My research interests include canonical bases in geometric representation theory, cluster algebras, and categorification.
Ongoing projects
- Tesler Matrices and Lusztig Data. This is a project inspired by Nathan Williams (Figure 1) with mentees Ivan Balashov, Constantine Bulavenko, and Yaroslav Molybog for Yulia's Dream program. We show that Tesler matrices are a subposet of Lusztig data, and we study implications for parking functions and diagonal harmonics.
- Quantized Duistermaat-Heckman measure. We extend the notion of Duistermaat–Heckman measure in the context of geometric Satake to the derived setting, identifying equivariant multiplicities of MV cycles w.r.t. loop rotation and certain invariants of quantized universal centralizers.
Past projects
- Spectral 2-actions, foams, and frames in the spectrification of Khovanov arc algebras with Meng Guo, Aaron Lauda and Andy Manion. 2402.11368.
- Extremal tensor products of Demazure crystals with Sami Assaf and Nicolle Gonzalez arXiv:2210.10236
- Heaps, crystals, and preprojective algebra modules with Balazs Elek, Joel Kamnitzer and Calder Morton-Ferguson arXiv:2202.02490
- Computing fusion products of MV cycles using the Mirkovic-Vybornov isomorphism with Roger Bai and Joel Kamnitzer arXiv:2106.07101
Thesis work
- Comparing two perfect bases arXiv:2105.14420 and Appendix to The Mirkovic-Vilonen basis and Duistermaat-Heckman measures with Joel Kamnitzer and Calder Morton-Ferguson arXiv:1905.08460
- Generalized orbital varieties for Mirkovic-Vybornov slices as affinizations of Mirkovic-Vilonen cycles arXiv:1905.08174