



Research Areas in the Mathematical Sciences
Algebra



 Complex manifolds
 Special algebraic varieties
 Geometry and physics



Dynkin diagrams of simple Lie algebras
(excerpt) 
 Representations of finite and infinitedimensional Lie
algebras
 Generalized HarishChandra modules: algebraic and geometric
constructions
 Structure and representation theory for locally finite Lie
algebras and Lie superalgebras
 Generalized flag realizations of homogeneous indvarieties
 Vector bundles of finite rank on homogeneous indvarieties

Applied Analysis


Simulation of shallow water flow 
 Partial differential equations:
 mathematical fluid dynamics
 geophysical fluid dynamics
 reactiondiffusion equations
 Numerical Analysis:
 structurepreserving algorithms



PDEbased 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
imagebasedcomputing
 multiscale and multigrid approaches

Dynamical Systems and Ergodic Theory


The free product of F_{3} and
F_{6}

 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



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 lowdimensional dynamics
 Thermodynamical formalism in holomorphic dynamics
 The Mandelbrot set
 Discrete geometry
 KneserPoulsen conjecture

Mathematical Physics


BoseEinstein condensate

 Quantum manybody systems
 Nonlinear Schrödinger equation
 Derivation of effective dynamics
 Dynamics of BoseEinstein condensates
 HartreeFock dynamics
 Spin wave theory
 Dynamics in the Heisenberg ferromagnet
 Relativistic quantum mechanics
 Wave functions on spacetime configurations (multitime wave
functions)



Pyrochlor lattice 
 Mathematical Physics
 Theoretical Particle Physics
 Noncommutative Geometry
 Quantum Gravity
 Quantum Spin Systems

Mathematics and its Applications
 MarcThorsten
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,
largescale 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, lowrank approximation, parallel and scalable
algorithms

