Meetings
Every Tuesday afternoon from 11:30 to 12:45, room B27, campus Kirchberg.
Organizer
 François Petit
 Jérémy Toulisse
Upcoming sessions

27.01.2015
Nicolas Tholozan (University of Luxembourg), "On the computation of the volumes of moduli spaces after M. Mirzakhani".
Abstract: As part of the Working group on Geometry of moduli spaces and topological recursion, I will give a series of 2 or 3 lectures on Mirzakhani’s computation of volumes of moduli spaces of bordered hyperbolic surfaces, one of the groundbreaking results which brought her the Fields medal last summer. The first session will be mainly devoted to the required background in hyperbolic geometry and topology of compact surfaces. Our aim will be to define properly the moduli spaces we are interested in and give a precise statement of Mirzakhani’s theorems. » 
03.02.2015
Nicolas Tholozan (University of Luxembourg), "On the computation of the volumes of moduli spaces after M. Mirzakhani" II.
Abstract: This will be the continuation of the talk of the 27/01/2015.The notes of the talks I, II are available here 
10.02.2015
Nicolas Tholozan (University of Luxembourg), "On the computation of the volumes of moduli spaces after M. Mirzakhani" III.
Abstract: This will be the continuation of the talk of the 03/02/2015. 
17.02.2015
Nicolas Tholozan (University of Luxembourg), "On the computation of the volumes of moduli spaces after M. Mirzakhani" IV.
Abstract: This will be the continuation of the talk of the 10/02/2015. 
24.02.2015
François Petit (University of Luxembourg), "An introduction to topological recursion" I.
Abstract: The topological recursion has been introduced in 2007 by E. Eynard and N. Orantin. It is a kind of universal recursive formula which was initially introduced to provide a general framework for studying the solutions of loop equations of several matrix models. It was later discovered that this type of recursion was appearing in several geometrical problems. In this talk our aim we will be to introduce topological recursions, present some of its properties and applications. 
02.03.2015
François Petit (University of Luxembourg), "An introduction to topological recursion" II.
Abstract: This will be the continuation of the talk of the 24/02/2015. 
09.03.2015
François Petit (University of Luxembourg), "An introduction to topological recursion" III.
Abstract: This will be the continuation of the talk of the 02/03/2015.
References
 O. Dumitrescu, M. Mulase, Quantum curves for Hitchin fibrations and the EynardOrantin theory, Letters in Mathematical Physics 104, 635671 (2014).
 B. Eynard, A short overview of the "Topological recursion", (ArXiv).
 M. Mirzakhani, Simple geodesics and WeilPetersson volumes of moduli spaces of bordered Riemann surfaces, Inventiones mathematicae, January 2007, Volume 167, Issue 1, pp 179222
 M. Mirzakhani, WeilPetersson volumes and intersection theory on the moduli space of curves, J. Amer. Math. Soc. 20 (2007), 123
Other working groups
 Working Group Algebra, Geometry and Quantization .
 Working group on Differential and homological geometry.