Mathematics - Post-Baccalaureate Certificate

Research/Areas of Interest: 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.

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

Research/Areas of Interest: 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.

Research/Areas of Interest: Geometric group theory, low-dimensional topology, CAT(0) spaces

Research/Areas of Interest: Noncommutative harmonic analysis, representations of Lie groups, integral geometry, and Radon transforms

Research/Areas of Interest: Geometrically motivated hyperbolic dynamics — 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. His publication profile can be viewed at https://mathscinet.ams.org/mathscinet/author?authorId=270790 (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.

Research/Areas of Interest: Numerical Linear and Multilinear Algebra, Scientific Computing, Image Reconstruction and Restoration

Research/Areas of Interest: The structure and representations of algebraic groups

Research/Areas of Interest: Machine learning, harmonic analysis, statistical learning, graph theory, data science, computational mathematics, image processing, signal processing

Research/Areas of Interest: Time-frequency analysis, pure, applied, and numerical harmonic analysis; analysis and differential equations on fractals and graphs.

Research/Areas of Interest: computational biology, algorithms, probability, fitness landscapes, evolution, protein structure, statistical inference

Research/Areas of Interest: Geometric Group Theory/Topology

Research/Areas of Interest: Algebraic Geometry

Research/Areas of Interest: High-Dimensional data analysis: Matrix completion, compressive sensing, and structured sparse recovery. Mathematical foundations of AI: Interpretable machine learning, dictionary learning, and geometry-aware representations. Applied optimization: Distance geometry, large-scale kernel methods, and algorithm unrolling for signal processing

Research/Areas of Interest: 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.

Research/Areas of Interest: Hyperbolic manifolds and orbifolds, low-dimensional topology, group actions