Winter term 2023/2024

Broadening Courses

• Differential Geometry I (T)[Spec]
• Commutative Algebra (T)[Spec]
• Algebraic Geometry (T)[Spec]
• Introduction to Functional Analysis (T)
• General Relativity and the Analysis of Black Hole Spacetimes (T)[Spec]
• Homotopy Theory I (T)[Spec]
• Topology I (T)
• Geometric Analysis (T)[Spec]
• Geometric group theory - Hyperbolic groups and small cancellation (Logic III) (T)[Spec]
• Logic 3: Abstract Topological Dynamics and Descriptive Set Theory (T)[Spec]
• Logic II - Introduction to set theory (T)
• Masterlecture: Mathematical Modeling and Analysis (A)[Spec]
• Masterlecture: Partial Differential Equations of Mathematical Physics (A)[Spec]
• Mathematical Finance (A)
• Mathematical Statistics (A)
• Probability Theory II (A)[Spec]
• Stochastic Geometry and Random Graphs (A)[Spec]
• Stochastic Analysis (A)[Spec]
• Statistical Learning Theory (A)[Spec]
• Calculus of Variations (A)[Spec]
• Inverse Problems (A)[Spec]
• Scientific Computing (A)[Spec]
• Numerics for partial differential equations (A)
• Regularity theory for elliptic partial differential equations (A)[Spec]
• Partial Differential Equations (AT)

Ma-S1 Differential Geometry

Lecture 1

• Harmonic Maps 2
• Differential Geometry II
• Global Analysis II

Lecture 2 or Seminar

• Graphs and Manifolds (S)

Tutorial

• Tutorial Harmonic Maps 2
• Tutorial Differential Geometry II
• Tutorial Global Analysis II

Ma-S2 Geometric Structures

Lecture 1

• Harmonic Maps 2
• Differential Geometry I
• General Relativity and the Analysis of Black Hole Spacetimes
• Differential Geometry II
• Geometric Analysis
• Global Analysis II
• Geometric group theory - Hyperbolic groups and small cancellation (Logic III)

Lecture 2 or Seminar

• Tea seminar (S)
• Research Seminar on Geometric Analysis (S)
• Cobordism Theory (S)
• Graphs and Manifolds (S)
• Reading Course: Morse Theory in Low Dimensions (S)
• Reading Seminar in Global Analysis (S)

Tutorial

• Tutorial Harmonic Maps 2
• Tutorial Differential Geometry I
• Tutorial "General Relativity and the Analysis of Black Hole Spacetimes"
• Tutorial Differential Geometry II
• Tutorial Geometric Analysis
• Tutorial Global Analysis II
• Tutorial "Geometric group theory"

Ma-S3 Operator Algebras and Noncommutative Geometry

Lecture Operator Algebras

• Operator Algebras

Lecture 2 or Seminar

• Topics in analytic group theory

Tutorial Operator Algebras

• Tutorial Operator Algebras

Ma-S4 Topology

Lecture 1

• Homotopy Theory I

Lecture 2 or Seminar

• Graphs and Manifolds (S)
• Seminar on Lie Groups (S)

Tutorial

• Tutorial THomotopy Theory I

Ma-S5 Group Theory and Representation Theory

Lecture 1

• Commutative Algebra
• Algebraic Geometry
• Geometric group theory - Hyperbolic groups and small cancellation (Logic III)

Lecture 2 or Seminar

• Elliptic Curves (S)
• Adic Spaces (S)

Tutorial

• Tutorial Commutative Algebra
• Tutorial Algebraic Geometry
• Tutorial "Geometric group theory"

Ma-S6 Applied Analysis

Lecture 1

• Masterlecture: Mathematical Modeling and Analysis
• Calculus of Variations

Lecture 2 or Seminar or Student Project

• Masterlecture: Partial Differential Equations of Mathematical Physics
• Regularity theory for elliptic partial differential equations
• Master Seminar: Current Research in PDE and Applications (S)
• Partial Differential Equations in Fluid Dynamics (S)
• Partial Differential Equations in Fluid Dynamics (S)
• Partial Differential Equations in Fluid Dynamics (S)
• MSc Seminar on Mathematical Image Processing and Inverse Problems (S)
• Non-linear modelling in the natural sciences (P)

Tutorial

• Tutorial Mathematical Modeling and Analysis
• Tutorial Calculus of Variations

Ma-S7 Numerics and Scientific Computing

Lecture 1

• Inverse Problems
• Scientific Computing

Lecture 2 or Seminar or Student Project

• Model Order Reduction
• MSc Seminar Scientific Computing (S)
• Master Seminar Advanced Numerical Methods and Applications (S)
• MSc Seminar on Mathematical Image Processing and Inverse Problems (S)
• Non-linear modelling in the natural sciences (P)

Tutorial

• Tutorial Inverse Problems
• Scientific Computing

Ma-S8 Probability and its Applications

Lecture 1

• Probability Theory II
• Stochastic Geometry and Random Graphs
• Stochastic Analysis
• Statistical Learning Theory

Lecture 2

Tutorial

• Tutorial to Probability Theory II
• Tutorial to Stochastic Geometry and Random Graphs
• Tutorial Stochastic Analysis
• Tutorial to Statistical Learning Theory

Ma-S9 Stochastic Processes

Lecture 1

• Probability Theory II
• Stochastic Geometry and Random Graphs
• Stochastic Analysis
• Statistical Learning Theory

Lecture 2

Tutorial

• Tutorial to Probability Theory II
• Tutorial to Stochastic Geometry and Random Graphs
• Tutorial Stochastic Analysis
• Tutorial to Statistical Learning Theory

Ma-S10 Logic

Lecture Mathematical Logic III

• Geometric group theory - Hyperbolic groups and small cancellation (Logic III)
• Logic 3: Abstract Topological Dynamics and Descriptive Set Theory

Lecture Mathematical Logic IV

Tutorial Mathematical Logic III

• Tutorial "Geometric group theory"
• Tutorial Model Theory of Valued Fields

Ma-S11 Number Theory and Arithmetic Geometry

Lecture 1

• Commutative Algebra
• Algebraic Geometry
• Geometric group theory - Hyperbolic groups and small cancellation (Logic III)

Lecture 2 or Seminar

• Elliptic Curves (S)
• Adic Spaces (S)

Tutorial

• Tutorial Commutative Algebra
• Tutorial Algebraic Geometry
• Tutorial "Geometric group theory"

Summer term 2023

Broadening Courses

• Model Theory of Valued Fields (T)[Spec]
• Topology II (T)[Spec]
• Lie Groups (T)
• Topics in Global Analysis (T)[Spec]
• Harmonic maps (T)[Spec]
• Selected Topics in Differential Geometry (T)[Spec]
• Operator Algebras II (T)[Spec]
• Linear Algebraic Groups (T)[Spec]
• Rough Path Theory (A)[Spec]
• Probability Theory (A)
• Advanced Financial Mathematics (A)[Spec]
• Applied Stochastic Models (A)[Spec]
• Optimal Transport (A)[Spec]
• Masterlecture: Harmonic Analysis (A)[Spec]
• Partial Differential Equations II (A)[Spec]
• Masterlecture: Kinetic Transport Theory for dilute gases (A)[Spec]

Ma-S1 Differential Geometry

Lecture 1

• Harmonic maps
• Selected Topics in Differential Geometry

Lecture 2 or Seminar

• Differential Geometry III

Tutorial

• Tutorial: Harmonic Maps
• Tutorial: Selected Topics in Differential Geometry

Ma-S2 Geometric Structures

Lecture 1

• Topics in Global Analysis

Lecture 2 or Seminar

• Geometric Wave Equations in General Relativity

Tutorial

• Tutorial Topics in Global Analysis

Ma-S3 Operator Algebras and Noncommutative Geometry

Lecture Operator Algebras

Lecture 2 or Seminar

• Operator Algebras II
• Seminar Spectral Theory (S)
• Tensor products and Kirchberg conjectures (S)

Tutorial Operator Algebras

Ma-S4 Topology

Lecture 1

• Topology II

Lecture 2 or Seminar

• Topology IV: Operads, Configurations and Trees

Tutorial

• Tutorial Topology II

Ma-S5 Group Theory and Representation Theory

Lecture 1

• Linear Algebraic Groups
• Smooth representations of p-adic groups

Lecture 2 or Seminar

• Homological algebra and Frobenius techniques (S)

Tutorial

• Tutorial Linear Algebraic Groups
• Tutorial Smooth representations of p-adic groups

Ma-S6 Applied Analysis

Lecture 1

• Rough Path Theory
• Masterlecture: Harmonic Analysis
• Variational Modelling in Materials Science
• Partial Differential Equations II
• Masterlecture: Kinetic Transport Theory for dilute gases

Lecture 2 or Seminar or Student Project

• Masterseminar: Direct Methods in the Calculus of Variations (S)
• Topics in Mathematical Fluid Dynamics (S)
• MSc Seminar on Mathematical Image Processing and Inverse Problems (S)
• Masterseminar: Topics in the dynamic of complex systems (S)
• Master Seminar: Partial Differential Equations: Theory and Mathematical Modelling (S)
• Master Seminar Analysis Renormalization Group (S)
• Non-linear modelling in the natural sciences (P)

Tutorial

• Tutorial Rough Path Theory
• Tutorial Harmonic Analysis
• Tutorial Variational Modelling in Materials Science
• Tutorial Partial Differential Equations II
• Tutorial Introduction to Mathematical Fluid Dynamics

Ma-S7 Numerics and Scientific Computing

Lecture 1

• New mathematical methods in bioelectromagnetism and their neuroscientific applications
• Numerical Optimization
• Numerical Methods for Partial Differential Equations II

Lecture 2 or Seminar or Student Project

• Bsc/Msc Seminar: High-Performance PDE Solvers (S)
• Seminar Mathematics for Artificial Neural Networks and Related Topics (S)
• Master Seminar Advanced Numerical Methods and Applications (S)
• MSc Seminar on Mathematical Image Processing and Inverse Problems (S)
• MSc Seminar Scientific Computing (S)
• Non-linear modelling in the natural sciences (P)

Tutorial

• New mathematical methods in bioelectromagnetism and their neuroscientific applications
• Tutorial Numerical Optimization
• Tutorial Numerical Analysis of Partial Differential Equations II

Ma-S8 Probability and its Applications

Lecture 1

• Rough Path Theory
• Advanced Financial Mathematics
• Applied Stochastic Models
• Optimal Transport

Lecture 2

Tutorial

• Tutorial Rough Path Theory
• Tutorial Advanced Financial Mathematics
• Tutorial to Applied Stochastic Models
• Tutorial to Optimal Transport

Ma-S9 Stochastic Processes

Lecture 1

• Rough Path Theory
• Advanced Financial Mathematics
• Applied Stochastic Models
• Optimal Transport

Lecture 2

Tutorial

• Tutorial Rough Path Theory
• Tutorial Advanced Financial Mathematics
• Tutorial to Applied Stochastic Models
• Tutorial to Optimal Transport

Ma-S10 Logic

Lecture Mathematical Logic III

• Model Theory of Valued Fields

Lecture Mathematical Logic IV

• Logic IV: Selected Topics from Set Theory

Tutorial Mathematical Logic III

• Tutorial Model Theory of Valued Fields

Ma-S11 Number Theory and Arithmetic Geometry

Lecture 1

• Linear Algebraic Groups
• Smooth representations of p-adic groups

Lecture 2 or Seminar

• Homological algebra and Frobenius techniques (S)

Tutorial

• Tutorial Linear Algebraic Groups
• Tutorial Smooth representations of p-adic groups

Winter term 2022/2023

Broadening Courses

• Logic II - Introduction to set theory (T)
• Logic III - Introduction to model theory (T)[Spec]
• Geometric group theory (T)[Spec]
• Non-Linear Wave equations (T)[Spec]
• Topology I (T)
• Topology III (T)[Spec]
• Algebraic Geometry III (T)[Spec]
• Differential Geometry I (T)
• Global Analysis (T)
• Operator Algebras (T)[Spec]
• Introduction to Functional Analysis (T)
• Commutative Algebra (T)[Spec]
• Mathematical Statistics (A)
• Mathematical Finance (A)
• Probability Theory II (A)
• Advanced Probability Theory (A)[Spec]
• Point Processes (A)[Spec]
• Random Recursive Equations (A)[Spec]
• Numerics for partial differential equations (A)
• Calculus of Variations (A)[Spec]
• Shape spaces - theory and numerics (A)[Spec]
• Scientific Computing (A)[Spec]
• Masterlecture: Introduction to Mathematical Fluid Dynamics (A)[Spec]
• Inverse Problems (A)[Spec]
• Partial Differential Equations (AT)

Ma-S1 Differential Geometry

Lecture 1

• Non-Linear Wave equations
• Differential Geometry II

Lecture 2 or Seminar

• Minimal surfaces
• Graphs and Manifolds (S)

Tutorial

• Tutorial Non-Linear Wave equations
• Tutorial Differential Geometry II

Ma-S2 Geometric Structures

Lecture 1

• Geometric group theory
• Non-Linear Wave equations
• Topology III
• Differential Geometry II

Lecture 2 or Seminar

• Minimal surfaces
• Translation surfaces and Teichmüller dynamics (S)
• Graphs and Manifolds (S)
• Seminar: Topics in Geometric Group Theory (S)

Tutorial

• Tutorial "Geometric group theory"
• Tutorial Non-Linear Wave equations
• Tutorial Topology III
• Tutorial Differential Geometry II

Ma-S3 Operator Algebras and Noncommutative Geometry

Lecture Operator Algebras

• Non-Linear Wave equations
• Operator Algebras

Lecture 2 or Seminar

• Master Seminar: Partial Differential Equations: Theory and Mathematical Modelling (S)

Tutorial Operator Algebras

• Tutorial Non-Linear Wave equations
• Tutorial Operator Algebras

Ma-S4 Topology

Lecture 1

• Topology III

Lecture 2 or Seminar

• Geometric group theory
• Translation surfaces and Teichmüller dynamics (S)
• Graphs and Manifolds (S)
• Seminar: Topics in Geometric Group Theory (S)

Tutorial

• Tutorial Topology III

Ma-S5 Group Theory and Representation Theory

Lecture 1

• Geometric group theory
• Algebraic Geometry III
• Commutative Algebra

Lecture 2 or Seminar

• Etale Cohomology (S)
• Seminar: Topics in Geometric Group Theory (S)

Tutorial

• Tutorial "Geometric group theory"
• Exercise for the lecture "Algebraic Geometry III"
• Exercise for the lecture "Commutative Algebra"

Ma-S6 Applied Analysis

Lecture 1

• Non-Linear Wave equations
• Calculus of Variations
• Shape spaces - theory and numerics
• Masterlecture: Introduction to Mathematical Fluid Dynamics
• Inverse Problems

Lecture 2 or Seminar or Student Project

• Master Seminar: Partial Differential Equations: Theory and Mathematical Modelling (S)
• Master Seminar: Partial Differential Equations: Theory and Mathematical Modelling (S)
• Master Seminar Mathematical modelling and analysis of rarefied gases (S)
• Master Seminar Mathematical Optimization: Shapes & Shape Spaces (S)
• Partial Differential Equations in Fluid Dynamics (S)
• MSc Seminar on Mathematical Image Processing and Inverse Problems (S)
• Non-linear modelling in the natural sciences (P)

Tutorial

• Tutorial Non-Linear Wave equations
• Tutorial Calculus of Variations
• Tutorial: Shape spaces - theory and numerics
• Tutorial Introduction to Mathematical Fluid Dynamics
• Tutorial Inverse Problems

Ma-S7 Numerics and Scientific Computing

Lecture 1

• Shape spaces - theory and numerics
• Scientific Computing
• Inverse Problems

Lecture 2 or Seminar or Student Project

• Master Seminar Mathematical Optimization: Shapes & Shape Spaces (S)
• MSc Seminar Scientific Computing (S)
• MSc Seminar on Mathematical Image Processing and Inverse Problems (S)
• Master Seminar Advanced Numerical Methods and Applications (S)
• Seminar Mathematics for Deep Neuronal Networks (S)
• Non-linear modelling in the natural sciences (P)

Tutorial

• Tutorial: Shape spaces - theory and numerics
• Scientific Computing
• Tutorial Inverse Problems

Ma-S8 Probability and its Applications

Lecture 1

• Stochastic Analysis
• Advanced Probability Theory
• Point Processes
• Random Recursive Equations

Lecture 2

Tutorial

• Tutorial Stochastic Analysis
• Tutorial to Advanced Probability Theory
• Tutorial to Point Processes
• Tutorial to Random Recursive Equations

Ma-S9 Stochastic Processes

Lecture 1

• Stochastic Analysis
• Advanced Probability Theory
• Point Processes
• Random Recursive Equations

Lecture 2

Tutorial

• Tutorial Stochastic Analysis
• Tutorial to Advanced Probability Theory
• Tutorial to Point Processes
• Tutorial to Random Recursive Equations

Ma-S10 Logic

Lecture Mathematical Logic III

• Logic III - Introduction to model theory
• Geometric group theory

Lecture Mathematical Logic IV

Tutorial Mathematical Logic III

• Tutorial Logic II
• Tutorial "Geometric group theory"

Ma-S11 Number Theory and Arithmetic Geometry

Lecture 1

• Algebraic Geometry III
• Commutative Algebra

Lecture 2 or Seminar

• Seminar on Algebra and Model Theory: Galois-characterization of p-adic numbers (S)
• Etale Cohomology (S)

Tutorial

• Exercise for the lecture "Algebraic Geometry III"
• Exercise for the lecture "Commutative Algebra"