UC Davis Mathematics
Schilling

Anne Schilling

Professor
Combinatorics, representation theory, mathematical physics, probability
Ph.D. (in Physics), 1997, State University of New York at Stony Brook
Publications:
Preferred listing: https://www.math.ucdavis.edu/~anne/research.html
Math arXiv
AMS Math Reviews
Google Scholar

Web Page: http://www.math.ucdavis.edu/~anne/
Email: anne@math.ucdavis.edu
Office: MSB 3222
Phone: 530-754-0497

Research

Professor Anne Schilling studies quantum algebras and representation theory using combinatorial methods. In particular she is interested in affine crystal graphs [2], which first arose in the exactly solvable lattice models in statistical mechanics. She is also involved in the study of affine Schubert calculus [1], which is a vast generalization of classical Schubert calculus. Many parts of her research involve computational experimentation. She is an active developer for Sage, http://www.sagemath.org/.

Selected Publications

  1. "Crystal Bases: Representations and Combinatorics" (with Daniel Bump), World Scientific, 2017, ISBN: 978-981-4733-43-4, 292pp
  2. "The Murnaghan-Nakayama rule for k-Schur functions,"(with Jason Bandlow and Mike Zabrocki), Journal of Combinatorial Theory, Series A, 118(5): 1588-1607, 2011. Full Text, (arXiv:1004.4886 [math.CO]).
  3. "K-theory Schubert calculus of the affine Grassmannian," (with Thomas Lam and Mark Shimozono), Compositio Mathematica, 146(4): 811-852, 2010. Full Text, (arXiv:0901.1506 [math.CO]).
  4. "Kirillov-Reshetikhin crystals for nonexceptional types," (with Ghislain Fourier and Masato Okado), Advances in Mathematics, 22(3): 1080-1116, 2009. Full Text, (arXiv:0810.5067 [math.RT])
  5. "Unified theory for finite Markov chains" (with John Rhodes), Advances in Mathematics 347 (2019) 739-779 ( arXiv:1711.10689 )

Honors and Awards

  • Humboldt Research Fellowship, 2002
  • Faculty Research Development Award, 2006
  • Chancellor's Fellowship, 2006
  • NSF Focused Research Group "Affine Schubert Calculus: Combinatorial, geometric, physical, and computational aspects," 2007-2010
  • Simons Fellowship, 2012-2013
  • AMS Fellow 2019

Last updated: 2019-09-14