Algebraic & Differential Geometry

The Algebraic & Differential Geometry research area brings together expertise across geometry, algebra, and analysis to study fundamental questions in the areas of differential geometry, symplectic geometry, geometric partial differential equations, geometric evolutions, noncommutative geometry, algebraic geometry, number theory, and mathematical physics.

Capabilities

• Ben Andrews: geometric partial differential equations (including mean curvature flow and Ricci flow), geometric variational problems (including isoperimetric problems and eigenvalue inequalities), and geometric approaches to the analysis of differential equations.
• Asilata Bapat: geometric and categorical representation theory, homological algebra, with connections to topology, combinatorics, and algebraic geometry.
• James Borger: algebra, especially number theory and algebraic geometry.
• Anand Deopurkar: algebraic geometry and its connections to number theory, representation theory, and mathematical physics, homological algebra.
• Mat Langford: Ricci flow, mean curvature flow and flows of hypersurfaces by nonlinear functions of their curvature, related nonlinear elliptic and parabolic PDE, and applications to topology, geometry and general relativity
• Ian Le: representation theory and algebraic combinatorics, cluster theory.
• Brett Parker: symplectic geometry, Gromov-Witten and related invariants using exploded manifolds.
• Bryan Wang: geometric properties of moduli spaces in symplectic topology, gauge theory.

Reasons to work with us

We are a broad mathematical research groups connected to a wide variety of research topics in modern mathematics. We support an active, collaborative research and learning environment. Our regular topics courses, seminars, and learning groups aimed at fostering interactions between mathematicians at all levels, from undergraduates through to continuing faculty. Our mathematicians are international leaders in their fields, and we maintain active collaborations with mathematicians all over the world.