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Mathias Braun

mathias.braun@epfl.ch https://sites.google.com/view/mathiasbraun

EPFL SB MATH
MA A1 354 (Bâtiment MA)
Station 8
1015 Lausanne

Teaching & PhD

Courses

Analysis IV

MATH-207(d)

The course studies the fundamental concepts of complex analysis and Laplace analysis with a view to their use to solve multidisciplinary scientific engineering problems.

Distribution and interpolation spaces

MATH-502

The goal of this course is to give an introduction to the theory of distributions and cover the fundamental results of Sobolev spaces including fractional spaces that appear in the interpolation theory. Those notions are central to the study of partial differential equations (PDE).

Functional analysis II

MATH-404

We introduce locally convex vector spaces. As an example we treat the space of test functions and the space of distributions. In the second part of the course, we discuss differential calculus in Banach spaces and some elements from nonlinear functional analysis.

Heat kernel and analysis on manifolds

MATH-418

This course develops the theory of the heat equation on Riemannian manifolds. We introduce the Laplace-Beltrami operator, the heat semigroup, and the heat kernel, study its fundamental properties, and explore how it "sees" the geometry of the underlying space.