Faculty Detail
David Speyer
Associate Professor
2844 East Hall
Phone: (734) 7646897
Email:
speyer@umich.edu

Affiliation(s)

Algebra/Algebraic Geometry
Combinatorics

Algebra/Algebraic Geometry

About
Algebraic geometry is the study of the geometry of the solutions to systems of polynomial equations. The simplest example of a theorem of algebraic geometry is that a polynomial of degree n has n solutions; this statement relates a feature of the equation (the number of monomials it contains) to a feature of its solution set (how many points there are). More generally, we may have many equations and want to answer questions like how manysolutions there are, where they are located and what sort of shape they form. I study areas of algebraic geometry which have a great deal of combinatorial structure, allowing connections to the tools of discrete math. In particular, I am interested in flag varieties and related configuration spaces, cluster algebras and toric varieties. On the combinatorial side side, I use ideas from Schubert calculus, matroids, lattice point enumeration and Coxeter groups.