Martha Precup

I am an Associate Professor in the Department of Mathematics at Washington University in St. Louis. My primary research interests are in algebraic geometry, combinatorics, and representation theory. Much of my work involves using Lie theory to strengthen and develop connections between combinatorics and geometry. I received my PhD from Notre Dame in 2013 under the direction of Sam Evens.

My research is supported by NSF CAREER grant DMS-2237057 and NSF grant DMS-1954001.

Preprints

4. "Restricted inversion polynomials," with Jeongwon Lee and Nathan Lesnevich; arXiv:2511.05676
3. "Richardson tableaux and components of Springer fibers equal to Richardson varieties," with Steven N. Karp; arXiv:2506.20792
2. "Matrix Hessenberg schemes over the minimal sheet," with Rebecca Goldin; arXiv:2501.02639
1. "Hessenberg varieties of codimension one in the flag variety," with Laura Escobar and John Shareshian; arXiv:2208.06299

Publications

22. "Regular Hessenberg varieties for the minimal indecomposable Hessenberg space," with Erik Insko and Alexander Woo; Michigan Mathematical Journal (to appear); arXiv:2411.17487
21. "K -Orbit closures and Hessenberg varieties," with Mahir Bilen Can, John Shareshian, and Ozlem Ugurlu; Forum of Mathematics, Sigma (2025); arXiv:2309.05770
20. "Geometric and combinatorial properties of extended Springer fibers," with William Graham and Amber Russell; Annales de l’Institut Fourier (to appear); arXiv:2309.13764
19. "Minimal semisimple Hessenberg schemes," with Rebecca Goldin; AMS conference proceedings, Contemporary Mathematics (to appear), arXiv:2408.07017
18. "Which Schubert varieties are Hessenberg varieties?," with Laura Escobar and John Shareshian, Transformation Groups (2023); arXiv:2107.07929
17. "Perverse sheaves, nilpotent Hessenberg varieties, and the modular law," with Eric Sommers, Pure and Applied Mathematics Quarterly (2025); arXiv:2201.13346
16. "Torus fixed point sets of Hessenberg Schubert varieties in regular semisimple Hessenberg varieties," with Megumi Harada, Osaka Journal of Mathematics (2023); arXiv:2112.13250
15. "A new approach to the generalized Springer correspondence," with William Graham and Amber Russell, Transactions of the American Mathematical Society (2023); arXiv:2002.12480
14. "Upper-triangular linear relations on multiplicities and the Stanley-Stembridge conjecture," with Megumi Harada, The Electronic Journal of Combinatorics (2022); arXiv:1812.09503
13. "Toward permutation bases in the equivariant cohomology rings of regular semisimple Hessenberg varieties," with Megumi Harada and Julianna Tymoczko, La Matematica (2022); arXiv:2101.03191
12. "Hessenberg varieties associated to ad-nilpotent ideals," with Caleb Ji, Communications in Algebra (2021); arXiv:1908.09821
11. "Hessenberg varieties of parabolic type," with Julianna Tymoczko, Geometriae Dedicata (2021); arXiv:1701.04140
10. "A filtration on the cohomology rings of regular nilpotent Hessenberg varieties," with Megumi Harada, Tatsuya Horiguchi, Satoshi Murai, and Julianna Tymoczko; Mathematische Zeitschrift (2021); arXiv:1912.12892
9. "An equivariant basis for the cohomology of Springer fibers," with Edward Richmond; Transactions of the American Mathematical Society, Series B (2021); arXiv:1912.08892
8. "Hessenberg varieties and the Stanley-Stembridge conjecture," Oberwolfach Reports (2019), Mini-Workshop on Degeneration Techniques in Representation Theory; https://www.mfo.de/occasion/1941b
7. "The cohomology of abelian Hessenberg varieties and the Stanley-Stembridge conjecture," with Megumi Harada, Algebraic Combinatorics (2019); arXiv:1709.06736
6. "The singular locus of semisimple Hessenberg varieties," with Erik Insko, Journal of Algebra (2019); arXiv:1709.05423
5. "Springer fibers and Schubert points," with Julianna Tymoczko, European Journal of Combinatorics (2019); arXiv:1701.03502
4. "The cohomology of abelian Hessenberg varieties and the Stanley-Stembridge conjecture," with Megumi Harada, Proceedings of the 30th International Conference on Formal Power Series and Algebraic Combinatorics, Séminaire Lotharingien de Combinatoire (2018)
3. "The Betti numbers of regular Hessenberg varieties are palindromic," Transformation Groups (2017); arXiv:1603.07662
2. "The connectedness of Hessenberg varieties," Journal of Algebra (2015); arXiv:1310.4212‎
1. "Affine pavings of Hessenberg varieties for semisimple groups," Selecta Mathematica (2013); arXiv:1205.3976v2
0. "Classification of Geometric Spirals," Pi Mu Epsilon Journal (2010)

Martha Precup

Preprints

Publications

E-mail: martha dot precup at wustl dot edu

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PhD Students