Conference

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Discussion on Langlands
- David Ben-Zvi The University of Texas at Austin
- Alexander Braverman University of Toronto
- Davide Gaiotto Perimeter Institute for Theoretical Physics
- Philsang Yoo Seoul National University
June 30, 2022

PIRSA:22060094
Mathematical Physics
Lie superalgebras and S-duality

Alexander Braverman University of Toronto
June 30, 2022

PIRSA:22060093
Mathematical Physics
The relative Langlands program via gauge theory cont.

David Ben-Zvi The University of Texas at Austin
June 30, 2022

PIRSA:22060092
Mathematical Physics
The relative Langlands program via gauge theory

David Ben-Zvi The University of Texas at Austin
June 30, 2022

PIRSA:22060091
Mathematical Physics
Discussion on 4d N=2
- Davide Gaiotto Perimeter Institute for Theoretical Physics
- Lotte Hollands Heriot-Watt University
- Joerg Teschner Deutsches Elektronen-Synchrotron DESY
- Fei Yan Rutgers University
June 29, 2022

PIRSA:22060090
Mathematical Physics
Field theory in the 1/2 Omega-background cont.

Lotte Hollands Heriot-Watt University
June 29, 2022

PIRSA:22060088
Mathematical Physics
Field theory in the 1/2 Omega-background

Lotte Hollands Heriot-Watt University
June 29, 2022

PIRSA:22060087
Mathematical Physics
Discussion on 3d A-model
- Tudor Dimofte University of Edinburgh
- Benjamin Gammage Harvard University
- Justin Hilburn
- Ahsan Khan Institute for Advanced Study (IAS)
June 28, 2022

PIRSA:22060086
Mathematical Physics
Abelian 3d mirror symmetry and boundary conditions

Benjamin Gammage Harvard University
June 28, 2022

PIRSA:22060085
Mathematical Physics
Holomorphic BF theory, 4d SYM and the analytic Geometric Langlands program

Davide Gaiotto Perimeter Institute for Theoretical Physics
June 28, 2022

PIRSA:22060083
Mathematical Physics
Discussion on knot homology
- Tudor Dimofte University of Edinburgh
- Lev Rozansky University of North Carolina at Chapel Hill
- Ben Webster University of Waterloo
June 27, 2022

PIRSA:22060082
Mathematical Physics
Defects, quantum trace map, and exact WKB

Fei Yan Rutgers University
June 27, 2022

PIRSA:22060081
Mathematical Physics

Discussion on Langlands
- David Ben-Zvi The University of Texas at Austin
- Alexander Braverman University of Toronto
- Davide Gaiotto Perimeter Institute for Theoretical Physics
- Philsang Yoo Seoul National University
June 30, 2022

PIRSA:22060094
Mathematical Physics
Lie superalgebras and S-duality

Alexander Braverman University of Toronto
June 30, 2022

PIRSA:22060093
Mathematical Physics
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.
The relative Langlands program via gauge theory cont.

David Ben-Zvi The University of Texas at Austin
June 30, 2022

PIRSA:22060092
Mathematical Physics
The relative Langlands program via gauge theory

David Ben-Zvi The University of Texas at Austin
June 30, 2022

PIRSA:22060091
Mathematical Physics
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.
Discussion on 4d N=2
- Davide Gaiotto Perimeter Institute for Theoretical Physics
- Lotte Hollands Heriot-Watt University
- Joerg Teschner Deutsches Elektronen-Synchrotron DESY
- Fei Yan Rutgers University
June 29, 2022

PIRSA:22060090
Mathematical Physics
Field theory in the 1/2 Omega-background cont.

Lotte Hollands Heriot-Watt University
June 29, 2022

PIRSA:22060088
Mathematical Physics
Field theory in the 1/2 Omega-background

Lotte Hollands Heriot-Watt University
June 29, 2022

PIRSA:22060087
Mathematical Physics
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.
Discussion on 3d A-model
- Tudor Dimofte University of Edinburgh
- Benjamin Gammage Harvard University
- Justin Hilburn
- Ahsan Khan Institute for Advanced Study (IAS)
June 28, 2022

PIRSA:22060086
Mathematical Physics
Abelian 3d mirror symmetry and boundary conditions

Benjamin Gammage Harvard University
June 28, 2022

PIRSA:22060085
Mathematical Physics
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.
Holomorphic BF theory, 4d SYM and the analytic Geometric Langlands program

Davide Gaiotto Perimeter Institute for Theoretical Physics
June 28, 2022

PIRSA:22060083
Mathematical Physics
I will review the embedding of the analytic Geometric Langlands program in four-dimensional gauge theory.
Discussion on knot homology
- Tudor Dimofte University of Edinburgh
- Lev Rozansky University of North Carolina at Chapel Hill
- Ben Webster University of Waterloo
June 27, 2022

PIRSA:22060082
Mathematical Physics
Defects, quantum trace map, and exact WKB

Fei Yan Rutgers University
June 27, 2022

PIRSA:22060081
Mathematical Physics
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.

Title	Speaker(s)	Date	Talk Type	Info link
Discussion on Langlands	David Ben-Zvi, Alexander Braverman, Davide Gaiotto, Philsang Yoo	2022-06-30	Conference	View details
Lie superalgebras and S-duality	Alexander Braverman	2022-06-30	Conference	View details
The relative Langlands program via gauge theory cont.	David Ben-Zvi	2022-06-30	Conference	View details
The relative Langlands program via gauge theory	David Ben-Zvi	2022-06-30	Conference	View details
Discussion on 4d N=2	Davide Gaiotto, Lotte Hollands, Joerg Teschner, Fei Yan	2022-06-29	Conference	View details
Field theory in the 1/2 Omega-background cont.	Lotte Hollands	2022-06-29	Conference	View details
Field theory in the 1/2 Omega-background	Lotte Hollands	2022-06-29	Conference	View details
Discussion on 3d A-model	Tudor Dimofte, Benjamin Gammage, Justin Hilburn, Ahsan Khan	2022-06-28	Conference	View details
Abelian 3d mirror symmetry and boundary conditions	Benjamin Gammage	2022-06-28	Conference	View details
Holomorphic BF theory, 4d SYM and the analytic Geometric Langlands program	Davide Gaiotto	2022-06-28	Conference	View details
Discussion on knot homology	Tudor Dimofte, Lev Rozansky, Ben Webster	2022-06-27	Conference	View details
Defects, quantum trace map, and exact WKB	Fei Yan	2022-06-27	Conference	View details

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Format results

Discussion on Langlands

Lie superalgebras and S-duality

The relative Langlands program via gauge theory cont.

The relative Langlands program via gauge theory

Discussion on 4d N=2

Field theory in the 1/2 Omega-background cont.

Field theory in the 1/2 Omega-background

Discussion on 3d A-model

Abelian 3d mirror symmetry and boundary conditions

Holomorphic BF theory, 4d SYM and the analytic Geometric Langlands program

Discussion on knot homology

Defects, quantum trace map, and exact WKB

Discussion on Langlands

Lie superalgebras and S-duality

The relative Langlands program via gauge theory cont.

The relative Langlands program via gauge theory

Discussion on 4d N=2

Field theory in the 1/2 Omega-background cont.

Field theory in the 1/2 Omega-background

Discussion on 3d A-model

Abelian 3d mirror symmetry and boundary conditions

Holomorphic BF theory, 4d SYM and the analytic Geometric Langlands program

Discussion on knot homology

Defects, quantum trace map, and exact WKB