Some new perspectives on moments of random matrices

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.

Information geometry in the analysis of phase transitions

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.

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.