Seminar on Arithmetic Geometry and Quantum Field Theory


Organisers: Jeff Harvey and Minhyong Kim

Wednesdays, 20:00 London time, approximately 30 weeks per year

If you are interested in attending this online seminar, please send an email to Minhyong Kim.

Past Events


Lecture Series at the Korea Institute for Advanced Study

(Check the KIAS webpages for detailed schedule. The slides and videos will be posted here for convenience.)


19-23 July, 2021

Theo Johnson-Freyd (Dalhousie/Perimeter)

Title: Operators and higher categories in quantum field theory

Abstracts:

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.

Slides 1

Video 1

Slides 2

Video 2-1

Video 2-2

Slides 3

Video 3

Slides 4

Video 4

Slides 5

Video 5




2-6 August, 2021

Eric Rowell (Texas A & M University)

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

Slides 1

Video 1

Slides 2

Video 2

Slides 3

Video 3

Slides 4

Video 4

Slides 5

Video 5




3,5,10,12 August, 2021

David Hansen (MPIM)

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


Video 1

Video 2

Video 3

Video 4




9-13 August, 2021

Hiraku Nakajima (IPMU)

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

Slides 1

Video 1

Slides 2

Video 2

Slides 3 and 4

Video 3

Video 4

Slides 5

Video 5




16-20 August, 2021

Dan Freed (UT Austin)

Title: Topics in Field Theory and Topological Phases of Matter

Slides 1

Video 1

Slides 2

Video 2

Slides 3

Video 3

Slides 4

Video 4

Slides 5

Video 5