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QFT for Mathematicians 2022

America/Toronto
Ben Webster (Perimeter Institute & University of Waterloo), Davide Gaiotto (Perimeter Institute), Kevin Costello (Perimeter Institute), Philsang Yoo (Tsinghua University), Tudor Dimofte (University of California, Davis)
Description

In recent decades, interaction between mathematics and quantum field theory has proven to be fertile for both fields. However, differences in language, training, and perspective have significantly hampered effective communication between the two parties. The aim of this workshop series is to tear down this wall, and help mathematicians to learn the way physicists think about QFT and strings and eventually ``speak'' QFT and strings fluently. This year we will focus on algebraic, geometric, and homological structures in supersymmetric gauge theories. We will use 3-dimensional N=4 gauge and N=2 theories --- which have seen an explosion of interest in both physical and mathematical communities in recent years --- as a key source of new examples, exploring their connections with integrability, boundary vertex algebras and elliptic cohomology, knot homology, 2d mirror symmetry, and the geometric Langlands program.  

The first week of this event will consist of an in person school and the second week will consist of a virtual conference.

Perimeter Institute will make every effort to host the school as an in-person event.  However, we reserve the right to change to an online program to align with changes in regulations due to the COVID-19 pandemic

PIRSA:  https://pirsa.org/C22011

 

Territorial Land Acknowledgement

Perimeter Institute acknowledges that it is situated on the traditional territory of the Anishinaabe, Haudenosaunee, and Neutral peoples.

Perimeter Institute is located on the Haldimand Tract. After the American Revolution, the tract was granted by the British to the Six Nations of the Grand River and the Mississaugas of the Credit First Nation as compensation for their role in the war and for the loss of their traditional lands in upstate New York. Of the 950,000 acres granted to the Haudenosaunee, less than 5 percent remains Six Nations land. Only 6,100 acres remain Mississaugas of the Credit land.

We thank the Anishinaabe, Haudenosaunee, and Neutral peoples for hosting us on their land. 

Participants
  • Abhiram Kidambi
  • Abolfazl Chaman Motlagh
  • Adam Teixido Bonfill
  • Aditya Basu
  • Adrian Khalil Lopez Raven
  • Adriano Pacifico
  • Ahmed Adel Mahmoud
  • Ahmed Halawani
  • Ahsan Khan
  • Aidan Lindberg
  • Aiden Suter
  • Ainesh Sanyal
  • Ajani McKay
  • Alan Goldfarb
  • Alex Karapetyan
  • Alexander Zahrer
  • Andrea Antinucci
  • Andrea Ferrari
  • Andrea Grossutti
  • Andrei Constantin
  • Andrey Glubokov
  • Anthony Nguyen
  • antoine song
  • Antonio Rieser
  • Arun Debray
  • Ben Webster
  • Benjamin Brown
  • Benjamin Gammage
  • Benjamin Haake
  • Brandon Lopez
  • Caleb Jonker
  • Campbell Wheeler
  • Carlos Ramos
  • Carlos Sáez
  • Catherine Lee
  • Che Shen
  • Chen-wei Lin
  • Chetan Vuppulury
  • Cheuk Yu Mak
  • Christian Vélez
  • Christoph Schweigert
  • Claudia Wenxi Yao
  • D. Zack Garza
  • Daniel Galviz
  • Daniel Herrera Correa
  • Danny Chupin
  • Danny Nackan
  • Dasheng Wang
  • David Ayala
  • Davide Gaiotto
  • Devin Garcia
  • Diego Villamizar
  • Dorin Boger
  • Dvij Mankad
  • Dylan Butson
  • Eddie Lam
  • Edoardo Spezzano
  • Eilind Karlsson
  • Eirik Eik Svanes
  • Elchanan Nafcha
  • Elise LePage
  • Elli Heyes
  • Erik Herrera
  • Erin Dolecheck
  • Fabian Hahner
  • Federico Ambrosino
  • Fei Yan
  • Felipe Ruiz
  • Fernando Villegas Negrete
  • Francis Bischoff
  • Francisco Zúñiga Frias
  • Gabriele Castellari
  • Garrett Oren
  • Girish Vishwa
  • Gregory Moore
  • Grigorios Giotopoulos
  • Guri Buza
  • GUSTAVO ALVES
  • Han Li
  • Hannah De Lázari
  • Hannes Knötzele
  • Haoshuo Fu
  • Haoyu Sun
  • Haridev S R
  • Hongjie Chen
  • Hongliang Jiang
  • Hongrui Zhang
  • Hsueh-Yung Lin
  • Huangcheng Yin
  • Hugo Forget
  • Ilka Brunner
  • Ioana Coman
  • Ioannis Lavdas
  • Irfan Javed
  • Ishan Gunjal
  • Ivan Mauricio Burbano Aldana
  • Jakob Stein
  • Jasmine Browne
  • Jelena Anic
  • Jennifer Brown
  • Jeremy Peters
  • Jiakang Bao
  • Jibranhusain Bohra
  • Jingxiang Wu
  • Joel Kamnitzer
  • Joerg Teschner
  • John Nolan
  • John Pardon
  • Jon Yard
  • Juan Camilo Guzman Martinez
  • Julien Korinman
  • Julien Queva
  • Justin Kulp
  • Kadri Berktav
  • Kai Xu
  • Kartikeya Chowdhry
  • Kasia Budzik
  • Kasia Rejzner
  • Katherine Maxwell
  • Keke Zhang
  • Kengo Maehara
  • Kurusch Ebrahimi-Fard
  • Kwokwai Chan
  • Lakshya Bhardwaj
  • Lee McCulloch-James
  • Lekan Adesina
  • Lennart Döppenschmitt
  • Lev Rozansky
  • Li Feng
  • Li Han
  • Liam Fox
  • Linus Setiabrata
  • Lotte Hollands
  • Luca Cassia
  • Luuk Stehouwer
  • Maksymilian Manko
  • Manuel Araújo
  • Manuel Tecchiolli
  • Marcelo Rezende Barbosa
  • Maria Anna Sisak
  • Maryam Ranjbar
  • Masahito Yamazaki
  • Mathew Bullimore
  • Matina Najafi
  • Matthew Satriano
  • Matthias Traube
  • Maziar Farahzad
  • Maziar Farahzad
  • Mee Seong Im
  • Meer Ashwinkumar
  • Meer Ashwinkumar
  • Mendrit Ljatifi
  • Michael Astwood
  • Michael Schultz
  • Michelangelo Tirelli
  • Michelle Dong
  • Miguel Pardina
  • Milad Mohammadi
  • Minghao Wang
  • Miroslava Mosso Rojas
  • Mohsen Karkheiran
  • Muhammad Ibrahim Abdulhamid
  • Muhammad Muzammil
  • Mykola Dedushenko
  • Nadir YAVUZKAN
  • Nafiz Ishtiaque
  • Nanna Aamand
  • Natalie Paquette
  • Nathan Haouzi
  • Neha Zaidi
  • Niklas Garner
  • Nils Carqueville
  • Nisha Kamble
  • Nivedita -
  • Oleg Lazarev
  • Oleksandr Tsymbaliuk
  • Oscar Kivinen
  • Pallav Goyal
  • Patricia Munoz Ewald
  • Patrick Kinnear
  • Paulo Moniz
  • Pawan Kumar Gupta
  • Pedram Karimi
  • Peter Mwaura
  • Philsang Yoo
  • Pietro Longhi
  • Piotr Bargiela
  • Piyush Kalambkar
  • Praful Shankar
  • Qianyu Hao
  • Radosław Kycia
  • Raphael Rouquier
  • Raphaël Belliard
  • Reese Lance
  • Robert Moscrop
  • Robert Windesheim
  • Roland Bittleston
  • Roman Mauch
  • Roman Travkin
  • Ruochen Ma
  • Ruocheng Yang
  • Ruozhen Gong
  • S M Naimul Mamun
  • Saarthak S
  • Saebyeok Jeong
  • Sagar Kumar Maity
  • Sam Brady
  • Samuel DeHority
  • Samuel Leigh
  • Sanath Devalapurkar
  • Sara Motalebi
  • Saurabh Kumar Shukla
  • Semen Rezchikov
  • Sergey Cherkis
  • Seyed Faroogh Moosavian
  • Shafeeq Rahman Thottoli
  • Shamuel Auyeung
  • Shohreh Abdolrahimi
  • Sidharth Soundararajan
  • Sirapat Lookrak
  • Som Dev Bishoyi
  • Stavros Garoufalidis
  • Steffen Schmidt
  • Subrabalan Murugesan
  • Sujay Nair
  • Sungkyung Kang
  • SURAJ DASH
  • Surya Raghavendran
  • Suvajit Majumder
  • Sylvain Lavau
  • Sylvie Paycha
  • Tai Wai Hu
  • TATIANA GATEVA-IVANOVA
  • Tejas Acharya
  • Thomas Brunner
  • Thomas Waddleton
  • Thorsten Heidersdorf
  • Tim Henke
  • Todor Milanov
  • Todor Popov
  • Tom Bridgeland
  • Tom Sutherland
  • Tomoyuki Arakawa
  • Trung Nghiem
  • Tudor Dimofte
  • Tzu-Chen Huang
  • Uroš Grandovec
  • Utkarsh Bajaj
  • Vaishnavi Kawale
  • Valdo Tatitscheff
  • Varun Lochab
  • Victor Gustavo
  • Victor Py
  • Vincent Thompson
  • Vivek Saxena
  • Vladimir Drinfeld
  • Wei Li
  • Wei Zhou
  • weifeng zhou
  • Wenjun Niu
  • Wille Liu
  • William Stewart
  • William Stewart
  • Xenia de la Ossa
  • Xiaobin Li
  • Xinchun Ma
  • Yakov Kononov
  • Yalong Cao
  • Yannic VARGAS
  • Yaoxian Yang
  • YAOXIONG WEN
  • Yi-Jun He
  • Yixuan Li
  • Yu Tung Yau
  • Yucong Jiang
  • Yucong Jiang
  • Yukai Zhang
  • Yunfan He
  • Yuxuan Hu
  • Zekai Yu
  • Zhengping Gui
  • Zhi Li
  • Zhiyuan Ding
  • Zihang Liu
  • Zijun Zhou
  • Zsolt Gyongyosi
  • Zuodong Mu
  • Ödül Tetik
Stephanie Mohl
    • 8:30 AM
      Registration
    • 1
      Welcome and Opening Remarks
      Speaker: Kevin Costello (Perimeter Institute)
    • 2
      3d Theories and Twists I
      Speaker: Kevin Costello (Perimeter Institute)
    • 10:30 AM
      Coffee Break
    • 3
      3d Gauge Theory and Elliptic Stable Envelopes I
      Speaker: Andrei Okounkov (Columbia University)
    • 12:30 PM
      Lunch
    • Problem Session
    • 3:00 PM
      Coffee Break
    • 4
      Classical BV Formalism and Topological Quantum Field Theory
      Speaker: Philsang Yoo (Seoul National University)
    • 5
      A and B models in 3d and 4d I
      Speaker: Justin Hilburn (Perimeter Institute)
    • 10:30 AM
      Coffee Break
    • 6
      3d B Models and Knot Homology I
      Speaker: Lev Rozansky (University of North Carolina, Chapel Hill)
    • 12:30 PM
      Lunch
    • Problem Session
    • 3:00 PM
      Coffee Break
    • 7
      On Boundary VOA's
      Speaker: Davide Gaiotto (Perimeter Institute)
    • 5:00 PM
      BBQ
    • 8
      3d Gauge Theory and Elliptic Stable Envelopes II
      Speaker: Mykola Dedushenko (Stony Brook University)
    • 10:30 AM
      Coffee Break
    • 9
      3d Theories and Twists II
      Speaker: Tudor Dimofte (University of Edinburgh)
    • 12:30 PM
      Lunch
    • Problem Session
    • 3:00 PM
      Coffee Break
    • 10
      Open Discussion
    • 11
      3d Gauge Theory and Elliptic Stable Envelopes III
      Speaker: Andrei Okounkov (Columbia University)
    • 10:30 AM
      Coffee Break
    • 12
      Geometrical structures in 4d N=2 class S theories

      I will give an introduction to 4d N=2 class-S theories. I will describe the construction of such theories, the roles played by extended defects such as line defects and surface defects, as well as connections to Hitchin systems.

      Speaker: Fei Yan (Rutgers University)
    • 12:30 PM
      Lunch
    • Problem Session
    • 3:00 PM
      Coffee Break
    • 13
      3d Gauge Theory and Elliptic Stable Envelopes IV
      Speaker: Mykola Dedushenko (Stony Brook University)
    • 14
      3d B Models and Knot Homology II
      Speaker: Lev Rozansky (University of North Carolina, Chapel Hill)
    • 10:30 AM
      Coffee Break
    • 15
      A and B Models in 3d and 4d II
      Speaker: Justin Hilburn (Perimeter Institute)
    • 12:30 PM
      Lunch
    • Problem Session
    • 3:00 PM
      Coffee Break
    • 16
      Open Discussion
    • 17
      Welcome and Opening Remarks
      Speaker: Ben Webster (Perimeter Institute & University of Waterloo)
    • 18
      Generalised Langlands, VOAs, and (generalised) tau-functions

      In the first part of my talk I'll briefly review some aspects of the relations between N=4, d=4 SYM and vertex operator algebras (VOAs) discussed in recent work of Gaiotto and collaborators. The resulting picture predicts conjectural generalisations of the geometric Langlands correspondence. We will focus on a class of examples figuring prominently in recent work of Creutzig-Dimofte-Garner-Geer, labelled by parameters n (rank) and k. For the case k=1,n=2 we will point out that the conformal blocks of the relevant VOA, twisted by local systems, represent sections of natural holomorphic line bundles over the moduli spaces of local systems closely related to the isomonodromic tau functions. Observing the crucial role of (quantised) cluster algebras in the definition of the holomorphic line bundles suggests natural generalisations of this story to higher values of the parameters k and n.

      Speaker: Joerg Teschner (University of Hamburg & DESY)
    • 10:30 AM
      Break
    • 19
      Generalised Langlands, VOAs, and (generalised) tau-functions cont.
      Speaker: Joerg Teschner (University of Hamburg & DESY)
    • 11:30 AM
      Break
    • 20
      Defects, quantum trace map, and exact WKB

      I will continue the discussions on line defects and surface defects in class S theories, making connections to the construction of the quantum trace map, as well as to the exact WKB method for higher order ODEs.

      Speaker: Fei Yan (Rutgers University)
    • 1:00 PM
      Break
    • 21
      Discussion on knot homology
      Speakers: Ben Webster (Perimeter Institute & University of Waterloo), Lev Rozansky (University of North Carolina, Chapel Hill), Tudor Dimofte (University of California, Davis)
    • 22
      Holomorphic BF theory, 4d SYM and the analytic Geometric Langlands program

      I will review the embedding of the analytic Geometric Langlands program in four-dimensional gauge theory.

      Speaker: Davide Gaiotto (Perimeter Institute)
    • 10:30 AM
      Break
    • 23
      Holomorphic BF theory, 4d SYM and the analytic Geometric Langlands program cont.
      Speaker: Davide Gaiotto (Perimeter Institute)
    • 11:30 AM
      Break
    • 24
      Abelian 3d mirror symmetry and boundary conditions

      3d mirror symmetry predicts an equivalence between A- and B-twists of a pair of dual 3d N=4 theories. Essentially the strongest invariants one can produce of the resulting 3-dimensional topological field theories are their 2-categories of boundary conditions. The B-side 2-category was first described by Kapustin-Rozansky-Saulinas, but the 2-categorical structure on A-side boundary conditions has not previously been understood. For abelian gauge theories with matter, we propose a model for the 2-category of A-type boundary conditions using Kapranov-Schechtman's "perverse schobers," and we prove a 3d mirror equivalence between dual 2-categories. By reducing to lower-dimensions, we can recover both the BFN construction and the BLPW Koszul duality for hypertoric categories O. This is joint work with Justin Hilburn and Aaron Mazel-Gee.

      Speaker: Benjamin Gammage (Harvard University)
    • 1:00 PM
      Break
    • 25
      Discussion on 4d N=2
      Speakers: Ahsan Khan (Institute for Advanced Study), Benjamin Gammage (Harvard University), Justin Hilburn (Perimeter Institute), Tudor Dimofte (University of California, Davis)
    • 26
      Field theory in the 1/2 Omega-background

      In this lecture I'll discuss various aspects of 4d N=2 and 5d N=1 supersymmetric QFT's in the 1/2 Omega-background (and along the way try to emphasize some relations to the 3d N=2 theories discussed in this workshop). Central to this story is the Nekrasov instanton partition function (or topological string partition function) in this background, which we will obtain through abelianization as an integral of a ratio of Wronskians of certain special solutions to the relevant Schrodinger equation. We will argue that a slight generalization of the above partition function solves an associated Riemann-Hilbert problem and defines a section of a distinguished line bundle over the moduli space of flat connections.

      Speaker: Lotte Hollands (Heriot-Watt University)
    • 10:30 AM
      Break
    • 27
      Field theory in the 1/2 Omega-background cont.
      Speaker: Lotte Hollands (Heriot-Watt University)
    • 11:30 AM
      Break
    • 28
      Fun with a holomorphic theory on twistor space

      I will summarize recent work with K. Costello, in which a local holomorphic theory on twistor space furnishes an isomorphism between 1. correlators of a 2d chiral algebra and 2. form factors (scattering amplitudes in the presence of a local operator insertion) of a 4d non-unitary CFT, with physics applications.

      Speaker: Natalie Paquette (University of Washington)
    • 1:00 PM
      Break
    • 29
      Discussion on 3d A-model
      Speakers: Davide Gaiotto (Perimeter Institute), Fei Yan (Rutgers University), Joerg Teschner (University of Hamburg & DESY), Lotte Hollands (Heriot-Watt University)
    • 30
      The relative Langlands program via gauge theory

      I will discuss a close parallel between Gaiotto and Witten's S-duality for supersymmetric boundary conditions in 4d N=4 SYM and the relative Langlands program, an enhancement of the Langlands program that was developed to provide a framework for the theory of integral representations of L-functions. A special and conjecturally self-dual class of boundary conditions is provided by quantizations of "small" or "multiplicity-free" hamiltonian spaces called hyperspherical varieties. I'll explain how a hyperspherical variety produces objects of interest in all the different settings of the Langlands program (local / global, geometric / arithmetic) and a collection of conjectures providing S-dual descriptions of these objects. The talk is based on forthcoming joint work with Yiannis Sakellaridis and Akshay Venkatesh.

      Speaker: David Ben-Zvi (University of Texas, Austin)
    • 10:30 AM
      Break
    • 31
      The relative Langlands program via gauge theory cont.
      Speaker: David Ben-Zvi (University of Texas, Austin)
    • 11:30 AM
      Break
    • 32
      Lie superalgebras and S-duality

      We present a series of (partly proven) conjectures describing geometric realizations of categories of (finite-dimensional) representations of quantum super-groups U_q(g) corresponding to Lie super-algebras g with reductive even part and a non-degenerate invariant form.
      We shall also discuss the meaning of these conjectures from the point of view of local geometric Langlands correspondence as well as a connection to the work of Ben-Zvi, Sakellaridis and Venkatesh.
      Based on joint works with M.Finkelberg, V.Ginzburg and R.Travkin as well as the work of R.Travkin and R.Yang.

      Speaker: Alexander Braverman (PI & U of Toronto)
    • 1:00 PM
      Break
    • 33
      Discussion on Langlands
      Speakers: Alexander Braverman (PI & U of Toronto), David Ben-Zvi (University of Texas, Austin), Davide Gaiotto (Perimeter Institute), Philsang Yoo (Seoul National University)