Multiple Speakers | 25/05/2021 | [NCNW03] New connections in number theory and physics

Описание: FIRST Speaker: Professor Boris Pioline (Sorbonne Université)
Date: 25 May 2021 - 14:30 to 15:30
Venue: INI Seminar Room 1 - VIRTUAL
Session Title: Exact BPS Couplings and Black Hole Counting
Event: [NCNW03] New connections in number theory and physics

In order to determine the exact spectrum of BPS states in four-dimensional string vacua with extended supersymmetry, a useful strategy is to consider certain BPS-saturated couplings in the low-energy effective action in three dimensions, after compactifying on a circle. These couplings are highly constrained by supersymmetry and dualities, and can sometimes be determined exactly. The BPS indices can then be read off from the Fourier expansion in the large radius limit. This strategy has been applied to the counting of 1/8-BPS (respectively 1/4, 1/2) states in string vacua with N=8 (respectively, 4,2) supersymmetry in four dimensions, leading to rather exotic types of automorphic functions from the point of view of mathematics, but quite natural from the point of view of physics. This includes theta liftings of genus two Siegel modular forms (in the N=8 and N=4 cases), as well as mock modular forms of higher depth (in the N=2 case, or in the closely related set up of N=4 super-Yang Mills theory).

SECOND Speaker: Professor Eric D’Hoker (University of California, Los Angeles)
Date: 25 May 2021 - 15:30 to 16:30
Venue: INI Seminar Room 1 - VIRTUAL
Session Title: Modular Graph Functions, Forms, and Tensors
Event: [NCNW03] New connections in number theory and physics

Modular graph functions map Feynman graphs to SL(2,Z)-invariant functions. They generalize non-holomorphic Eisenstein series, multiple zeta values, and are related to single-valued elliptic polylogarithms. They may be generalized to modular graph forms, which are covariant under SL(2,Z), and obey infinite families of algebraic and differential identities. String theory amplitudes produce modular graph functions and forms associated with Riemann surfaces of genus one and naturally lead to a generalization of modular graph functions at higher genus, where they generalize Kawazumi-Zhang and Faltings invariants. Various algebraic and differential identities between modular graph functions and tensors at higher genus have recently been established.

THIRD Speaker: Professor Edward Witten (Institute for Advanced Study, Princeton)
Date: 25 May 2021 - 16:45 to 17:45
Venue: INI Seminar Room 1 - VIRTUAL
Session Title: Quantization by Branes and Geometric Langlands
Event: [NCNW03] New connections in number theory and physics