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

Dierk Schleicher



The Mandelbrot set
  • Dynamical systems
    • Holomorphic and symbolic dynamics
    • Newton's root finding algorithm as a dynamical system
  • Complex variables and hyperbolic geometry
  • Conformal and fractal geometry

Mathematical Physics

Peter Schupp



Pyrochlor lattice
  • Mathematical Physics
  • Theoretical Particle Physics
  • Non-commutative Geometry
  • Quantum Gravity
  • Quantum Spin Systems

Mathematics and its Applications

Frank Oliver Glöckner, Professor of Bioinformatics
Marc-Thorsten Hütt, Professor of Computational Systems Biology
Herbert Jaeger, Professor of Computational Science
Arzhang Khalili, Professor of Computational Science
Ulrich Kleinekathöfer, Professor of Physics
Michael Kohlhase, Professor of Computer Science
Lars Linsen, Professor of Computational Science and Computer Science
Agostino Merico, Professor of Ecology
Joachim Vogt, Professor of Physics