Professor

### Biography

PhD, University of California, San Diego, 1994

SB, MIT, 1990

My research is in algebraic combinatorics. Combinatorics is the study of counting and bijective proofs, so an algebraic combinatorialists counts algebraic objects. In particular, I am interested in Schubert polynomials, Schubert varieties, flag manifolds, Kazhdan-Lusztig polynomials, Stanley symmetric functions, Bruhat order, Weyl group and root systems of all types etc. I am a strong advocate of using computers to do math research, in particular for obtaining data for conjectures and computer verified proofs. Recently, I have been interested in problems which are not decidable by any possible algorithm in finite time.

### Courses Taught

### Autumn 2024

### Spring 2024

- MATH 381 A: Discrete Mathematical Modeling
- MATH 381 B: Discrete Mathematical Modeling
- MATH 550 B: Seminar in Geometry

### Winter 2024

### Autumn 2023

- MATH 208 A: Matrix Algebra with Applications
- MATH 208 B: Matrix Algebra with Applications
- MATH 550 B: Seminar in Geometry

### Spring 2023

### Winter 2023

### Autumn 2022

### Spring 2022

### Winter 2022

### Autumn 2021

### Spring 2021

### Winter 2021

### News & Events

### Related News

- Sara Billey is co-recipient of A&S Bergstrom Award (April 26, 2018)
- Sara Billey featured in 2013 AWM Grand Prize Winning Essay (April 1, 2013)
- AMS Fellows Named (November 1, 2012)

### Related Events

- Math Department: UW Math Alumni Gathering -
- Combinatorics and Geometry Seminar: TBA -
- Combinatorics and Geometry Seminar: TBA -
- Combinatorics and Geometry Seminar: TBA -
- Career Transitions: Transition into Research -
- Combinatorics and Geometry Seminar: TBA -
- Combinatorics and Geometry Seminar: Log-Concavity of the Alexander Polynomial for Special Alternating Links -
- Combinatorics and Geometry Seminar: Smooth Points on Positroid Varieties -
- Combinatorics and Geometry Seminar: Cyclically ordered quivers -
- Combinatorics and Geometry Seminar: Standard monomials for positroid varieties -
- Career Transitions, Current Topics Seminar: Internship Ideas and Planning -
- Career Transitions, Current Topics Seminar: Jobs Lunch -
- Combinatorics and Geometry Seminar: Dissecting an Integer Polymatroid -
- UW Math Hour: Math 381 Service Learning Poster Session -
- Career Transitions: "3-minute Thesis Talks" and "Things I wish I had known: advice from graduating students." -
- Combinatorics and Geometry Seminar: Colorful Permutation Statistics and Cycle Type -
- Combinatorics and Geometry Seminar: The merging operation and (d-i)-simplicial i-simple d-polytopes -
- Combinatorics and Geometry Seminar: h-vector Inequalities Under Weak Maps -
- Combinatorics and Geometry Seminar: The inhomogeneous multispecies PushTASEP and Macdonald polynomials -
- Career Transitions: Industrial Panel 2024 -
- Combinatorics and Geometry Seminar: Smooth Combinatorial Cubes are IDP -
- Career Transitions: Surviving and Thriving in the First Year of Grad School -
- Combinatorics and Geometry Seminar: Shuffle bases and quasisymmetric power sums -
- Combinatorics and Geometry Seminar: The Poincare-Extended ab-Index -
- Combinatorics and Geometry Seminar: Increasing subsequences, orbit harmonics, and shadow play -
- Combinatorics and Geometry Seminar: The first bijective proof of the ASM theorem -
- Combinatorics and Geometry Seminar: Incidences and Tilings -
- Combinatorics and Geometry Seminar: Solving puzzles of shellable simplicial spheres -
- Combinatorics and Geometry Seminar: Moshe's Insanity -
- CANCELED: Combinatorics and Geometry Seminar: The Poincare-Extended ab-Index -
- Combinatorics and Geometry Seminar: Tropicalization of the principal minors of positive semidefinite matrices -
- Combinatorics and Geometry Seminar: Farahat-Higman Algebras for Classical Linear Groups -
- Combinatorics and Geometry Seminar: Distributional properties of colored multiset Eulerian polynomials -
- Combinatorics and Geometry Seminar: A regular unimodular triangulation of the matroid base polytope -
- Combinatorics and Geometry Seminar: Numerical semigroups, minimal presentations, and posets -
- Combinatorics and Geometry Seminar: A noncommutative Schur function approach to chromatic symmetric functions -
- Career Transitions: Transition into Research -
- Combinatorics and Geometry Seminar: Extremal crystals and atom-positivity -
- Combinatorics and Geometry Seminar: Matroid Schubert varieties and equivariant compactifications -
- Combinatorics and Geometry Seminar: Quantum Bruhat graphs and tilted Richardson varieties -
- Combinatorics and Geometry Seminar: Snake Graphs for Graph LP Algebras -
- Combinatorics and Geometry Seminar: Projections of Richardson Varieties -
- Combinatorics and Geometry Seminar: Face Numbers and Angles of Polytopes -
- Combinatorics and Geometry Seminar: Combinatorics of two-boundary Temperley-Lieb algebras -
- Career Transitions: Career Transitions: Academic Jobs Panel -
- Combinatorics and Geometry Seminar: Combinatorics of CAT(0) cubical complexes, crossing complexes and co-skeletons -
- Combinatorics and Geometry Seminar: Central transversals and hyperplane arrangements -
- Combinatorics and Geometry Seminar: Tautological classes of matroids -
- Combinatorics and Geometry Seminar: Mixed Volumes of Normal Complexes -
- Combinatorics and Geometry Seminar: Chip-firing game on metric graphs and combinatorics of their Jacobians -
- Career Transitions: Industrial Panel 2023 -
- Combinatorics and Geometry Seminar: SL_4 web bases from hourglass plabic graphs -
- Combinatorics and Geometry Seminar: The Polyhedral Combinatorics of Pivot Rules -
- Combinatorics and Geometry Seminar: Higher Weak Order of Affine Permutations -
- Combinatorics and Geometry Seminar: Algebra, Geometry & Combinatorics of the Pinhole Camera -
- Combinatorics and Geometry Seminar: The geometric method, matroids and related simplicial complexes -
- Combinatorics and Geometry Seminar: Vertex labeling properties on graphs and complexes -
- Combinatorics and Geometry Seminar: Combinatorial mutations and birational maps -
- Combinatorics and Geometry Seminar: Unimodular triangulations of sufficiently large dilations -
- Combinatorics and Geometry Seminar: Transfer systems and model structures for combinatorialists -
- Combinatorics and Geometry Seminar: Problems around Combinatorial Graphs and Distance Geometry -
- Combinatorics and Geometry Seminar: Subdivisions of Shellable Complexes -
- Combinatorics and Geometry Seminar: Odd diagrams and patterns -
- Combinatorics and Geometry Seminar: 3D plabic graphs and cluster structures on type A braid varieties -
- Combinatorics and Geometry Seminar: 2-LC triangulated manifolds are exponentially many -
- Combinatorics and Geometry Seminar: On the anisotropy theorem of Papadakis and Petrotou -
- Combinatorics and Geometry Seminar: Enumerating interval graphs and d-representable complexes -
- Combinatorics and Geometry Seminar: Hurwitz numbers via topological recursion -
- Combinatorics and Geometry Seminar: A Pattern Avoidance Criteria for Smoothness of Positroid Varieties Via Decorated Permutations, Spirographs, and Johnson Graphs -
- Combinatorics and Geometry Seminar: Maximal Chain Descent Orders -
- Combinatorics and Geometry Seminar: Flavors of the Fubini-Bruhat Order -
- Combinatorics and Geometry Seminar: Higher Categorical Associahedra -
- Combinatorics and Geometry Seminar: Pattern-avoiding parking functions -
- Combinatorics and Geometry Seminar: Graph limits and graph homomorphism inequalities -
- Combinatorics and Geometry Seminar: A Proof of Grünbaum’s Lower Bound Conjecture for polytopes, lattices, and strongly regular pseudomanifolds -
- Career Transitions: Career Transitions: Industrial Panel 2022 -
- Combinatorics and Geometry Seminar: q-Whittaker functions, finite fields, and Jordan forms -
- Combinatorics and Geometry Seminar: Grothendieck-to-Lascoux Expansions -
- Combinatorics and Geometry Seminar: Linear relations among Schubert structure coefficients -
- Career Transitions: Microsoft Presentation -
- Combinatorics and Geometry Seminar: Planar Tanglegram Layouts and Edge Insertion -
- Combinatorics and Geometry Seminar: Common tangents to polytopes and convex bodies -
- Combinatorics and Geometry Seminar: Non-realizability of polytopes via linear programming -
- Combinatorics and Geometry Seminar: Braiding and twisting open positroid varieties -
- Combinatorics and Geometry Seminar: From symmetric functions, to knots, and back again -
- CANCELED: Combinatorics and Geometry Seminar: Braiding and twisting open positroid varieties -
- Combinatorics and Geometry Seminar: Multiplicities of maximal dominant weights of some affine Lie algebra modules -
- Combinatorics and Geometry Seminar: When is the probability of avoiding a graph super-exponentially small? -
- Combinatorics and Geometry Seminar: Helly type problems: topology, the cascade conjecture, and graph coloring -
- Combinatorics and Geometry Seminar: Combinatorial atlas for log-concave inequalities -
- Combinatorics and Geometry Seminar: Bumpless pipe dreams encode Gröbner geometry of Schubert polynomials -
- Combinatorics and Geometry Seminar:
*f**- and*h**-vectors - - Combinatorics and Geometry Seminar: P-partition generating functions of naturally labeled posets -
- Career Transitions: Post-Prelim Chat -
- Career Transitions: Surviving graduate school in the COVID era -
- Career Transitions: Surviving and Thriving in the First Year of Grad School -
- Current Topics Seminar: Session 8 -
- Career Transitions: Career Transitions: Academic Jobs Panel -
- Career Transitions: Career Transitions: Industry Panel -
- UW-PIMS Colloquium: Patterns in Standard Young Tableaux -
- Career Transitions: Career Transitions: Industry Panel -