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Allen Knutson


Allen Knutson

Educational Background

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



  • Mathematics

Graduate Fields

  • Mathematics


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.



Spring 2022

Fall 2022


  • 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.