Cursos

Cursos

Lecture 3/4: The singular set of a Sobolev mapping, or when differential geometry comes into play

Ponente:  Antoine Detaille (Université de Lyon)
Fecha:  lunes 11 de noviembre de 2024 - 12:00 - 13:15
Lugar:  Aula Gris 2, ICMAT

Resumen:

After having discovered that Sobolev mappings are not always strongly approximable by smooth mappings, we will turn to the question of detecting which mappings can nevertheless by strongly approached. This will show a beautiful connection with one more area of mathematics, namely differential geometry, through the construction of objects such as the Jacobian.

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Minicourse: Analytic, geometric, and topological methods for Sobolev mappings to manifolds (4, 7, 11 & 14 November)

In this minicourse, we will explore the theory of Sobolev mappings with values into a compact manifold. The study of such mappings is motivated by applications coming from geometry, physics, computer graphics, and numerical methods, and their study per se raises many beautiful and challenging problems. The objective is to give an overview of some of these problems, and to explain a few tools that have been developed to tackle them. The ideas will systematically be illustrated on insightful model cases, avoiding too much technicality. The only prerequisite is a relative comfort with functional analysis, especially classical Sobolev spaces. All concepts of topology and geometry that will be used in the course shall be duly reminded.

Poster