Ph.D. from University of Chicago, 2009
B.S. from Washington & Lee University, 2003
Budapest Semesters in Mathematics, 2001 - 2002
- Assistant Professor, Haverford College, 2012 - present
- 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 Grassmannians, flag varieties, and affine Deligne-Lusztig varieties using the methods of algebraic combinatorics and combinatorial representation theory. Related interests include the study of the partially ordered set of Newton polygons associated to elements in the affine Weyl group, the development of models for quantum and affine Schubert calculus, and affine Hecke algebras.
Publications and Preprints
- "Dimensions of affine Deligne-Lusztig varieties: a new approach via labeled folded alcove walks and root operators," joint with Petra Schwer and Anne Thomas, preprint available online at arXiv:1504.07076, 2015.
- "Equivariant quantum cohomology of the Grassmannian via the rim hook rule," joint with Anna Bertiger and Kaisa Taipale, preprint available online at arXiv:1403.6218, 2014.
- "Bijective projections on parabolic quotients of affine Weyl groups," joint with Margaret Nichols, Min Hae Park, XiaoLin Shi, and Alexander Youcis, to appear in J. Algebraic Combin., preprint available online at arXiv:1212.0771, 2012.
- "Maximal Newton polygons via the quantum Bruhat graph (extended abstract)," 24th International Conference on Formal Power Series and Algebraic Combinatorics, Discrete Math. Theor. Comput. Sci. Proc., 2012.
- "Affine Deligne-Lusztig varieties associated to additive affine Weyl group elements," J. Algebra 349, no. 1, p. 63-79, 2012.
- "Codimensions of Newton strata for SL(3) in the Iwahori case," Math. Zeit. 263, no. 3, p. 499-540, 2009.