Por Benoît Merlet (Laboratoire Paul Painlevé, Université de Lille).

Por Clément Cancès (Inria Lille - Nord Europe).

Abstract: We present an original model for immiscible two-phase mixtures. This model can be interpreted as the generalised gradient flow of the same energy as for the classical degenerate Canh-Hilliard model, but for a different geometry. Our model is shown to dissipate faster. Existence of weak solutions is established based on the convergence of a JKO semi discretization (joint work with Flore Nabet and Daniel Matthes).

Por Boris Zilber (Oxford University).

Por Pieter Roffelsen (SISSA).

Por Philipp Harms (FREIS, Univ. Freiburg).

Abstract: Fluid dynamics and shape analysis are linked by a common underlying geometric structure, namely, Sobolev-type Riemannian metrics on manifolds of mappings. I will characterize the degeneracy and non-degeneracy of the corresponding geodesic distances, establish local well-posedness of the corresponding geodesic equations, and discuss applications of these results to shape analysis and fluid dynamics.

Por B. Shapiro (Stockholm University).

Por Jean Lagacé (University College, London).

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.