 pm - 4 pm Problem and Q/A session

Coffee and Tea break

5 pm - 6 pm Problem and Q/A session

Tuesday

9.30 am - 10.30 am Lecture 3: Hochschild homology and free loop spaces

Coffee and Tea break

11.30 am - 12.30 pm Lecture 4: Hochschild homology and free loop spaces

Lunch break

2 pm - 4 pm  Problem and Q/A session

7 pm  Conference dinner at Restaurant Schlossgarten         

Wednesday

9.30 am - 10.30 am   Lecture 5: String topology and its applications

Coffee and Tea break (Entrance Hall)

11 am (!) - 12 pm   Lecture 6: String topology and its applications

 


1. Introduction

  • Several equivalent definitions of free loop spaces
  • The algebraic structure of free loop spaces
  • Free loop spaces in symplectic geometry


2. The closed geodesic problem

  • The problem and its partial solutions
  • Strategy for completing the solution


3. Hochschild homology and free loop spaces

  • The bar and cobar constructions
  • The Hochschild and coHochschild complexes
  • The algebraic structure of (co)Hochschild complexes
  • The relation to (co)homology of free loop spaces
  • Topological Hochschild homology and free loop spaces


4. String topology, loop groups and field theories

  • Homological conformal field theories
  • String topology
    • The intersection product and its lift to free loop spaces
    • Operations in string topology
    • String topology and field theories
    • Connections with symplectic geometry
  • Loop groups and field theories



Participants:

Peter Albers (Münster)

Pedro Boavida (Münster)

Lucio Cirio (Münster)

Alexander Fauck (Berlin)

Aron Fischer (New York)

Urs Frauenfelder (Münster)

Viktor Fromm (Berlin)

Urs Fuchs (Münster)

Masahiro Tutaki (Antwerpen)

Andreas Gerstenberger (Hamburg)

Pavel Hájek (München)

Johannes Huster (Hamburg)

Jungsoo Kang (Münster)

Fabian Kirchner (Hamburg)

Marc Lange (Hamburg)

Janko Latschev (Hamburg)

Jun Young Lee (Münster)

Snigdhayan Mahanta (Münster)

Stephan Mescher (Bochum)

Jan-David Salchow (Berlin)

Wend Werner (Münster)

Christoph Winges (Münster)

Stephanie Ziegenhagen (Hamburg)


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