# Gauge Theory, Geometric Langlands and Vertex Operator Algebras

COVID-19 information for PI Residents and Visitors

Conference Date:
Thursday, March 22, 2018 (All day) to Saturday, March 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 StudyGauge 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-MadisonOverview of the global Langlands correspondence Sky Room 12:00 – 2:00pm Lunch Bistro – 2nd Floor 2:00 – 3:00pm Davide Gaiotto, Perimeter InstituteGauge 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 ChicagoIntroduction 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 UniversityThe 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 UniversityOn 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 UniversityRing 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 TorontoVertex 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

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.

Introduction to local geometric Langlands

Edward Witten, Institute for Advanced Study

Gauge Theory, Geometric Langlands, and All That

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

Saturday Mar 24, 2018
Speaker(s):

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

Saturday 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:

## Discussion 4

Saturday Mar 24, 2018

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

Saturday Mar 24, 2018
Speaker(s):

## The Master Chiral Algebra

Friday Mar 23, 2018
Speaker(s):

## Discussion 2

Friday Mar 23, 2018

## Introduction to local geometric Langlands

Friday Mar 23, 2018
Speaker(s):

## Discussion 1

Thursday Mar 22, 2018

## Gauge theory, vertex algebras and quantum Geometric Langland dualities

Thursday 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:

## Overview of the global Langlands correspondence

Thursday 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
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