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## Mathematics

The Department of Mathematics offers BA, BS, MA and PhD degrees. Faculty research interests include low-dimensional topology, differential geometry, partial differential equations, analysis, algebra, number theory and computational science.

The Applied Mathematics group maintains active collaborative research projects with faculty in Chemical Engineering, Electrical and Computer Engineering, Chemistry and Biochemistry, Computer Science, Materials Science, and the Materials Research Laboratory. We are also partners of an industrial consortium, the Complex Fluids Design Consortium. The Applied group members are also core faculty of the Computational Science and Engineering graduate program with an IGERT grant and are currently participating in the creation of a new interdisciplinary program on Computational Soft Materials.

Our String Theory group represents a new interdisciplinary direction for the department. David Morrison belong to the Algebra group with a joint appointment in Physics, Sergei Gukov belongs to Geometry/Topology with a joint appointment in Physics. These recent hires, the synergies offered by the presence of KITP, and our recent national prominence in algebraic geometry make this an exciting opportunity for growth.

Understanding of the fundamental processes of the natural word is based to a large extent on partial differential equations (PDE). For example, the Einstein equations describe the geometry of space-time and its interaction with matter. The dynamics of fluids and elastic solids are governed by partial differential equations that go back to Euler and Cauchy. Electro-magnetic waves including the propagation of light in various media are modeled by Maxwell's equations.

Geometry/Topology: The department's strength in low dimensional topology is recognized both nationally and internationally. One of the most exciting recent events in geometry is Perelman's work on the Poincare conjecture using Hamilton's Ricci flow. It combines geometric insights and techniques with analytic machineries to solve long standing topological problems.

The Algebra group is active across a broad spectrum such as representation theory applied to Lie groups, Poisson geometry, integrable systems, finite dimensional algebras, number theory, quadratic forms, and quantum groups. Particularly exciting are recent stunning breakthroughs in complex algebraic geometry.

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