Research
Research
In my research, I use tools from algebraic geometry, topology, and algebraic combinatorics to study the relationship between affine Springer fibers and triply graded link homology.
There are several interesting open questions and conjectures about the homology of affine Springer fibers and their cell structure, as well as open problems around computing Khovanov-Rozansky homology (denoted HHH) of links. My research so far has focused on studying unramified affine Springer fibers and on computing HHH for the associated Coxeter links and comparing the results.
Affine Springer Fibers and Generalized Haiman Ideals (with an Appendix by Eugene Gorsky and Joshua P. Turner) International Mathematics Research Notices (2024), https://doi.org/10.1093/imrn/rnae146, arXiv:2310.07215.
Triply Graded Link Homology for Coxeter Braids on 4 Strands arXiv preprint (2024), arXiv:2410.03068
Haiman Ideals, Link Homology, and Affine Springer Fibers.
-Topology Seminar, October 8, 2024, UNC Chapel Hill.
-Combinatorics Seminar, September 11, 2024, UC Berkeley.
-Algebra Seminar, April 11, 2024, University of Oregon.
-Student Run Research Seminar, April 3, 2024, UC Davis.
GKM Theory and Koszul Duality. Reading Course on GKM Theory, November 2023, UC Davis.
Properties of the Euler Class. Reading Course on Characteristic Classes, November 2023, UC Davis.
Affine Springer Fibers. Reading Course on HOMFLY Homology, February 26, 2023, UC Davis.
Homology of Affine Springer Fibers. Student Run Research Seminar, November 9, 2022, UC Davis.
Braids Reunion Workshop, July 2024, ICERM.
WAGS (Western Algebraic Geometry Symposium), April 2024, UC Davis. Presented a poster on Affine Springer Fibers and Haiman Ideals.
Workshop on the Enumerative geometry of the Hilbert scheme of points, January 2024, SwissMAP Research Station.
Joint Mathematics Meetings (JMM), January 2024, San Francisco, CA.
WAGS, November 2023, WashU - Presenting a poster on Affine Springer Fibers.
Algebra, Geometry, and Combinatorics of Link Homology Workshop, August 2023, AIM, Pasadena.
FPSAC, July, 2023, UC Davis.
WAGS, April 2023, University of Washington. Presented a Poster on Affine Springer Fibers.
WAGS, November 2022, UC Riverside.
Summer School in Geometric Representation Theory, July 2022, MIT.