Ph.D. from University of Chicago, 2009
B.S. from Washington & Lee University, 2003
Budapest Semesters in Mathematics, 2001 - 2002
- Associate Professor, Haverford College, 2019 - present
- Assistant Professor, Haverford College, 2012 - 2019
- Assistant Professor, Williams College, 2010 - 2012
- RTG Hildebrandt Assistant Professor, University of Michigan, 2009 - 2010
My research program explores interactions between modern methods in algebraic geometry, algebraic combinatorics, and representation theory. In particular, I am interested in answering geometric and topological questions about algebraic varieties such as (affine) Grassmannians and flag varieties, and affine Deligne-Lusztig varieties using the methods of algebraic combinatorics, combinatorial representation theory, and even geometric group theory. Related interests include the study of the partially ordered set of Newton polygons associated to elements in the affine Weyl group, the Peterson isomorphism relating quantum and affine Schubert calculus, and various affine Hecke algebras.
- NSF DMS #2202017, "RUI: Geometry of Conjugacy and K-Theory in Affine Weyl Groups", $169,979 individual research grant over 3 years
- ARC Discovery Project #180102437, "Affine flags, folded galleries and Euclidean reflection groups", joint with Petra Schwer (Karlsruhe Institute of Technology) and Anne Thomas, Lead PI (University of Sydney), $317,288 AUD travel, conference, and postdoc funding over 3 years
- NSF DMS #1728937, "Mid-Atlantic Algebra, Geometry, and Combinatorics Workshop", joint with Linda Chen (Swarthmore), Jennifer Morse (Drexel), and Greta Panova (UPenn), $23,250 conference grant over 3 years
- NSF DMS #1600982, "RUI: Affine Flags, p-adic Representations, and Quantum Cohomology", $128,000 individual research grant over 3 years
- Simons Collaboration Grant #318716, "p-adic Representations, Affine Flag Varieties, and Alcove Walks", $35,000 individual research grant over 5 years
Publications and Preprints
- "Alcove Walks and GKM Theory for Affine Flags," joint with Kaisa Taipale, Springer INdAM Series: Approximation Theory and Numerical Analysis Meet Algebra, Geometry, Topology, 2023+.
- "Chimney retractions in affine buildings encode orbits in affine flag varieties," joint with Petra Schwer and Anne Thomas, Innov. Incidence Geom. (special volume in memory of Jacques Tits), 2023+.
- "Affine Deligne-Lusztig varieties and folded galleries governed by chimneys," joint with Petra Schwer and Anne Thomas, Ann. Inst. Fourier (Grenoble), 2022+.
- "A gallery model for affine flag varieties via chimney retractions," joint with Yusra Naqvi, Petra Schwer, and Anne Thomas, Transform. Groups, 2022+.
- "An equivariant quantum Pieri rule for the Grassmannian on cylindric shapes," joint with Anna Bertiger, Dorian Ehrlich (HC '14), and Kaisa Taipale, Electron. J. Combin., Vol. 29, no. 2, Paper No. 2.8, 2022.
- "An affine approach to Peterson comparison," joint with Linda Chen and Jennifer Morse, Algebr. Represent. Theory, 2021.
- "Maximal Newton points and the quantum Bruhat graph," Michigan Math. J., Vol. 70, no. 3, p. 451-502, 2021.
- "Generic Newton points and the Newton poset in Iwahori double cosets," joint with Eva Viehmann, Forum of Mathematics, Sigma, 8, E50, 2020.
- "Dimensions of affine Deligne-Lusztig varieties: a new approach via labeled folded alcove walks and root operators," joint with Petra Schwer and Anne Thomas, Mem. Amer. Math. Soc., 261(1260):0, 2019.
- "Applying parabolic Peterson: affine algebras and the quantum cohomology of the Grassmannian," joint with Tessa Cookmeyer (HC '17), J. Comb., Vol. 10, no. 1, p. 129-162, 2019.
- "Enumerations relating braid and commutation classes," joint with Susanna Fishel, Rebecca Patrias, and Bridget Eileen Tenner, European J. Combin., Vol. 74, p. 11-26, December 2018.
- "Equivariant quantum cohomology of the Grassmannian via the rim hook rule," joint with Anna Bertiger and Kaisa Taipale, Algebr. Comb., Vol. 1, no. 3, p. 327-352, 2018.
- "Bijective projections on parabolic quotients of affine Weyl groups," joint with Margaret Nichols, Min Hae Park, XiaoLin Shi, and Alexander Youcis, J. Algebraic Combin. Vol. 41, no. 4, p. 911-948, 2015.
- "Affine Deligne-Lusztig varieties associated to additive affine Weyl group elements," J. Algebra, Vol. 349, no. 1, p. 63-79, 2012.
- "Codimensions of Newton strata for SL(3) in the Iwahori case," Math. Zeit., Vol. 263, no. 3, p. 499-540, 2009.