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Gauge Theory, Geometric Langlands and Vertex Operator Algebras

Conference Date: 
Jeudi, Mars 22, 2018 (All day) to Samedi, Mars 24, 2018 (All day)
Scientific Areas: 
Mathematical Physics

 

The workshop will explore the relation between boundary conditions in four-dimensional gauge theory, the Geometric Langlands program and Vertex Operator Algebras.

Sponsosrship for this workshop has been provided by:

  • Tomoyuki Arakawa, Kyoto University
  • Dima Arinkin, University of Wisconsin-Madison
  • Alexander Braverman, Perimeter Institute & University of Toronto
  • Davide Gaiotto, Perimeter Institute
  • Dennis Gaitsgory, Harvard University
  • Hiraku Nakajima, Kyoto University
  • Sam Raskin, University of Chicago
  • Edward Witten, Institute for Advanced Study
  • Paolo Aluffi, Florida State University & University of Toronto
  • Tomoyuki Arakawa, Kyoto University
  • Dima Arinkin, University of Wisconsin-Madison
  • Alexander Atanasov, Yale University
  • Dario Beraldo, University of Oxford
  • Alexander Braverman, Perimeter Institute & University of Toronto
  • Emily Cliff, University of Illinois Urbana-Champaign
  • Kevin Costello, Perimeter Institute
  • Thomas Creutzig, University of Alberta
  • Chris Elliott, Institut des Hautes Etudes Scientifiques 
  • Davide Gaiotto, Perimeter Institute
  • Dennis Gaitsgory, Harvard University
  • Naoki Genra, Kyoto University
  • Victor Ginzburg, University of Chicago
  • Sergei Gukov, California Institute of Technology
  • Justin Hilburn, University of Pennsylvania
  • Raeez Lorgat, Massachusetts Institute of Technology
  • Matilde Marcolli, Perimeter Institute, University of Toronto & California Institute of Technology
  • Sayed Faroogh Moosavian, Perimeter Institute
  • Hiraku Nakajima, Kyoto University
  • Natalie Paquette, California Institute of Technology
  • Surya Raghavendran, Perimeter Institute
  • Miroslav Rapcak, Perimeter Institute
  • Sam Raskin, University of Chicago
  • Nick Rozenblyum, University of Chicago
  • Laura Schaposnik, University of Illinois at Chicago
  • Jeorg Teschner, DESY
  • Ben Webster, University of Waterloo
  • Alex Weekes, Perimeter Institute
  • Edward Witten, Institute for Advanced Study
  • Philsang Yoo, Yale University
  • Yehao Zhou, Perimeter Institute

Thursday, March 22, 2018

Time

Event

Location

9:00 – 9:30am

Registration

Reception

9:30 – 10:30am

Edward Witten, Institute for Advanced Study
Gauge Theory, Geometric Langlands, and All That

Sky Room

10:30 – 11:00am

Coffee Break

Bistro – 1st Floor

11:00 – 12:00pm

Dima Arinkin, University of Wisconsin-Madison
Overview of the global Langlands correspondence

Sky Room

12:00 – 2:00pm

Lunch

Bistro – 2nd Floor

2:00 – 3:00pm

Davide Gaiotto, Perimeter Institute
Gauge theory, vertex algebras and quantum Geometric Langland dualities

Sky Room

3:00 – 3:30pm

Coffee Break

Bistro – 1st Floor

3:30 – 5:00pm

Discussion 1

Sky Room

6:00pm onwards

Banquet

Bistro – 2nd Floor

 
Friday, March 23, 2018

Time

Event

Location

9:30 – 10:30am

Sam Raskin, University of Chicago
Introduction to local geometric Langlands

Sky Room

10:30 – 11:00am

Coffee Break

Bistro – 1st Floor

11:00 – 12:00pm

Discussion 2

Sky Room

12:00 – 2:00pm

Lunch

Bistro – 2nd Floor

2:00 – 3:00pm

Dennis Gaitsgory, Harvard University
The Master Chiral Algebra

Sky Room

3:00 – 3:30pm

Coffee Break

Bistro – 1st Floor

3:30 – 5:00pm

Discussion 3

Sky Room

 

Saturday, March 24, 2018

Time

Event

Location

9:30 – 10:30am

Tomoyuki Arakawa, Kyoto University
On recent development of representation theory of W-algebras and related topics

Sky Room

10:30 – 11:00am

Coffee Break

Bistro – 1st Floor

11:00 – 12:00pm

Discussion 4

Sky Room

12:00 – 2:00pm

Lunch

Bistro – 1st Floor

2:00 – 3:00pm

Hiraku Nakajima, Kyoto University
Ring objects in the equivariant derived Satake category and 3d N=4 QFT

Sky Room

3:00 – 3:30pm

Coffee Break

Bistro – 1st Floor

3:30 – 4:30pm

Alexander Braverman, Perimeter Institute & University of Toronto
Vertex algebras from holomorphically twisted 3d theories and quasi-classical limit of geometric Langlands duality

Sky Room

4:30 - 5:30pm Discussion 5 Sky Room
 

 

Tomoyuki Arakawa, Kyoto University

On recent development of representation theory of W-algebras and related topics

Dima Arinkin, University of Wisconsin-Madison

Overview of the global Langlands correspondence

In this talk, I plan to review the global Langlands correspondence in the de Rham setting. The focus will be on the `big picture': the formulation of the correspondence, its expected properties, and possible approaches towards its proof. 

Alexander Braverman, Perimeter Institute & University of Toronto

Vertex algebras from holomorphically twisted 3d theories and quasi-classical limit of geometric Langlands duality

Davide Gaiotto, Perimeter Institute

Gauge theory, vertex algebras and quantum Geometric Langland dualities

I will review the gauge theory setup relevant for quantum Geometric Langland applications, the relation to vertex algebras and some conjectural mathematical implications.

Dennis Gaitsgory, Harvard University

The Master Chiral Algebra

Hiraku Nakajima, Kyoto University

Ring objects in the equivariant derived Satake category and 3d N=4 QFT

The mathematical definition of Coulomb branches of 3d N=4 gauge theories gives ring objects in the equivariant derived Satake category. We have another fundamental example of a ring object, namely the regular sheaf. It corresponds to the 3d N=4 QFT T[G], studied by Gaiotto-Witten. We also have operations on ring objects, corresponding to products, restrictions, Coulomb/Higgs gauging in the `category' of 3d N=4 QFT's. Thus we conjecture that arbitrary 3d N=4 QFT with G-symmetry gives rise a ring object in the derived Satake for G.

Sam Raskin, University of Chicago

Introduction to local geometric Langlands

Edward Witten, Institute for Advanced Study

Gauge Theory, Geometric Langlands, and All That

 

 

Samedi mar 24, 2018

The mathematical definition of Coulomb branches of 3d N=4 gauge theories gives ring objects in the equivariant derived Satake category. We have another fundamental example of a ring object, namely the regular sheaf. It corresponds to the 3d N=4 QFT T[G], studied by Gaiotto-Witten. We also have operations on ring objects, corresponding to products, restrictions, Coulomb/Higgs gauging in the `category' of 3d N=4 QFT's. Thus we conjecture that arbitrary 3d N=4 QFT with G-symmetry gives rise a ring object in the derived Satake for G.

Scientific Areas: 

 

Jeudi mar 22, 2018
Speaker(s): 

I will review the gauge theory setup relevant for quantum Geometric Langland applications, the relation to vertex algebras and some conjectural mathematical implications.

Scientific Areas: 

 

Jeudi mar 22, 2018
Speaker(s): 

In this talk, I plan to review the global Langlands correspondence in the de Rham setting. The focus will be on the `big picture': the formulation of the correspondence, its expected properties, and possible approaches towards its proof.

Scientific Areas: 

Pages

Scientific Organizers:

  • Alexander Braverman, Perimeter Institute & University of Toronto
  • Davide Gaiotto, Perimeter Institute
  • Philsang Yoo, Yale University