# Research Teams

## Fields of Research

## Algebraic Geometry and Number Theory

Essen Seminar for Algebraic Geometry and Arithmetic

**Algebraic Geometry, Prof. Dr. Georg Hein**

Derived categories, moduli spaces of vector bundles, generalized theta divisors.

**Algebraic Geometry, Prof. Dr. Jochen Heinloth**

Algebraic stacks, moduli of bundles, geometric Langlands program. [Research team]

**Algebraic Geometry and ****Algebraic Topology, Prof. Dr. Marc Levine**

Algebraic \(K\)-theory, algebraic geometry, motivic homotopy theory. [Research team]

**Algebraic and Complex Geometry, Prof. Dr. Daniel Greb **

Birational Geometry, Geometric Invariant Theory, Moduli spaces of vector bundles, Kähler Geometry, Hamiltonian group actions and momentum maps. [Research team]

**Arithmetic Geometry, Prof. Dr. Massimo Bertolini****, Prof. Dr. Wolfgang Lempken **

Group theory, representation theory of finite groups, especially: Theory of finite simple groups, character theory of finite groups, permutation codes.

Arithmetic geometry and number theory, especially: Elliptic curves, modular forms, \(L\)-functions, rational points, algebraic cycles. [Research team]

**Arithmetic Geometry, Prof. Dr. Jan Kohlhaase**

Representation theory of \(p\)-adic Lie groups, Galois groups of local fields, moduli spaces of formal groups. [Research team]

**Arithmetic Geometry, Prof. Dr. Vytautas Paškūnas**

Representation theoretic methods in number theory, \(p\)-adic Langlands program. [Research team]

**Number Theory and Arithmetic Geometry, in particular explicit and algorithmic methods****, Prof. Dr. Ulrich Görtz, ****Prof. Dr. Dr. h.c. Gerhard Frey (i.R.)**

Modular forms, automorphic representations and Galois representations - Langlands program - Elliptic curves, modular curves, Shimura varieties - Representations of absolute Galois groups of number fields - Linear algebraic groups and their combinatorics - Applications in coding theory and cryptography. [Research team]

**Number theory and Arithmetic Geometry****, Prof. Dr. Johannes Sprang**

Special values of \(L\)-functions, Eisenstein classes, irrationality of zeta values, \(p\)-adic cohomology theories. [Research team]

## Analysis

**Applied Functional Analysis, Analysis of Partial Differential Equations, Prof. Dr. Petra Wittbold **

Nonlinear evolution equations, nonlinear semigroups, monotone/accretive operators, \(L^1\)-theory, Lebesgue spaces with variable exponents and generalized Orlicz spaces, scalar conservation laws, nonlinear PDEs of mixed type (in particular, elliptic-parabolic equations), integro-partial differential equations (in particular, with fractional derivative in time), nonlinear nonlocal diffusion equations, stochastic nonlinear PDEs, numerical approximation methods (in particular, finite volume methods) for nonlinear PDEs.** **[Research team]

**Geometric Analysis, Prof. Dr. Andreas Gastel**

Differential equations and variational problems of Geometric Analysis: existence, regularity, symmetry, nonuniqueness. [Research team]

**Nonlinear Analysis and Modeling**, **Prof. Dr. Patrizio Neff**, **Prof. Dr. Mircea Birsan**

Analysis and numerics of nonlinear PDE systems, elliptic regularity, calculus of variations, modeling in continuum mechanics, elasticity and plasticity theory, microstructures, shells and plates, membranes. [Research team]

**Nonlinear partial differential equations, Prof. Dr. Georg Weiß**

Free boundary problems, free surface flow, singular limits, calculus of variations, regularity questions. [Research team]

**Partial Differential Equations and Calculus of Variations, Prof. Dr. Christoph Scheven**

Geometric variational problems, geometric flows, degenerate and singular parabolic equations and systems, obstacle problems. [Research team]

## Didactics of Mathematics

**Prof. Dr. Bärbel Barzel**

[Research team]

**Prof. Dr. Andreas Büchter**

Active hands-on learning in mathematics instruction for understanding and development of mathematical concepts - Mathematics learning and language skills - Spatial abilities and mathematics achievement - Student’s perceptions about mathematical concepts - Curriculum research and development - Mathematics during the initial phase of different courses of studies. [Research team]

**Prof. Dr. Lisa Hefendehl-Hebeker ****(i.R.)**

**Prof. Dr. Florian Schacht**

Concept formation in mathematics - Digital technologies - Mathematics and language - Epistemological questions and theories in mathematics education - Inferentialism in mathematics education. [Research team]

**Prof. Dr. Petra Scherer**

Research in education and learning processes. [Research team]

## Numerical Mathematics

**Applied Mathematics and Numerical Analysis, Prof. Paola Pozzi, PhD**

Numerical analysis, finite elements methods, geometrical partial differential equations. [Research team]

**Numerical Methods for Partial Differential Equations, Prof. Dr. Johannes Kraus**

Numerical Solution of Partial Differential Equations, Finite Element Methods,Numerical Linear Algebra, Multigrid and Algebraic Multilevel Methods, Block Factorization Preconditioners. [Research team]

**Numerical Mathematics, Prof. Dr. Gerhard Starke**

Mixed Finite Elements, Numerical Solid and Fluid Mechanics. [Research team]

**Numerical Mathematics, Prof. Dr. Irwin Yousept**

Numerical Analysis, Numerical Methods in Electromagnetism, FEM, a priori and a posteriori error analysis. [Research team]

**Numerical Mathematics and Numeric Simulation**, **Prof. Dr. Axel Klawonn**

University of Cologne (co-opted member). [Research team]

## Optimization

**Infinite-dimensional Optimization, ****Prof. Dr. Antoine Laurain**

Shape and topology optimization, Free boundary problems, PDE-constrained optimization, Inverse problems, Asymptotic analysis, Level set methods, Numerical analysis.

**Nonlinear Optimization, Prof. Dr. Arnd Rösch**

Numerical Methods for Nonlinear Optimization Problems Governed by Partial Differential Equations - Optimality Conditions - Discretization and Regularization Concepts. [Research team]

**Optimization and Algorithmic Discrete Mathematics, Prof. Dr. Rüdiger Schultz**

Stochastic integer programming - two-stage stochastic programming and risk minimization - multi-stage stochastic programming - stochastic shape optimization - test sets for integer programming and computer-algebraic methods - optimization in energy networks under uncertainty - on-line optimization in procedural facilities for more than one output. [Research team]

## Stochastics

**Applied Stochastics, Prof. Dr. Denis Belomestny, Prof. Dr. Volker Krätschmer,**** ****Prof. Dr. Mikhail Urusov**

Mathematical Statistics, Stochastic Algorithms, Financial and Insurance Mathematics, Quantitative Risk Management. [Research team]

**Probability Theory**, Prof. Dr. Anita Winter

Stochastic Analysis, Mathematical Biology, Metric Geometry, Measure-valued Diffusion, Interacting Particle Systems. [Research team]

**Stochastic Analysis, Prof. Martin Hutzenthaler**

*Stochastic Analysis:* Regularity of stochastic (partial) differential equations, Numerical approximations of stochastic (partial) differential equations, Numerical approximations of stochastic backward differential equations, Malliavin Calculus and Stein's method. *Mathematical Biology:* Effect of fluctating selection, Models with persisting altruism. [Research team]

## Professors emeritae and emeriti

**Algebra, Combinatorics and Cryptology, Prof. Dr. Trung van Tran**

**Differential Equations and Differential Geometry, Prof. Dr. Ulrich Dierkes, Prof. Dr. Gerhard Freiling, Prof. Dr. Wolfgang Schreiber**

Partial differential equations - Calculus of variations - Differential geometry - Ordinary differential equations.

**Didactics of Mathematics, ****Prof. Dr. Hans Niels Jahnke**

Genesis of argumention and proof – History of mathematics – History of mathematics in education.

**Didactics of Mathematics, ****Prof. Dr. Heinz Steinbring**

Basic research in mathematics education – Epistemological analysis of mathematical interaction processes – Development and research of mathematical teaching and learning processes in cooperation with school praxis.

**Discrete Mathematics and Algebra, Prof. Dr. Günter Törner**

**Engineering Mathematics, Prof. Dr. Wilhelm Heinrichs**

Spectral and pseudospectral methods - multilevel - Stokes and Navier-Stokes equations - splitting techniques for saddle point problems - stabilization techniques for convection-diffusion problems.

**Mathematical Informatics, Prof. Dr. h. c. Heiner Gonska**