Research Areas
Mathematics research at UCR could be summarized into several overlapping areas: Algebra, Analysis, Geometry and Topology, Lattice Theory and Quantum Mathematics. Faculty at UCR Math typically conducts research in cross-disciplinary manner. Below is a very brief summary of our research area and faculty listing, often in multiple areas. You may also go to faculty's individual webpage to find their specific interests or publications.
Algebra
Faculty activities in this area include commutative algebra, representation theory, combinatorics, combinatoric number theory and algebraic geometry.
Faculty: M. C. Chang, V. Chari, J. Greenstein, Z. Guan, L. H. Harper, Y. S. Poon, Z. Ran, D. Rush.
Analysis
Research activities in this area include Functional Analysis, Partial Differential Equations, Operator Algebras, Several Complex Variables, Probability Theory, Mathematical Physics, and Approximation Theory.
Faculty: M. Asaeda, J. Baez, B. Chalmers, L. O. Ferguson, N. E. Gretsky, L. H. Harper, M. Lapidus, M. M. Rao, B. Wong, F. Xu, Q. S. Zhang.
Geometry and Topology
Research activities in this area include Low Dimension Topology, Geometric Topology, Differential Topology, Transformation Group, Riemannian Geometry, Complex Differential Geometry, and Geometric Analysis.
Faculty: M. Asaeda, Z. Guan, X. S. Lin, Y. S. Poon, R. Schultz, S. Vidussi, F. Wilhelm, B. Wong, Q. Zhang.
Lattice Theory: G. Gierz, A. Stralka
Quantum mathematics
This is a collection of mathematics that has come from work on quantum mechanics, quantum field theory, quantum gravity and string theory. This work connects different branches of mathematics in new and interesting ways. Areas within quantum mathematics include quantum groups, affine Lie algebras, vertex operator algebras, higher categories, new invariants of knots and manifolds, and the relation between number theory and quantum mechanics.
Faculty: M. Asaeda, J. Baez, V. Chari, J. Greenstein, M. Lapidus, X. S. Lin, F. Xu.
