# Anne Schilling

Professor

Combinatorics, representation theory, mathematical physics, probability

Ph.D. (in Physics), 1997, State University of New York at Stony BrookWeb Page: http://www.math.ucdavis.edu/~anne/

Email: anne@math.ucdavis.edu

Office: MSB 3222

Current Courses: MAT 245

Office Hours: MWF 4-5 after every class

Phone: 530-754-0497

Publications:

Preferred listing: https://www.math.ucdavis.edu/~anne/research.htmlMath arXiv

AMS Math Reviews

Google Scholar

### 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

- "Crystal Bases: Representations and Combinatorics" (with Daniel Bump), World Scientific, 2017, ISBN: 978-981-4733-43-4, 292pp
- "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]). - "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]). - "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]) - "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*