GFM

Deformation theory of symplectic and orthogonal sheaves

Por Emílio Franco (IST).

Abstract: While it is well known that the moduli space of G-bundles over a smooth projective curve is compact, it is not the case for an arbitrary base variety. This motivated the definition of G-sheaves by Gomez and Sols who proved that their moduli space is a compactification of the moduli space of G-bundles. In this talk I will study the deformation and obstruction theory of these objects when G is either the symplectic or the orthogonal group.

A two-phase two fluxes degenerate Cahn-Hilliard model as constrained Wasserstein gradient flow

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).

Riemannian geometry on mapping spaces and relations to shape analysis and fluid dynamics

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.

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