These are the Advanced Courses for the summer semester 2019.

**1. Differential geometry, global analysis, and mathematical physics** Title: K3 surfaces

Lecturer: Klingler, HU

Type: Seminar (2h)

Title: Quantization of Gauge Theories

Lecturer: Kreimer, HU

Type: Lecture (3h) + tutorial (1h)

See also here.

Title: Symplectic geometry

Lecturer: Mohnke, HU

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

See also here.

Title: Differential geometry and mathematical physics

Lecturer: Bobenko, TU

Type: Seminar (2h)

See also here.

Title: Differential geometry III: Complex and quaternionic line bundles

Lecturer: Pinkall, TU

Type: Lecture (4h)

See also here.

Title: Visualization in mathematics

Lecturer: Pinkall, TU

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

See also here.

Title: Mathematical physics II

Lecturer: Suris, TU

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

Title: Group actions in geometry and quantum field theory

Lecturer: Paycha, UP

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

Title: Quantum communication and quantum networks (MATH+)

Lecturer: Eisert, FU

Type: Seminar (2h)

Please note the special format of this course.

**2. Algebraic and arithmetic geometry, number theory** Title: Research module: Algebra

Lecturer: Altmann, FU

Type: Seminar (2h)

Title: Research seminar: Algebra

Lecturer: Altmann, FU

Type: Research seminar (2h)

Please note that you cannot obtain credits from research seminars.

Title: Homological algebra

Lecturer: Kohrita, FU

Type: Lecture (2h) + tutorial (1h)

See also here.

Title: Linear algebraic group and finite groups of Lie type

Lecturer: Ersoy, FU

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

See also here.

Title: Number theory

Lecturer: Agostini, HU

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

Title: Algebra

Lecturer: Kummer, TU

Type: Seminar (2h)

See also here.

Title: Algebraic curves: enumerative, combinatorial and computational aspects

Lecturer: Farkas, HU

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

See also here.

Title: Algebra

Lecturer: Große-Klönne, HU

Type: Seminar (2h)

See also here.

Title: Adic spaces and perfectoid spaces

Lecturer: Klingler, HU

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

Title: D-modules

Lecturer: Krämer, HU

Type: Lecture (2h) + tutorial (1h)

See also here.

Title: Variations on Bezout's theorem

Lecturer: Bürgisser, TU

Type: Lecture (2h)

Title: Condition: Geometry of numerical algorithms

Lecturer: Bürgisser, TU

Type: Lecture (4h)

Title: Software seminar: Numerical nonlinear algebra

Lecturer: Bürgisser, TU

Type: Seminar (2h)

Title: Algebra III: Real algebra

Lecturer: Kummer, TU

Type: Lecture (2h) + tutorial (1h)

Title: Polyhedral methods in algebraic geometry

Lecturer: Haase, FU

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

See also here.

Title: Research seminar: Polytopes and algebraic geometry

Lecturer: Haase, FU

Type: Research seminar (2h)

See also here and here.

Please note that you cannot obtain credits from research seminars.

**3. Stochastics and mathematical finance** Title: Stochastic analysis and control theory

Lecturer: Becherer, HU

Type: Seminar (2h)

Title: Financial mathematics II

Lecturer: Bank, TU

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

Title: The filtering problem and portfolio optimization under partial information

Lecturer: Belak, TU

Type: Seminar (2h)

See also here.

Title: Stochastic models in neuroscience

Lecturer: Stannat, TU

Type: Seminar (2h)

Title: Stochastic partial differential equations

Lecturer: Scheutzow, TU

Type: Lecture (2h)

See also here.

Title: Stochastic control theory

Lecturer: Stannat, TU

Type: Lecture (2h)

Title: Measurement and integration theory

Lecturer: Friz, TU

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

Title: Stochastic financial mathematics II

Lecturer: Horst, HU

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

Title: Stochastic models in neuroscience

Lecturer: Schwalger, TU

Type: Seminar (2h)

Title: Stochastics

Lecturer: Kurt, TU

Type: Seminar (2h)

See also here.

Title: Stochastic differential equations

Lecturer: Gräser, HU

Type: Lecture (2h) + tutorial (1h)

Title: Topics in random walks

Lecturer: Orenshtein, TU

Type: Lecture (2h)

See also here.

Title: Models of biological neural networks

Lecturer: Schwalger, TU

Type: Lecture (2h)

**4. Discrete mathematics and optimization** Title: Finite geometry

Lecturer: Szabó, FU

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

See also here.

Title: Research seminar: Combinatorics

Lecturer: Szabó, FU

Type: Research seminar (2h)

See also here.

Please note that you cannot obtain credits from research seminars.

Title: Optimization in public transport

Lecturer: Borndörfer; Lindner, FU

Type: Seminar (2h)

Title: Graphs, algorithms and optimization

Lecturer: Mütze, TU

Type: Seminar (2h)

See also here.

Title: Algorithmic mixed-integer programming

Lecturer: Gleixner, FU

Type: Seminar (2h)

Title: Advanced topics in optimization

Lecturer: Hintermüller, HU

Type: Lecture (2h) + tutorial (1h)

See also here.

Title: Optimization

Lecturer: Kröner, HU

Type: Seminar (2h)

See also here.

Title: Selected topics in Quantitative methods/Network games and Mechanism design (MATH+)

Lecturer: Klimm, HU

Type: Seminar (2h)

Please note the special format of this course.

**5. Geometry, topology, and visualization**Title: Discrete geometry II

Lecturer: Blagojević, FU

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

Title: Research module: Topology

Lecturer: Reich, FU

Type: Seminar (2h)

Title: Discrete and computational topology

Lecturer: Lutz, TU

Type: Lecture (4h)

Title: Discrete geometry III

Lecturer: Paffenholz, TU

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

Title: Research seminar: Geometry and topology

Lecturer: Reich, FU

Type: Research seminar (2h)

Please note that you cannot obtain credits from research seminars.

Title: Real algebra and optimization

Lecturer: Sinn; Sjöberg, FU

Type: Seminar (2h)

See also here.

Title: Tropical geometry and optimization (MATH+)

Lecturer: Joswig, TU

Type: Seminar (2h)

Please note the special format of this course.

Title: Discrete and convex geometry

Lecturer: Henk, TU

Type: Seminar (2h)

See also here.

**6. Numerical analysis and scientific computing**Title: Seminar multiscale methods in molecular simulations

Lecturer: Delle Site, FU

Type: Seminar (2h)

Title: Deep learning

Lecturer: Noé, FU

Type: Lecture (2h) + tutorial (1h)

Title: Numerical mathematics

Lecturer: Nabben, TU

Type: Seminar (2h)

Title: Control theory

Lecturer: Mehrmann, TU

Type: Lecture (4h)

Title: Numerical linear algebra II

Lecturer: Nabben, TU

Type: Lecture (2h)

Title: Research seminar: Geophysical fluid dynamics

Lecturer: Vercauteren, FU

Type: Research seminar (2h)

Please note that you cannot obtain credits from research seminars.

Title: Mathematics of learning: From Hilbert’s 13th problem to fluctuating hydrodynamics

Lecturer: Kornhuber; Gräser, FU

Type: Seminar (2h)

Title: Inverse problems

Lecturer: Sullivan, FU

Type: Lecture (2h) + tutorial (1h)

See also here.

Title: Control theory deepening

Lecturer: Mehrmann, TU

Type: Lecture (2h)

Title: Numerical mathematics

Lecturer: Bertrand, HU

Type: Lecture (2h) + tutorial (1h)

Title: Numeric of partial differential equations II

Lecturer: Bertrand, HU

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

See also here.

Title: Variational calculation and optimal control

Lecturer: Zwicknagl, TU

Type: Lecture (4h)

Title: Mathematical aspects of quantization

Lecturer: Müller, HU

Type: Seminar (2h)

See also here.

**7. Applied analysis and differential equations**Title: Mathematical modeling in climate research

Lecturer: Vercauteren, FU

Type: Lecture (2h) + tutorial (1h)

Title: Quantum computational methods

Lecturer: Delle Site, FU

Type: Seminar (2h)

Title: Differential equations III - dynamical Systems III - delay Equations

Lecturer: Schneider, FU

Type: Lecture (2h) + tutorial (1h)

See also here.

Title: Oberseminar: Nonlinear dynamics

Lecturer: Schneider, FU

Type: Oberseminar (2h)

See also here.

Title: Research Projekt: Advanced differential equations

Lecturer: Schneider, FU

Type: Research Projekt (4h)

See also here.

Title: Applied analysis

Lecturer: Zwicknagl, TU

Type: Seminar (2h)

Title: Highdimensional PDEs

Lecturer: Schneider, TU

Type: Seminar (2h)

Title: Differential equations III

Lecturer: Lasarzik, TU

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

Title: Stochastic partial differential equations

Lecturer: Horst, HU

Type: Lecture (2h) + tutorial (1h)

Title: Optimization of partial differential equations

Lecturer: Kröner, HU

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

Title: Partial differential equations I

Lecturer: Ecker, FU

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

See also here.

Title: Seminar: Partial differential equations

Lecturer: Ecker, FU

Type: Seminar (2h)

See also here.

Title: The Navier-Stokes equations and applications toward data assimilation

Lecturer: Titi, FU

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

**8. Mathematics of data science**Title: Mathematics of machine learning: Reinforcement learning

Lecturer: Gurevich, FU

Type: Seminar (2h)

See also here.

Title: Statistics

Lecturer: Deuschel, TU

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

Title: Mathematical statistics

Lecturer: Spokoiny, HU

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

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

below.