Research
1. Explicit formulas for mixed Hodge polynomials of character varieties of nilpotent groups
With Rahul Singh, submitted. arXiv: 2410.10008.
Let $\text{Hom}^0(\Gamma,G)$ be the path-connected component of the identity representation of the variety of representations of a finitely generated nilpotent group $\Gamma$ into a connected reductive complex affine algebraic group $G$. With the formulas given by Florentino, Lawton and Silva, we provide explicit partition type formulas for the mixed Hodge polynomials of character varieties when $G=Sp_{2n}$ and $G=SO_{n}$.
2. Motivic classes of stacks in finite characteristic and applications to stacks of Higgs bundles and bundles with connections
In Preparation. Poster/Slides
Let $X$ be a smooth projective curve over a field of finite characteristic. We calculate the motivic classes of the moduli stack of semistable Higgs bundles and bundles with connections on $X$. We follow the strategy of Fedorov and Soibelmans for motivic classes in characteristic zero. The main new ingredient is a version of Hua’s formula relating the motivic classes of bundles with endomorphisms to the motivic classes of geometrically indecomposable bundles with endomorphisms.