## Martha Precup

I am an Assistant Professor in the department of mathematics and statistics 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 grant DMS-1954001.

### Preprints

- 6. "A new approach to the generalized Springer correspondence," with William Graham and Amber Russell; arxiv:2002.12480
- 5. "A filtration on the cohomology rings of regular nilpotent Hessenberg varieties," with Megumi Harada, Tatsuya Horiguchi, Satoshi Murai, and Julianna Tymoczko; arXiv:1912.12892
- 4. "An equivariant basis for the cohomology of Springer fibers," with Edward Richmond; arXiv:1912.08892
- 3. "Hessenberg varieties associated to ad-nilpotent ideals," with Caleb Ji; arXiv:1908.09821
- 2. "Upper-triangular linear relations on multiplicities and the Stanley-Stembridge conjecture," with Megumi Harada; arXiv:1812.09503
- 1. "Hessenberg varieties of parabolic type," with Julianna Tymoczko; arXiv:1701.04140

### Publications

- 9. "Hessenberg varieties and the Stanley-Stembridge conjecture," Oberwolfach Reports (2019), Mini-Workshop on Degeneration Techniques in Representation Theory; https://www.mfo.de/occasion/1941b
- 8. "The cohomology of abelian Hessenberg varieties and the Stanley-Stembridge conjecture," with Megumi Harada, Algebraic Combinatorics (2019); arXiv:1709.06736
- 7. "The singular locus of semisimple Hessenberg varieties," with Erik Insko, Journal of Algebra (2019); arXiv:1709.05423
- 6. "Springer fibers and Schubert points," with Julianna Tymoczko, European Journal of Combinatorics (2019); arXiv:1701.03502
- 5. "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)
- 4. "The Betti numbers of regular Hessenberg varieties are palindromic," Transformation Groups (2017); arXiv:1603.07662
- 3. "The connectedness of Hessenberg varieties," Journal of Algebra (2015); arXiv:1310.4212
- 2. "Affine pavings of Hessenberg varieties for semisimple groups," Selecta Mathematica (2013); arXiv:1205.3976v2
- 1. "Classification of Geometric Spirals," Pi Mu Epsilon Journal (2010)