**1. Differential geometry, global analysis, and mathematical physics**Title: Differential geometry III: fluid mechanics

Lecturer: Pinkall, TU

Type: Lecture (4h)

See also here.

Title: Ennumerative theory of complex curves

Lecturer: Guéré, HU

Type: Seminar (2h)

Title: Symplectic geometry

Lecturer: Mohnke, HU

Type: Seminar (2h)

See also here.

Title: Dyson Schwinger equations and quantization of gauge theories

Lecturer: Kreimer, HU

Type: Lecture (see here)

See also here.

Title: Differentialgeometry – gauge theory and Dirac operators

Lecturer: Baum, HU

Type: Lecture (4h)

See also here.

Title: Differentialgeometry

Lecturer: Baum, HU

Type: Seminar (2h)

See also here.

Title: Mathematical physics II

Lecturer: Suris, TU

Type: Lecture (4h) + tutorials (2h)

**2. Algebraic and arithmetic geometry, number theory**Title: Representation theory

Lecturer: Bürgisser, TU

Type: Lecture (2h)

See also here.

Title: Algebra

Lecturer: Bürgisser, TU

Type: Seminar (2h)

See also here.

Title: Linear algebraic groups

Lecturer: Große-Klönne, HU

Type: Lecture (4h)

See also here.

Title: Perfectoid fields

Lecturer: Große-Klönne, HU

Type: Seminar (2h)

See also here.

Title: Quotients and invariants in algebraic geometry

Lecturer: Farkas, HU

Type: Seminar (2h)

Title: Tensor categories and representation theory

Lecturer: Krämer (substitute professor), HU

Type: Seminar (2h)

See also here.

Title: Number theory II

Lecturer: Esnault, FU

Type: Lecture (4h) + tutorials (2h)

Title: p-adic Hodge theory

Lecturer: Esnault, FU

Type: Lecture (4h) + tutorials (2h)

See also here.

Title: Models of curves and abelian varieties

Lecturer: Pepin Lehalleur, FU

Type: Lecture (2h)

See also here.

Title: Galois theory

Lecturer: Kindler, FU

Type: Seminar (2h)

See also here.

**3. Probability, statistics, and financial mathematics**

Title: Stochastic processes in neuroscience I

Lecturer: Stannat, TU

Type: Lecture (2h) + tutorials (2h)

Title: Stochastic processes in neuroscience

Lecturer: Stannat, TU

Type: Seminar (2h)

Title: Extreme value theory and point processes

Lecturer: Soares dos Santos, TU

Type: Lecture (2h)

Title: Multivariate statistics

Lecturer: Bodnar, HU

Type: Lecture (4h)

Title: Stochastic financial mathematics

Lecturer: Horst, HU

Type: Lecture (4h)

Title: Infinite dimensional stochastic calculus

Lecturer: Horst, HU

Type: Seminar (2h)

Title: Fourier analysis and stochastic integration

Lecturer: Imkeller, HU

Type: Lecture (4h)

Title: Stochastic optimization

Lecturer: Henrion, HU

Type: Lecture (4h)

Title: Nonparametric statistics

Lecturer: Altmeyer / Wahl, HU

Type: Lecture (4h)

Title: Ergodic theory and transfer operators

Lecturer: Koltai, FU

Type: Lecture (2h)

**4. Discrete mathematics and combinatorial optimization**

Title: Discrete optimization

Lecturer: Skutella, TU

Type: Lecture (4h) + tutorials (2h)

See also here.

Title: Geometrical representation

Lecturer: Felsner, TU

Type: Seminar (2h)

Title: Designs and codes

Lecturer: Das, FU

Type: Lecture (2h) + tutorials (2h)

See also here.

Title: Optimization

Lecturer: Borndörfer, FU

Type: Lecture (4h)

**5. Geometry, topology and visualisation**

Title: Convex geometry II

Lecturer: Henk, TU

Type: Lecture (4h) + tutorials (2h)

Title: Discrete and convex geometry

Lecturer: Henk, TU

Type: Seminar (2h)

Title: Discrete geometry II

Lecturer: Henk, TU

Type: Lecture (4h) + tutorials (2h)

Title: Computational topology

Lecturer: Lutz, TU

Type: Lecture (4h) + tutorials (2h)

Title: Discrete geometry

Lecturer: Joswig, TU

Type: Seminar (2h)

Title: Topologie III: Introduction to homotopy theory

Lecturer: Vogt, FU

Type: Lecture (2h)

Title: Categories and homotopy theory

Lecturer: Egas Santander, FU

Type: Lecture (2h)

It is strongly advised that students that take this course should also take Topology III.

Title: Hyperplanes, matroids & broken circuits

Lecturer: Haase, FU

Type: Seminar (2h)

See also here.

Title: Discrete geometry II

Lecturer: Blagojevic, FU

Type: Lecture (4h) + tutorials (2h)

Title: Topological data analysis

Lecturer: Kelly, FU

Type: Seminar (2h)

Title: Infinity categories

Lecturer: Kelly, FU

Type: Seminar (2h)

**6. Numerical analysis and scientific computing**

Title: Numerical methods for PDEs II

Lecturer: Schneider, TU

Type: Lecture (4h)

Title: Multilevel methods for solving linear systems of equations

Lecturer: Nabben, TU

Type: Lecture (2h)

Title: Numerical methods

Lecturer: Nabben, TU

Type: Seminar (2h)

Title: Control theory

Lecturer: Altmann, TU

Type: Lecture (4h)

See also here.

Title: Numerical linear algebra II

Lecturer: Liesen, TU

Type: Lecture (2h) + tutorials (2h)

Title: Theory and methods of nonsmooth optimization

Lecturer: Hintermüller, HU

Type: Lecture (4h)

See also here.

Title: Computational partial differential equations II

Lecturer: Carstensen, HU

Type: Lecture (4h)

Title: Numerics of differential algebraic equations

Lecturer: Tischendorf, HU

Type: Lecture (4h)

Title: Complex dynamic in fluids

Lecturer: Höfling, FU

Type: Lecture (2h)

Title: Theory of electronic excitation

Lecturer: Klein, FU

Type: Lecture (2h)

Title: Mathematical modelling in climate science

Lecturer: Vercauteren, FU

Type: Lecture (2h) + tutorials (2h)

Title: Mathematical aspects in machine learning

Lecturer: Schütte, FU

Type: Lecture (2h)

Title: Mathematical of machine learning: from linear models to neural networks

Lecturer: Gurevich, FU

Type: Seminar (2h)

See also here.

**7. Applied analysis and differential equations**Title: Differential equations with time delay

Lecturer: Yanchuk, TU

Type: Lecture (2h)

See also here.

Title: Nonlinear dynamics and their applications II

Lecturer: Yanchuk, TU

Type: Lecture (2h)

Title: Functional analysis III

Lecturer: Kutyniok, TU

Type: Lecture (4h) + tutorials (2h)

Title: Functional analysis and data science

Lecturer: Kutyniok, TU

Type: Seminar (2h)

Title: Functional analytical methods in classical physics II

Lecturer: Stephan, HU

Type: Lecture (2h)

See also here.

Title: Uncertainty quantification: High dimensional probability with applications to data science

Lecturer: Sullivan, FU

Type: Seminar (2h)

See also here.

The BMS Advanced Courses take place at all three universities which do their best to coordinate the schedules according to the scheme below.