Mathematics

Source: https://catalog.caltech.edu/current/areas-of-study-and-research/mathematics/ Parent: https://catalog.caltech.edu/

Areas of Research

Students in mathematics have the opportunity to work in many fields of current research. The main active areas of research by the faculty include the following:

Algebra. Finite group theory, algebraic groups, representation theory, symmetric functions, algebraic K-theory.
Algebraic Geometry. Moduli spaces, birational geometry, Hodge theory, Calabi-Yau varieties, arithmetic geometry.
Analysis. Classical real and complex analysis, harmonic analysis, functional analysis and operator theory, orthogonal polynomials; complex, smooth, and random dynamical and Hamiltonian systems, fractals, integrable systems, partial differential equations.
Combinatorics. Combinatorial designs and matrix theory, coding theory, extremal set theory.
Geometry and Topology. Low-dimensional topology, hyperbolic geometry, geometric group theory and foliations; symplectic geometry and topology, topological gauge theory, knot theory, and their interface with theoretical physics.
Mathematical Logic. Set theory and its interactions with analysis, combinatorics, dynamical systems, and model theory.
Mathematical Physics. Schrödinger operators, random matrices.
Noncommutative Geometry.
Number Theory. Algebraic number theory, automorphic forms, Shimura varieties, Galois representations, and L-functions.

Physical Facilities

The mathematics department is housed in the Ronald and Maxine Linde Hall of Mathematics and Physics and the W.K. Kellogg Radiation Laboratory. In addition to offices for the faculty and graduate students, there are classrooms, conference rooms, discussion areas, a lecture hall, and a lounge for informal gatherings of the students and staff. The mathematics collection is housed nearby in the Sherman Fairchild Library.

Published Date: June 3, 2025