Summer School: Geometric representation theory and low-dimensional topology

3-7 June 2019

ICMS, The Bayes Centre, 47 Potterrow, Edinburgh EH8 9BT

Scientific Organisers

  • Dan Freed, University of Texas, Austin
  • David Jordan, University of Edinburgh
  • Peter Samuelson, University of California, Riverside
  • Olivier Schiffmann, University of Paris-Sud, Orsay

The aim of the workshop at ICMS the following week after this summer school is to bring together researchers in topological field theory, geometric representation theory, mathematical physics, and algebraic combinatorics to report on recent progress and open questions at the intersection of these fields. In recent years, several independent research groups have raised the possibility of new 3- and 4-dimensional topological field theories tying together Khovanov-Rozansky knot homology, double affine Hecke algebras and elliptic Hall algebras, super Yang-Mills theory, Betti quantum geometric Langlands, and Hilbert schemes. As each of these topics constitutes a specialist field in its own right, it is essential that we bring researchers together to exchange ideas and insights.

The aim of this summer school, therefore, is to prepare students for the breadth of topics covered in the workshop, through a lecture series delivered by experts in each respective field. It is expected that applicants to the summer school will also attend the workshop. This summer school is partially supported by the NSF, Division of Mathematical Sciences.

Programme:

The programme is shown below. Abstracts are available here.

Links to videos of all recorded talks, photos from the conference dinner, group photos, and lecture notes and slides where applicable are available here.

Monday 3 June 2019


09:00-09:45

Registration & coffee

09:45-10:00

Welcome & opening

10:00-11:00

Hiro Lee Tanaka (Texas State University)
Factorization homology, infinity-categories, and topological field theories I

11:00-12:00

Monica Vazirani (University of California, Davis)
Hecke algebras and representation theory I

12:00-13:30

Lunch

13:30-14:30

Tina Kanstrup (University of Massachusetts Amherst)
Knot homologies and matrix factorizations I

14:30-15:00

Tea & coffee

15:00-16:00

Pavel Safronov (University of Zurich)
Shifted Poisson structures in representation theory I
(pdf of presentations I - III)

16:00-17:00

Gregor Masbaum (CNRS)
Introduction to Skein theory

17:00-19:00

Wine & beer reception with pizza at 18:00

 

Tuesday 4 June 2019


09:00-10:30

Hiro Lee Tanaka (Texas State University)
Factorization homology, infinity-categories, and topological field theories II

10:30-11:00

Tea & coffee

11:00-12:30

Pavel Safronov (University of Zurich)
Shifted Poisson structures in representation theory II

12:30-14:00

Lunch

14:00-15:00

Jose Simental Rodriguez (University of California, Davis)
Rational double affine Hecke algebras

15:00-15:30

Tea & coffee

15:30-17:00

Tina Kanstrup (University of Massachusetts Amherst)
Knot homologies and matrix factorizations II

17:30

Doors open for public lecture

18:00-19:00

Public lecture by Dan Freed (University of Texas, Austin)
Geometry from afar

19:00-20:00

Wine reception

 

Wednesday 5 June 2019


09:00-10:00

Monica Vazirani (University of California, Davis)
Hecke algebras and representation theory II

10:00-10:30

Tea & coffee

10:30-12:00

Tina Kanstrup (University of Massachusetts Amherst)
Knot homologies and matrix factorizations III

12:00-13:30

Lunch

13:30-14:30

Gus Schrader (Columbia University)
The cluster approach to character varieties

14:30-15:30

Kostiantyn Tolmachov (Perimeter Institute and University of Toronto)
Knot homologies and geometric Hecke categories

15:30-16:00

Tea & coffee

16:00-17:30

Pavel Safronov (University of Zurich)
Shifted Poisson structures in representation theory III

 

Thursday 6 June 2019


09:00-10:30

Hiro Lee Tanaka (Texas State University)
Factorization homology, infinity-categories, and topological field theories III

10:30-11:00

Tea & coffee

11:00-12:00

Juliet Cooke (University of Edinburgh)
Skein categories

12:00-13:00

Alexander Shapiro (University of Edinburgh)
Around character varieties in 50 minutes

13.00-14:30

Lunch

14:30-15:30

Quoc Ho (Institute of Science and Technology Austria (IST Austria)
Arithmetic applications of factorization homology

15:30-16:00

Tea & coffee

16:00-17:00

Monica Vazirani (University of California, Davis)
Hecke algebras and representation theory III

 

Friday 7 June 2019


09:00-10:00

Alexandre Minets (IST Austria)
Cohomological Hall algebras and sheaves on surfaces

10:00-10:30

Tea & coffee

10:30-11:30

Nicolle Gonzalez (University of California)
The higher structure of the Heisenberg and Clifford algebras

11:30-12:30

Monica Vazirani (University of California, Davis)
Hecke algebras and representation theory IV

12:30-12:40

Group photo

12:40-14:30

Lunch

14:30-17:00

Write!

 

ICMS does NOT use third parties to arrange accommodation.  If you are approached by a third party (e.g. Business Travel Management) asking for booking details, please ignore.  If you have any concerns please contact ICMS.

How to apply

The deadline for applications for the summer school has passed and all applicants have been advised of decisions. We cannot accept late applications. The organizers are strongly committed to fair gender balance and to the inclusion of participants of diverse backgrounds.