arrow grid linear view icon
The College of Arts Sciences
Search

You are here

Allen Knutson

Professor

Allen Knutson juggling 5 balls

Malott Hall, Room 515
ak596@cornell.edu
607-255-2389

Educational Background

  • Ph.D. (1996) Massachusetts Institute of Technology

Website(s)

Departments/Programs

  • Mathematics

Graduate Fields

  • Mathematics

Research

Algebraic geometry and algebraic combinatorics

In recent years I have been studying algebraic varieties carrying large groups of symmetries, such as toric varieties, flag manifolds, Schubert varieties, and quiver cycles. While individually complicated, these can be broken up (really, degenerated) into many simple pieces, at which point their study becomes a matter of combinatorics rather than geometry.

 

Courses

Publications

  • Complete moduli spaces of branchvarieties (with Valery Alexeev), Crelle's Journal (to appear).
  • Four positive formulae for type A quiver polynomials (with Ezra Miller and Mark Shimozono), Inventiones Mathematicae 166 (2006), no. 2.
  • Gröbner geometry of Schubert polynomials (with Ezra Miller), Annals of Mathematics 161 (2005), 1245–1318.
  • Puzzles and (equivariant) cohomology of Grassmannians (with Terence Tao), Duke Math. J. 119 (2003), no. 2, 221–260.
  • The honeycomb model of GL(n) tensor products I: proof of the saturation conjecture (with Terence Tao), Journal of the AMS 12(1999), no. 4, 1055–1090.