Research Areas in the Mathematical Sciences

Algebra

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
Ulrich Kleinekathöfer, Professor of Physics
Agostino Merico, Professor of Ecology
Joachim Vogt, Professor of Physics
Peter Zaspel, Professor of Computer Science