Por Sergey V. Smirnov (Moscow State University).
Por Fabio Deelan Cunden (University College Dublin).
Abstract: The study of ‘moments’ of random matrices (expectations of traces of powers of the matrix) is a rich and interesting subject, mainly due to its connections to enumerative geometry. I will give some background on this and then describe some recent work which offers some new perspectives (and new results).
This talk is based on joint works with Antoine Dahlqvist, Francesco Mezzadri, Neil O’Connell and Nick Simm.
Por Carlos Florentino (DM, Faculdade de Ciências da ULisboa).
Abstract: Given a finitely generated group F and a complex reductive Lie group G, the G-character variety of F, denoted $X_F G=Hom(F,G)//G$, is typically a singular algebraic variety with interesting geometric and topological properties and appears in many contexts within Mathematical-Physics.
Por Gregory Berkolaiko (Texas A&M University).
Por Bruno Mera (IST).
Abstract: The Uhlmann connection is a mixed state generalization of the Berry connection. The latter has a very important role in the study of topological phases at zero temperature. Closely related, the quantum fidelity is an information theoretical quantity which is a measure of distinguishability of quantum states. Moreover, it has been extensively used in the analysis of quantum phase transitions.
Por Giuseppe Buttazzo (Università di Pisa).
Turbulent solutions of the nonlinear Schrodinger equation: a link between the scattering theory and the Arnold diffusion
Por Nikolay Tzvetkov (Université de Cergy-Pontoise).
Por Michael Röckner (University of Bielefeld).
Por Jiří Lipovský (Department of Physics, Faculty of Science, University of Hradec Kralove).
Introduction to Wall-Crossing formulae and Riemann-Hilbert problems from Bridgeland stability conditions
Por Anna Barbieri (University of Sheffield).
Abstract: I will give a brief and gentle introduction through examples from quivers to Bridgeland stability conditions and wall-crossing formulae for invariants counting semistable objects. Such stability conditions are encoded in the formal notions of BPS structures or Kontsevich-Soibelman stability data. I will show how Riemann-Hilbert problems naturally appears in this context.