Cohomological Hall Algebras in Mathematics and Physics

Conference Date: 
Monday, February 25, 2019 (All day) to Friday, March 1, 2019 (All day)
Scientific Areas: 
String Theory
Mathematical Physics

 

This workshop will bring together leading mathematicians and physicists interested in the Cohomological Hall algebra, as it appears in the study of moduli spaces and in gauge and string theory.

  • Alexander Braverman, Perimeter Institute & University of Toronto
  • Kevin Costello, Perimeter Institute
  • Thomas Creutzig, University of Alberta
  • Ben Davison, University of Edinburgh
  • Pavel Etingof, Massachusetts Institute of Technology
  • Davide Gaiotto, Perimeter Institute
  • Sergei Gukov, California Institute of Technology
  • Mikhail Kapranov, Kavli IPMU, Tokyo
  • Peter Koroteev, University of California, Davis
  • Fyodor Malikov, University of Southern California
  • Anton Mellit, University of Vienna
  • Andrei Negut, Massachusetts Institute of Technology
  • Natalie Paquette, California Institute of Technology
  • Nicolo' Piazzalunga, Stony Brook University
  • Miroslav Rapcak, Perimeter Institute
  • Francesco Sala, Kavli IPMU, Tokyo
  • Yan Soibelman, Kansas State University
  • Balazs Szendroi, University of Oxford
  • Yegor Zenkevich, Institute for Theoretical and Experimental Physics & Milano Bicocca University
  • Gufang Zhao, University of Melbourne

 

  • Ian Le, Perimeter Institute
  • Tadashi Okazaki, Perimeter Institute
  • Thomas Przezdziecki, Max Planck Institute
  • Alexander Weekes, Perimeter Institute
  • Junya Yagi, Perimeter Institute
  • Philsang Yoo, Yale University

Monday, February 25, 2019

Time

Event

Location

9:00 – 9:25am

Registration

Reception

9:25 – 9:30am

Yan Soibelman, Kansas State University
Welcome and Opening Remarks

Sky Room

9:30 – 10:30am

Yan Soibelman, Kansas State University

Sky Room

10:30 – 11:00am

Coffee Break

Bistro – 1st Floor

11:00 – 12:00pm

Davide Gaiotto, Perimeter Institute

Sky Room

12:00 – 2:00pm

Lunch

Bistro – 2nd Floor

2:00 – 3:00pm

Nicolo' Piazzalunga, Stony Brook University
Magnificent Four with color

Sky Room

3:00 – 3:15pm

Break

Bistro – 1st Floor

3:15 – 4:15pm

Yegor Zenkevich,
Institute for Theoretical and Experimental Physics
& Milano Bicocca University
Networks of intertwiners, 3d theories and superalgebras

Sky Room

4:15 – 4:45pm

Coffee Break

Bistro – 1st Floor

4:45 – 5:45pm

Mikhail Kapranov, Kavli IPMU, Tokyo

Sky Room

 

Tuesday, February 26, 2019

Time

Event

Location

9:30 – 10:30am

Ben Davison, University of Edinburgh
Yangians from cohomological Hall algebras

Sky Room

10:30 – 11:00am

Coffee Break

Bistro – 1st Floor

11:00 – 12:00pm

Sergei Gukov, California Institute of Technology

Sky Room

12:00 – 12:10pm

Conference Photo

TBA

12:10 – 2:30pm

Lunch

Bistro – 2nd Floor

2:30 – 3:30pm

Francesco Sala, Kavli IPMU, Tokyo
Categorification of 2d cohomological Hall algebras

Sky Room

3:30 – 4:00pm

Coffee Break

Bistro – 1st Floor

4:00 – 5:00pm

Pavel Etingof, Massachusetts Institute of Technology
Short star-products for filtered quantizations

Sky Room

5:30 – 8:00pm

Banquet

Bistro – 2nd Floor


Wednesday, February 27, 2019

Time

Event

Location

9:30 – 10:30am

Kevin Costello, Perimeter Institute

Sky Room

10:30 – 11:00am

Coffee Break

Bistro – 1st Floor

11:00 – 12:00pm

Gufang Zhao, University of Melbourne

Sky Room

12:00 – 2:00pm

Lunch

Bistro – 2nd Floor

2:00 – 3:30pm

Mikhail Kapranov, Kavli IPMU, Tokyo
Colloquium

Time Room

3:30 – 4:00pm

Coffee Break

Bistro – 1st Floor

4:00 – 5:00pm

Natalie Paquette, California Institute of Technology

Sky Room

 

Thursday, February 28, 2019

Time

Event

Location

9:30 – 10:30am

Balazs Szendroi, University of Oxford
Partition functions and the McKay correspondence

Sky Room

10:30 – 11:00am

Coffee Break

Bistro – 1st Floor

11:00 – 12:00pm

Andrei Negut, Massachusetts Institute of Technology

Sky Room

12:00 – 2:30pm

Lunch

Bistro – 2nd Floor

2:30 – 3:30pm

Miroslav Rapcak, Perimeter Institute

Sky Room

3:30 – 4:00pm

Coffee Break

Bistro – 1st Floor

4:00 – 5:00pm

Thomas Creutzig, University of Alberta

Sky Room

 

Friday, March 1, 2019

Time

Event

Location

9:30 – 10:30am

Alexander Braverman, Perimeter Institute & University of Toronto

Sky Room

10:30 – 11:00am

Coffee Break

Bistro – 1st Floor

11:00 – 12:00pm

Anton Mellit, University of Vienna
Fusion Hall algebra and shuffle conjectures

Sky Room

12:00 – 2:30pm

Lunch

Bistro – 2nd Floor

2:30 – 3:30pm

Fyodor Malikov, University of Southern California
On one example of a chiral Lie group

Sky Room

3:30 – 4:00pm

Coffee Break

Bistro – 1st Floor

4:00 – 5:00 pm

Peter Koroteev, University of California, Davis

Sky Room

 

 

Ben Davison, University of Edinburgh

Yangians from cohomological Hall algebras

Pavel Etingof, Massachusetts Institute of Technology

Short star-products for filtered quantizations 

Fyodor Malikov, University of Southern California

On one example of a chiral Lie group

Anton Mellit, University of Vienna

Fusion Hall algebra and shuffle conjectures

The classical Hall algebra of the category of representations of one-loop quiver is isomorphic to the ring of symmetric functions, and Hall-Littlewood polynomials arise naturally as the images  of objects. I will talk about a second "fusion" product on this algebra, whose structure constants are given by counting of bundles with nilpotent endomorphisms on P^1 with restrictions at 0, 1 and infinity. The two products together make up a structure closely related to the elliptic Hall algebra. In the situations when bundles can be explicitly enumerated, I will explain how this leads to q,t-identities conjectured by combinatorists, such as the shuffle conjecture and its generalizations. This is a joint project with Erik Carlsson.

Nicolo' Piazzalunga, Stony Brook University

Magnificent Four with color

I will present the rank N magnificent four theory, which is the supersymmetric localization of U(N) super-Yang-Mills theory with matter on a Calabi-Yau fourfold, and conjecture an explicit formula for the partition function Z: it has a free-field representation, and surprisingly it depends on Coulomb and mass parameters in a simple way. Based on joint work with N.Nekrasov.

Francesco Sala, Kavli IPMU, Tokyo

Categorification of 2d cohomological Hall algebras

Let $\mathcal{M}$ denote the moduli stack of either coherent sheaves on a smooth projective surface or Higgs sheaves on a smooth projective curve $X$. The convolution algebra structure on the Borel-Moore homology of $\mathcal{M}$ is an instance of two-dimensional cohomological Hall algebras.
 
In the present talk, I will describe a full categorication of the cohomological Hall algebra of $\mathcal{M}$. This is achieved by exhibiting a derived enhancement of $\mathcal{M}$. Furthermore, this method applies also to several other moduli stacks, such as the moduli stack of vector bundles with flat connections on $X$ and the moduli stack of finite-dimensional representations of the fundamental group of $X$. In the second part of the talk, I will focus on the case of curves and discuss some relations between the Betti, de Rham, and Dolbeaut categorified cohomological Hall algebras. This is based on a work in progress with Mauro Porta.
 
Balazs Szendroi, University of Oxford
 
Partition functions and the McKay correspondence 
 
I will explain some results on certain sheaf-theoretic partition functions defined on Calabi-Yau orbifolds, and their connection to the McKay correspondence, the representation theory of affine Lie algebras, and cohomological Hall algebras. Based on joint work with Gyenge and Nemethi, respectively Davison and Ongaro
 
Yegor Zenkevich, Institute for Theoretical and Experimental Physics & Milano Bicocca University
 
Networks of intertwiners, 3d theories and superalgebras

 

Scientific Organizers:

  • Kevin Costello, Perimeter Institute
  • Yan Soibelman, Kansas State University
  • Yaping Yang, University of Melbourne