Allen Knutson

Professor of Mathematics

Web Site www.math.cornell.edu/~allenk/ Contact Information Office:  515 Malott Hall Phone:  (607) 255-2389 Fax:  (607) 255-7149 Email:  allenk@math.cornell.edu Courses & Office Hours

Education

Ph.D. (1996) Massachusetts Institute of Technology

Research Area: 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.

Selected Publications

The honeycomb model of GL(n) tensor products I: proof of the saturation conjecture (with Terence Tao), Journal of the AMS 12 no. 4 (1999), 1055–1090.

Puzzles and (equivariant) cohomology of Grassmannians (with Terence Tao), Duke Math. J. 119 no. 2 (2003), 221–260.

Gröbner geometry of Schubert polynomials (with Ezra Miller), Annals of Mathematics 161 (May 2005), 1245–1318.

Four positive formulae for type A quiver polynomials (with Ezra Miller and Mark Shimozono), Inventiones Mathematicae 166 no. 2 (November 2006).

Complete moduli spaces of branchvarieties (with Valery Alexeev), Crelle's Journal (to appear).

Last modified: January 21, 2009