Department of Mathematics

Differential Geometry and Geometric Analysis

Differential Geometry is the study of manifolds and other geometric objects using calculus; Geometric Analysis extends this by applying techniques from Partial Differential Equation, and also uses geometric methods to study PDEs. There are important interactions with mathematical physics (General Relativity and physical gauge theories) and with topology (symplectic topology and mathematical gauge theories).

The work and interests of our group ranges broadly across the areas of contemporary research in differential geometry and geometric analysis. Areas of particular interest include the following.

  • Gauge Theory
  • Symplectic geometry and Gromov-Witten theory
  • Geometric Flows
  • General Relativity

Our group works closely with both the Topology and the Mathematical Physics groups - we have many overlapping interests and hold many joint seminars. In particular, the combined Geometry/Topology group at MSU has a long history of producing strong collaborative research and successful graduate students.