Differential geometry is a vast subject that has its roots in both the classical theory of curves and surfaces and in the work of Gauss and Riemann motivated by the calculus of variations. The subjects with strong representation at Cornell are symplectic geometry, Lie theory, and geometric analysis.

Symplectic geometry is a branch of differential geometry and differential topology that has its origins in the Hamiltonian formulation of classical mechanics. Geometric analysis is a mathematical discipline at the interface of differential geometry and differential equations. Richard Hamilton and James Eells Jr. did some of their groundbreaking work while at Cornell.

Lie groups are named after the 19th century mathematician Sophus Lie, who was motivated by the problem of analyzing the continuous symmetries of differential equations. This area has expanded to encompass a wide variety of topics related to finite and continuous groups. It has significant applications to harmonic analysis, number theory, and mathematical physics. One of the most influential mathematicians working in Lie theory in the early 1950s was Eugene Dynkin, a member of the Cornell mathematics department from 1977 to 2014.

H. C. Wang was a member of the department from 1966 to 1978 and made groundbreaking contributions to differential geometry, topology, and Lie groups. The H. C. Wang instructorship is named in his honor. William Thurston, one of the most influential modern geometers was active in the department from 2003 to 2012.

Faculty Members

Dan M. Barbasch Representation theory of reductive Lie groups
Yuri Berest Representation theory, noncommutative geometry, mathematical physics
Xiaodong Cao Differential geometry and geometric analysis
Robert Connelly Discrete geometry, computational geometry and the rigidity of discrete structures
Benjamin Dozier Dynamical systems, Riemann surfaces
Tara Holm Symplectic geometry
John H. Hubbard Analysis, differential equations, differential geometry
Allen Knutson Algebraic geometry and algebraic combinatorics
Reyer Sjamaar Symplectic geometry
Birgit E. Speh Lie groups, automorphic forms, representation theory
Nicolas Templier Number theory, automorphic forms, and mathematical physics
Xin Zhou Geometric Analysis and Calculus of Variations

Emeritus and Other Faculty

Christian Gaetz Algebraic Combinatorics
Ritvik Ramkumar Algebraic geometry, commutative algebra
Morgan Weiler Geometry, topology

Related people

Image of Xiaodong Cao
Xiaodong Cao


Image of Kelly Delp
Kelly Delp

Senior Lecturer

Image of Benjamin Dozier
Benjamin Dozier

Assistant Professor

Image of Tara Holm
Tara Holm


Image of Allen Knutson
Allen Knutson


Image of Yun Liu
Yun Liu

Ph.D Candidate

Image of Reyer Sjamaar
Reyer Sjamaar


Image of Birgit Speh
Birgit Speh

Distinguished Professor of Arts and Sciences in Mathematics

Image of Xin Zhou
Xin Zhou

Associate Professor

All research areas

Algebra    Analysis    Applied Mathematics    Combinatorics and Discrete Geometry    Geometry    Logic    Probability and Statistics    Topology