Core Courses

The BMS Core Course sequences in RTA 7 cover the fundamental concepts, results, methods of...

Functional Analysis
◦ Metric and Normed Spaces
◦ Linear Operators and Dual Spaces
◦ Fundamental Theorems of Functional Analysis such as Hahn-Banach and Banach-Steinhaus
◦ Weak Convergence and Weak Topology
◦ Hilbert Spaces and the Riesz Representation Theorem
◦ Spectral Theory for Compact and Self-Adjoint Operators

Partial Differential Equations
◦ Scalar first order equations
◦ Elementary PDEs: heat equation, wave equation, Laplace equation
◦ Sobolev spaces
◦ Strong and weak solutions
◦ Elliptic problems via Lax–Milgram theory
◦ Additional topics like distributions, Galerkin schemes, monotone operators, semilinear equations, etc.

Mathematical Modelling with PDEs
◦ General principles of continuum mechanics and thermodynamics
◦ Symmetries and conservation laws
◦ Variational principles
◦ Derivation and discussion of models from hydrodynamics, solid mechanics, thermoelasticity, geodynamics, climate research or quantum mechanics

 

Spectrum of Advanced Courses
Regularly offered advanced courses include Nonlinear Functional Analysis, Evolution Equations, Calculus of Variations, Nonlinear Partial Differential Equations, Nonlinear Dynamical Systems, and Bifurcation Theory, and Rough paths and Regularity Structures. More specialized courses on current topics complement these choices.