Recent progress in birational geometry

In this talk I will discuss advances in birational geometry in recent years. Much of the relevant results are concerned with boundedness properties of linear systems and of singularities which are in turn closely related with moduli theory of algebraic varieties

Well-posedness and Qualitative Behavior of Peskin's problem of an Immersed Elastic Filament in 2D Stokes Flow

A prototypical fluid-structure interaction problem is that of an closed elastic filament immersed in 2D Stokes flow, where the fluids inside and outside the closed filament have equal viscosity. This problem was probably first introduced in the context of Peskin's immersed boundary method, and is often used to test computational methods for FSI problems. Here, we study the well-posedness and qualitative behavior of this problem.

Universal Wave Patterns

A feature of solutions of a (generally nonlinear) field theory can be called "universal" if it is independent of side conditions like initial data. I will explain this phenomenon in some detail and then illustrate it in the context of the sine-Gordon equation, a fundamental relativistic nonlinear wave equation. In particular I will describe some results (joint work with R. Buckingham) concerning a universal wave pattern that appears for all initial data that crosses the separatrix in the phase portrait of the simple pendulum.

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Discrete Surface Ricci Flow (II)

A discrete surface is a simplicial complex which is locally isometric to $R^2$ or upper half plane, and we can define Gaussian curvature and circle packing metric on it, then we’ll explain the discrete Gauss-Bonnet theorem. Also, we can compute the relation between length of simplices and the metric and define Ricci flow, then I’ll prove the convergence of the discrete Ricci flow.

Introduction to GMT -- approximate tangent spaces of rectifiable sets (I)

This time I am going to prove one side of the theorem which was mentioned in the last talk.

References:

L. Simon, Lectures on Geometric Measure Theory, Sections 11.
R. Hardt & L. Simon, Seminar on Geometric Measure Theory, Lecture 2 [S].

Characterization and computation of eigenvalues of operators with gaps. Applications in relativistic Quantum Mechanics

Professor Maria J. Esteban is a Basque-French mathematician. In her research, she studies nonlinear partial differential equations, mainly by the use of variational methods, with applications to physics and quantum chemistry. She has also worked on fluid-structure interaction. She did her PhD thesis at the Pierre and Marie Curie University (Paris), under the direction of Pierre-Louis Lions. After graduation, she became full-time researcher at CNRS, where she holds now a position of director of research. From 2015 to 2019, she is president of International Council for Industrial and Applied Mathematics (ICIAM). She was president of the Société de Mathématiques Appliquées et Industrielles from 2009 to 2012 and chair of the Applied Mathematics Committee of the European Mathematical Society in 2012 and 2013. She participated in the Forward Look on "Mathematics and Industry" funded by the European Science Foundation and is one of the launchers of the EU-MATHS-IN European network for industrial mathematics.