Mathematics - Post-Baccalaureate Certificate

Scientific computing and numerical analysis: Efficient computational methods for complex fluids, plasma physics, electromagnetism and other physical applications.

Geometric Group Theory/Topology

Applied dynamical systems, applied probability theory, kinetic theory, agent-based modeling, mathematical models of the economy, theoretical and computational fluid dynamics, complex systems science, quantum computation Current research emphasis is on mathematical models of economics in general, and agent-based models of wealth distributions in particular. The group's work has shed new light on the tendency of wealth to concentrate, and has discovered new results for upward mobility, wealth autocorrelation, and the flux of agents and wealth. The group's mathematical description of the phenomenon of oligarchy has also shed new light on functional analysis in general and distribution theory in particular. Secondary projects include new directions in lattice Boltzmann and lattice-gas models of fluid dynamics, kinetic theory, and quantum computation.

Anomalous diffusion, mathematical neuroscience

Geometry of groups and surfaces

Noncommutative harmonic analysis, representations of Lie groups, integral geometry, and Radon transforms

Dynamical systems: Hyperbolicity, invariant foliations, geodesic flows, contact flows, and related topics — Hasselblatt's research, undertaken with colleagues from several continents, is in the modern theory of dynamical systems, with an emphasis on hyperbolic phenomena and on geometrically motivated systems. He also writes expository and biographical articles, writes and edits books, and organizes conferences and schools. Information about his publications can be viewed on MathSciNet by those at an institution with a subscription. Former doctoral students of his can be found in academic positions at Northwestern University, George Mason University, the University of New Hampshire, and Queen's University as well as among the winners of the New Horizons in Mathematics Prize.

Scientific computing and numerical analysis; Parallel multigrid and multilevel methods for large-scale coupled systems; Efficient numerical methods for reservoir simulation, fluid-structure interaction, and other applications.

Numerical Linear and Multilinear Algebra, Scientific Computing, Image Reconstruction and Restoration

The structure and representations of algebraic groups

To each point on a curve, one can often associate in a natural way a line or plane (or higher dimensional linear variety) that moves with the point in the curve. This set of linear spaces is called a vector bundle. Vector bundles appear in a variety of questions in Physics (like the computation of Gromov-Witten invariants) . Moreover, they provide new insights into old mathematical problems and have been used to give beautiful proofs to long standing conjectures as well as striking counterexamples to some others.

Algebraic geometry, topology, and differential geometry

Hyperbolic manifolds and orbifolds, low-dimensional topology, group actions