# Research

Cornell has a tradition of strength in a wide range of research areas of mathematics, pure and applied. The department offers a rich research environment for its students and faculty and strives to be at the forefront of current mathematical research.

Visit the pages linked below to learn more about our research groups and their activities. Faculty typically belong to more than one group. The department embraces a unified view of mathematics and encourages interactions between different areas.

The algebra group includes experts in algebraic geometry, computational methods and commutative algebra, group theory, number theory, and representation theory.

Areas currently active at Cornell include dynamics, harmonic analysis, potential analysis, partial differential equations, geometric analysis, applied analysis, and numerical methods.

Applied mathematics is regarded as an interdisciplinary activity that results from the interaction of mathematics with other sciences and engineering. Cornell's “applied” group includes mathematicians working in dynamical systems theory, PDEs, calculus of variations, computational algebra, applied probability theory, statistics, numerical analysis, and scientific computing.

Faculty interests include algebraic and topological combinatorics, polytopes, matroids, combinatorial Hopf algebras and rigidity in discrete geometric structures.

Faculty pursue research in symplectic geometry, Lie theory, and geometric analysis, including geometric flows.

Many logicians have been trained at Cornell. Current interests of our faculty include mathematical logic, set theory, recursion theory, and computability theory.

The department has a long history of strength in both probability and statistics.

The Cornell Topology Festival is an internationally known event conducted annually since 1962. Current research interests include low-dimensional topology, symplectic geometry, the geometric and combinatorial study of discrete groups, and dynamical systems.

### Research Opportunities for Undergraduates

- Undergraduate Research Programs
- The department has offered a summer research program for undergraduates since 1994. Formerly an REU and now called SPUR, the 8-week program brings talented students here from across the country to work on research projects directed by Cornell faculty members. It is open to all students currently enrolled in an undergraduate program.
- Undergraduate Senior Theses
- Cornell mathematics majors have the opportunity to write a senior thesis based on independent research conducted with a faculty member on an advanced topic.

### Research Training Groups (RTGs)

- RTG Dynamics, Probability and PDEs in Pure and Applied Mathematics
- This NSF supported Research Training Group at Cornell University (DMS-1645643) provides research training at the nexus of dynamics, probability, and PDEs. Two themes are emphasized: the interplay between theory and applications, and the importance of communicating mathematical ideas across fields and to diverse audiences.