Algebra and Geometry

Alan Huckleberry
Complex manifolds Special algebraic varieties Geometry and physics
Ivan Penkov		Dynkin diagrams of simple Lie algebras (excerpt)
Representations of finite- and infinite-dimensional Lie algebras Generalized Harish-Chandra modules: algebraic and geometric constructions Structure and representation theory for locally finite Lie algebras and Lie superalgebras Generalized flag realizations of homogeneous ind-varieties Vector bundles of finite rank on homogeneous ind-varieties

Applied Analysis

Marcel Oliver		Simulation of shallow water flow
Partial differential equations: mathematical fluid dynamics geophysical fluid dynamics reaction-diffusion equations Numerical Analysis: structure-preserving algorithms
Tobias Preusser		PDE-based flow visualization
Partial Differential Equations modeling and simulation of biomedical processes mathematical image processing stochastic PDEs for modeling of uncertain parameters scientific visualization with PDEs Numerical Analysis viscosity solutions for geometric PDEs Numerical Methods efficient numerical implementation for image-based-computing multiscale and multigrid approaches

Dynamical Systems and Ergodic Theory

Keivan Mallahi-Karai		The free product of F3 and F6
Infinite groups and their geometric properties Kazhdan's Property (T) Discrete subgroups of Lie groups Dynamics of the Lie group actions and application to number theory Probability Financial Mathematics
Igors Gorbovickis		Critical points of the multiplier maps equidistribute on the boundary of the Mandelbrot set
Dynamical systems Holomorphic dynamics in one and several variables Renormalization in low-dimensional dynamics Thermodynamical formalism in holomorphic dynamics The Mandelbrot set Discrete geometry Kneser-Poulsen conjecture

Mathematical Physics

Sören Petrat		Bose-Einstein condensate
Quantum many-body systems Non-linear Schrödinger equation Derivation of effective dynamics Dynamics of Bose-Einstein condensates Hartree-Fock dynamics Spin wave theory Dynamics in the Heisenberg ferromagnet Relativistic quantum mechanics Wave functions on space-time configurations (multi-time wave functions)
Peter Schupp		Pyrochlor lattice
Mathematical Physics Theoretical Particle Physics Non-commutative Geometry Quantum Gravity Quantum Spin Systems

Mathematics and its Applications

Marc-Thorsten Hütt, Professor of Computational Systems Biology

• Teaching: Nonlinear Dynamics, Computational Systems Biology
• Research: Biological networks, genome signatures, analysis of spatiotemporal patterns

Ulrich Kleinekathöfer, Professor of Physics

• Teaching: Computational Physics
• Research: Computational physics and biophysics, in particular wave function calculations for nonlinear spectroscopy, density matrix theory for electron and exciton transfer, large-scale classical molecular dynamics

Agostino Merico, Professor of Ecology

• Research: Population dynamics, marine ecology, marine geochemistry; paleoclimate; modeling of interactions between climate, ecology, and social and economic systems

Joachim Vogt, Professor of Physics

• Teaching related to ACM: ESS Computational Modeling, ESS Data Analysis Techniques
• Research: Space physics, computational magnetohydrodynamics, analysis of data from magnetospheric satellite missions

Peter Zaspel, Professor of Computer Science

• Research: Machine learning, data assimilation, uncertainty quantification, approximation in reproducing kernel Hilbert spaces, low-rank approximation, parallel and scalable algorithms