Allen Knutson

Prof. Allen Knutson is a Professor of Mathematics at Cornell University, affiliated with the College of Arts and Sciences. He earned his Ph.D. from the Massachusetts Institute of Technology in 1996. His research focuses on algebraic geometry, algebraic combinatorics, and geometric representation theory, with an emphasis on Schubert calculus, quiver varieties, and the combinatorial structures underlying geometric problems.

Education: Ph.D. (1996) from MIT. His work often involves degenerating complex algebraic varieties into simpler combinatorial pieces, bridging geometry and discrete mathematics. Notable contributions include foundational results in Schubert calculus, honeycomb models, and the use of puzzles in cohomology computations.

Research Interests: Algebraic geometry, algebraic combinatorics, Schubert calculus, quiver varieties, geometric representation theory, and applications to integrable systems. His interdisciplinary approach integrates algebraic, geometric, and combinatorial methods to solve problems in mathematics and theoretical physics.

Advising: Current students include Portia Anderson, Raj Gandhi, and others. Past advisees have contributed to areas like flag manifolds, Frobenius splitting, and Bruhat atlases. He has taught advanced courses on topics such as symplectic resolutions, differentiable manifolds, and algebraic geometry.

Labs/Teams: Collaborates widely, with contributions to projects like the ICM 2022 paper on Schubert calculus and quiver varieties. His work often involves visual tools like puzzles and pipe dreams to encode geometric invariants.