DMG University of Trieste - Seminar announcement - Alessandro Giacchetto

[mattia mecchia]

Seminar announcement

Dipartimento di Matematica e Geoscienze

Università di Trieste

*Monday  9 May 2022, at 2.30 p.m.*

**

*Alessandro Giacchetto  (Université Paris-Saclay)***

**

*Title: A proof of Witten’s conjecture à la Mirzakhani*

Abstract:
In the early ‘90s, Witten formulated a fundamental conjecture, proved 
shortly after by Kontsevich, establishing a new connection between 
algebraic geometry and mathematical physics: he considered some 
intersection numbers over the moduli space of curves, and conjectured 
that their generating series satisfies an integrable hierarchy of KdV 
type. In this talk, I will present a new geometric proof of Witten’s 
conjecture based on the symplectic structure of the combinatorial moduli 
and Teichmüller spaces parametrising metric ribbon graphs. Namely, I 
will show that certain length and twist coordinates are Darboux for the 
symplectic form, and show a Mirzakhani-type identity on the 
combinatorial Teichmüller space. The integration of this identity is 
equivalent to Kontsevich’s recursion for the intersection numbers. The 
talk is based on a joint work with J.E. Andersen, G. Borot, S. 
Charbonnier, D. Lewański and C. Wheeler.

Venue: Seminar Room, 3rd floor, H2bis building, Via A. Valerio 12/1, Trieste

All those interested are much welcome to attend.

The seminar will also be broadcast by Zoom:


Entra nella riunione in Zoom
https://us02web.zoom.us/j/87289747554?pwd=UVhMaXNjUmFsQVZxSDhzYkw5MUdOUT09

ID riunione: 872 8974 7554
Passcode: 546723


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*Mattia Mecchia*
Professore associato | Associate Professor
Università degli Studi di Trieste | University of Trieste
Dipartimento Matematica e Geoscienze
Via Valerio 12/1 - 34127 Trieste(Italy)
mmecchia at units.it
Tel.| Ph. +39-0405582645
Skype: mmecchia33
http://www.dmi.units.it/~mecchia/