Le contenu de cette page n’est pas disponible en français. Veuillez nous en excuser.

# Mathematical Physics

This series consists of talks in the area of Mathematical Physics.

## Seminar Series Events/Videos

Currently there are no upcoming talks in this series.

## Positive geometries and the amplituhedron

Lundi oct 22, 2018
Speaker(s):

Positive geometries are real semialgebraic spaces that are
equipped with a meromorphic canonical form" whose residues reflect
the boundary structure of the space.  Familiar examples include
polytopes and the positive parts of toric varieties.  A central, but
conjectural, example is the amplituhedron of Arkani-Hamed and Trnka.
In this case, the canonical form should essentially be the tree
amplitude of N=4 super Yang-Mills.

Collection/Series:
Scientific Areas:

## Yangians from Nakajima quiver varieties

Lundi oct 15, 2018
Speaker(s):

One can associate to any finite graph Q the skew-symmetic Kac-Moody Lie algebra g_Q. While this algebra is always infinite, unless Q is a Dynkin diagram of type ADE, g_Q shares a lot of the nice features of a semisimple Lie algebra. In particular, the cohomology of Nakajima quiver varieties associated to Q gives a geometric representations of g_Q. Encouraged by this story, one could hope to define the Yangian of g_Q, for general Q, as a subalgebra of the algebra of endomorphisms of cohomology of quiver varieties.

Collection/Series:
Scientific Areas:

## Towards a categorification of a projection from the affine to the finite Hecke algebra in type A

Lundi sep 24, 2018

Work of Bezrukavnikov on local geometric Langlands correspondence and works of Gorsky, Neguţ, Rasmussen and Oblomkov, Rozansky on knot homology and matrix factorizations suggest that there should be a categorical version of a certain natural homomorphism from the affine Hecke algebra to the finite Hecke algebra in type A, sending basis lattice elements on the affine side to Jucys-Murphy elements on the finite side.

Collection/Series:
Scientific Areas:

## Langlands duality and self-duality for Hitchin systems

Lundi sep 24, 2018
Speaker(s):

I will sketch why self-dual versions of the moduli of G-Higgs bundles are expected to arise physically from the study of 4d theories of class S. I will then describe an extension of the Langlands duality results of Hausel-Thaddeus (G=SL(n)) and Donagi-Pantev (arbitrary reductive G) that yields self-dual moduli spaces as a corollary.

Collection/Series:
Scientific Areas:

## Toward AGT for general algebraic surfaces

Jeudi sep 20, 2018
Speaker(s):

The Alday-Gaiotto-Tachikawa correspondence connects gauge theory on a fourfold with conformal field theory. We are interested in a certain algebro-geometric incarnation of this framework, where the fourfold is an algebraic surface and instantons/differential geometry are replaced with sheaves/algebraic geometry. In this talk, we will present a certain approach to AGT that yields partial results for quite general surfaces, and ask questions about what still needs to be done to state and prove the full correspondence in the language of algebraic geometry.

Collection/Series:
Scientific Areas:

## Localization theory for W-algebras

Lundi sep 10, 2018
Speaker(s):

The localization theorem, which has played a central role in representation theory since its discovery in the 1980s, identifies a regular block of Category O for a semisimple Lie algebra with certain D-modules on its flag variety. In this talk we will explain work in progress which produces a similar picture for the Virasoro algebra and more generally for affine W-algebras.

Collection/Series:
Scientific Areas:

## Quantized lattices and combinatorics - Zsuzanna Dancso

Lundi juil 09, 2018

Quantized lattices, or q-lattices, appear naturally through categorification constructions (for example from zigzag-algebras), but they haven't been studied from a lattice theory point of view. After establishing the necessary background, we'll explain the q-versions of various lattice theory concepts illustrated with examples from combinatorics and graph theory, and we'll list a number of open problems.

Collection/Series:
Scientific Areas:

## TBA

Mercredi juil 04, 2018
Speaker(s):

Abstract TBA.

Collection/Series:
Scientific Areas:

## MPIM/PI teleseminar on categorified knot invariants - 4

Vendredi mai 18, 2018
Speaker(s):
Collection/Series:
Scientific Areas:

## MPIM/PI teleseminar on categorified knot invariants - Higher structures and 4-manifolds

Vendredi mai 18, 2018
Speaker(s):

In this talk we will discuss three (intimately related) examples of 4-manifold invariants based on higher structures:
- VOA[M4] from transgression of EFTs;
- SW and Donaldson invariants as chiral algebra correlators;
- Massey triple products from trisections.
These topics are based, respectively, on work with A.Gadde, P.Putrov (and work to appear with B.Feigin); recent paper with M.Dedushenko and P.Putrov; and a solo paper of the speaker.

Collection/Series:
Scientific Areas: