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QFT for Mathematicians 2022

Jun 20 – 30, 2022
America/Toronto timezone

Stephanie Mohl

Contribution List

33 out of 33 displayed
  1. 1. Welcome and Opening Remarks
    Kevin Costello (Perimeter Institute)
    6/20/22, 8:50 AM
  2. 2. 3d Theories and Twists I
    Kevin Costello (Perimeter Institute)
    6/20/22, 9:00 AM
  3. 3. 3d Gauge Theory and Elliptic Stable Envelopes I
    Andrei Okounkov (Columbia University)
    6/20/22, 11:00 AM
  4. 4. Classical BV Formalism and Topological Quantum Field Theory
    Philsang Yoo (Seoul National University)
    6/20/22, 3:30 PM
  5. 5. A and B models in 3d and 4d I
    Justin Hilburn (Perimeter Institute)
    6/21/22, 9:00 AM
  6. 6. 3d B Models and Knot Homology I
    Lev Rozansky (University of North Carolina, Chapel Hill)
    6/21/22, 11:00 AM
  7. 7. On Boundary VOA's
    Davide Gaiotto (Perimeter Institute)
    6/21/22, 3:30 PM
  8. 8. 3d Gauge Theory and Elliptic Stable Envelopes II
    Mykola Dedushenko (Stony Brook University)
    6/22/22, 9:00 AM
  9. 9. 3d Theories and Twists II
    Tudor Dimofte (University of Edinburgh)
    6/22/22, 11:00 AM
  10. 10. Open Discussion
    6/22/22, 3:30 PM
  11. 11. 3d Gauge Theory and Elliptic Stable Envelopes III
    Andrei Okounkov (Columbia University)
    6/23/22, 9:00 AM
  12. 12. Geometrical structures in 4d N=2 class S theories
    Fei Yan (Rutgers University)
    6/23/22, 11:00 AM

    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.

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  13. 13. 3d Gauge Theory and Elliptic Stable Envelopes IV
    Mykola Dedushenko (Stony Brook University)
    6/23/22, 3:30 PM
  14. 14. 3d B Models and Knot Homology II
    Lev Rozansky (University of North Carolina, Chapel Hill)
    6/24/22, 9:00 AM
  15. 15. A and B Models in 3d and 4d II
    Justin Hilburn (Perimeter Institute)
    6/24/22, 11:00 AM
  16. 16. Open Discussion
    6/24/22, 3:30 PM
  17. 17. Welcome and Opening Remarks
    Ben Webster (Perimeter Institute & University of Waterloo)
    6/27/22, 9:25 AM
  18. 18. Generalised Langlands, VOAs, and (generalised) tau-functions
    Joerg Teschner (University of Hamburg & DESY)
    6/27/22, 9:30 AM

    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...

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  19. 19. Generalised Langlands, VOAs, and (generalised) tau-functions cont.
    Joerg Teschner (University of Hamburg & DESY)
    6/27/22, 10:45 AM
  20. 20. Defects, quantum trace map, and exact WKB
    Fei Yan (Rutgers University)
    6/27/22, 12:00 PM

    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.

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  21. 21. Discussion on knot homology
    Ben Webster (Perimeter Institute & University of Waterloo), Lev Rozansky (University of North Carolina, Chapel Hill), Tudor Dimofte (University of California, Davis)
    6/27/22, 2:00 PM
  22. 22. Holomorphic BF theory, 4d SYM and the analytic Geometric Langlands program
    Davide Gaiotto (Perimeter Institute)
    6/28/22, 9:30 AM

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

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  23. 23. Holomorphic BF theory, 4d SYM and the analytic Geometric Langlands program cont.
    Davide Gaiotto (Perimeter Institute)
    6/28/22, 10:45 AM
  24. 24. Abelian 3d mirror symmetry and boundary conditions
    Benjamin Gammage (Harvard University)
    6/28/22, 12:00 PM

    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...

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  25. 25. Discussion on 4d N=2
    Ahsan Khan (Institute for Advanced Study), Benjamin Gammage (Harvard University), Justin Hilburn (Perimeter Institute), Tudor Dimofte (University of California, Davis)
    6/28/22, 2:00 PM
  26. 26. Field theory in the 1/2 Omega-background
    Lotte Hollands (Heriot-Watt University)
    6/29/22, 9:30 AM

    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...

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  27. 27. Field theory in the 1/2 Omega-background cont.
    Lotte Hollands (Heriot-Watt University)
    6/29/22, 10:45 AM
  28. 28. Fun with a holomorphic theory on twistor space
    Natalie Paquette (University of Washington)
    6/29/22, 12:00 PM

    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.

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  29. 29. Discussion on 3d A-model
    Davide Gaiotto (Perimeter Institute), Fei Yan (Rutgers University), Joerg Teschner (University of Hamburg & DESY), Lotte Hollands (Heriot-Watt University)
    6/29/22, 2:00 PM
  30. 30. The relative Langlands program via gauge theory
    David Ben-Zvi (University of Texas, Austin)
    6/30/22, 9:30 AM

    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...

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  31. 31. The relative Langlands program via gauge theory cont.
    David Ben-Zvi (University of Texas, Austin)
    6/30/22, 10:45 AM
  32. 32. Lie superalgebras and S-duality
    Alexander Braverman (PI & U of Toronto)
    6/30/22, 12:00 PM

    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...

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  33. 33. Discussion on Langlands
    Alexander Braverman (PI & U of Toronto), David Ben-Zvi (University of Texas, Austin), Davide Gaiotto (Perimeter Institute), Philsang Yoo (Seoul National University)
    6/30/22, 2:00 PM