Seminar on Arithmetic Geometry and Quantum Field Theory


Organizers: Jeff Harvey and Minhyong Kim; 

Time/Duration: Wednesdays, 20:00 London time, approximately 30 weeks per year; 

The talks are as follows.

Title: Relative Langlands Duality

Title: Background on periods and L-functions

Title: Nonalgebraic attractor points on higher-dimensional Calabi-Yau manifolds

Title: An introduction to the Langlands correspondence

An Introduction to the Langlands Correspondence, Part II

Title: Symplectic constructions for l-adic local systems and their deformations

Title: Conformal Field Theories with Sporadic Group Symmetry

Title: Algebraic structure of boundary conditions in (T)QFT

Title: Algebraic structure of boundary conditions in (T)QFT, Part II

Title: Arithmetic field theories with finite coefficients

Title: On the rationality of MUMs and 2-functions

Title: Defects, boundaries and monads in Betti quantum geometric Langlands

Title: Physical Discretization and Arithmetic Geometry

Title: Arithmetic Topology and Chiral Algebras

Title: Toward Geometric Foundations for Arithmetic Field Theories

Title: Categorification of the Langlands correspondence and Iwasawa theory

Title: Chern-Simons theory on cylinders and generalized Hamilton-Jacobi actions

Title: Symplectic, or mirrorical, look at the Fargues-Fontaine curve

Title: Quantum modular forms from three-manifolds

Online Mini-Conference on the Geometric Langlands Correspondence

Dates: 13 January to 17 February, 2021

Description/Timeline: This virtual conference will extend over 6 weeks with one talk per week. We will start out with a three-week mini-course by Sam Raskin, Nick Rosenblyum, and Dennis Gaitsgory. This will be followed by lectures by Edward Witten, Edward Frenkel, and David Kazhdan. If you are not on the regular mailing list for the seminar on arithmetic geometry and quantum field theory but would like to attend this conference, write to Minhyong Kim.

The talks are as follows.

Title: Geometric Langlands for l-adic sheaves

Title: Spectral decomposition in geometric Langlands

Title: Automorphic forms as categorical trace

Title: Branes, Quantization, and Geometric Langlands

Title: An analytic version of the Langlands correspondence for complex curves

Title: A proposal of a categorical construction of the algebraic version of L2(BunG)

Date: 17 February, 2021, 18:00 GMT (CHANGE OF TIME!)

Speaker: David Kazhdan (Hebrew)

Materials: Video, Slides

Title: Counting half and quarter BPS states - and their geometric counterparts

Title: Higher Galois closures

Title :Multiple Zeta Values in Deformation Quantization

Title: Modularity of (rational) flux vacua

Title: Conformal blocks and factorisable sheaves

Title: Local geometric Langlands and roots of unity

Title: Factorizable sheaves and local systems of conformal blocks

Title: The Bezrukavnikov-Finkelberg-Schechtman theory from the point of view of Geometric Langlands

Lecture Series at the Korea Institute for Advanced Study (Online Seminar)

Talk 1: Operators and higher categories in quantum field theory 

I. A complete mathematical definition of quantum field theory does not yet exist. Following the example of quantum mechanics, I will indicate what a good definition in terms could look like. In this good definition, QFTs are defined in terms of their operator content (including extended operators), and the collection of all operators is required to satisfy some natural properties.

II. After reviewing some classic examples, I will describe the construction of Noether currents and the corresponding extended symmetry operators.

III. One way to build topological extended operators is by "condensing" lower-dimensional operators. The existence of this condensation procedure makes the collection of all topological operators into a semisimple higher category.

IV. Topological operators provide "noninvertible higher-form symmetries". These symmetries assign charges to operators of complementary dimension. This assignment is a version of what fusion category theorists call an "S-matrix".

V. The Tannakian formalism suggests a way to recognize higher gauge theories. It also suggests the existence of interesting higher versions of super vector spaces with more exotic tangential structures.

Talk 2: The Mathematical Foundations of Topological Quantum Computation: Anyons, Braids and Categories

Talk 3: Geometric Eisenstein series and the Fargues-Fontaine curve I, II, III, IV 

Talk 4: A mathematical approach towards Coulomb branches of 3d SUSY gauge theories and related topics

Talk 5: Topics in Field Theory and Topological Phases of Matter