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 Rosa Sena-Dias (IST).

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 Maria Elisa Fernandes (Universidade de Aveiro).

Por Rui Albuquerque (Universidade de Évora / Centro de Investigação em Matemática e Aplicações).

Por Daniel Barlet (Inst. Élie Cartan, Lorraine).

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.

This conference is devoted to all aspects of Algebraic Geometry and Analysis, and aims at reinforcing the bridge between the fields of Higgs bundles and D-modules.

Por Luisa Fiorot (Università degli Studi di Padova).

Por Herwig Hauser (Universidade de Viena).

Abstract: Assume that a complex polynomial P has a common root with each of its derivatives up to order deg(P) - 1 (not necessarily the same root for all derivatives). How does P look like?