Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Online research seminar: Algebra, Geometry & Physics

Tuesdays 2pm-3.30pm

Organisers: Gaëtan Borot (HU Berlin), Yuri Manin (MPIM)

New connection link: https://hu-berlin.zoom.us/j/61339297016

For HU students in Maths -- or Physics P27 or P28 -- this is 2SWS and you can get credits by regular attendance (>50%) and writing at least one report on a talk of your choice during the term. If you intend to do so, please contact me at the beginning of the semester.

Archive of talks

 

Wintersemester 21-22


19 Oct. 2021
Maxim Kazarian (HSE & Skoltech, Moscow)
Topological recursion in Hurwitz theory
The topological recursion or Chekhov-Eynard-Orantin recursion is an inductive procedure for an explicit computation of correlator functions appearing in a large number of problems in mathematical physics, from matrix integrals and Gromov-Witten invariants to enumerations of maps and meromorphic functions with prescribed singularities. In spite of existence of a huge number of known cases where this procedure does work, its validity and universality still remains mysterious in much extend. We develop a new tool based on the theory of KP hierarchy that allows one not only formally prove it in a unified way for a wide class of problems but also to understand its true nature and the origin. These problems include enumeration various kinds of Hurwitz numbers: ordinary ones, orbifold, double, monotone, r-spin Hurwitz numbers, as well as enumeration of (hyper) maps and extends much beyond. The talk is based on a joint work with B. Bychkov, P. Dunin-Barkowski, S. Shadrin.


26 Oct. 2021
Enno Keßler (MPIM Bonn)
Super J-holomorphic curves
J-holomorphic curves or pseudoholomorphic curves are maps from Riemann surfaces to symplectic manifolds satisfying the Cauchy-Riemann equations.
J-holomorphic curves are of great interest because they allow to construct invariants of symplectic manifolds and those invariants are deeply related to topological superstring theory. A crucial step towards Gromov–Witten invariants is the compactification of the moduli space of J-holomorphic curves via stable maps which was first proposed by Kontsevich and Manin. In this talk, I want to report on a supergeometric generalization of J-holomorphic curves and stable maps where the domain is a super Riemann surface. Super Riemann surfaces have first appeared as generalizations of Riemann surfaces with anti-commutative variables in superstring theory. Super J-holomorphic curves couple the equations of classical J-holomorphic curves with a Dirac equation for spinors and are critical points of the superconformal action. The compactification of the moduli space of super J-holomorphic curves via super stable maps might, in the future, lead to a supergeometric generalization of Gromov-Witten invariants. Based on arXiv:2010.15634 [math.DG] and arXiv:1911.05607 [math.DG], joint with Artan Sheshmani and Shing-Tung Yau.


2 Nov. 2021
no seminar


9 Nov. 2021
Katherine Maxwell (MPIM Bonn)
The super Mumford form and Sato Grassmannian
In 1986, Manin conjectured that representations of the Neveu-Schwarz (NS) algebra must be related to the moduli space of SUSY curves. We present a new way to explain this relationship which utilizes the super Sato Grassmannian. This method is a super generalization of the classical story of Kontsevich; Arbarello, De Concini, Kac, and Procesi; and Kawamoto, Namikawa, Tsuchiya, and Yamada. We find that the Lie superalgebra of global superconformal vector fields on an affine SUSY curve is perfect, and that the NS algebra acts on the line bundle of the super Mumford isomorphism with zero central charge. We discuss why this new approach may have interesting applications for integrating over the moduli space of SUSY curves.
 

16 Nov. 2021
Thomas Walpuski (HU Berlin)
TBA
 

23 Nov. 2021
Olaf Hohm (HU Berlin)
TBA


30 Nov. 2021
Laura Monk (MPIM Bonn)
TBA


7 Dec. 2021
Alexander Gorodnik (Universität Zürich)
TBA


14 Dec. 2021
Joshua Lieber (MPIM Bonn)
TBA
 

21 Dec. and 28 Dec. 2021
no seminar

4 Jan. 2022
TBA

11 Jan. 2022
TBA

18 Jan. 2022
no seminar

25 Jan. 2022
Xian Dai (Heidelberg Universität)
TBA

1 Feb. 2022
TBA

8 Feb. 2022
Luca Lionni (Radboud University/Heidelberg University)
TBA

15 Feb. 2022
TBA