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.

3. Motives of moduli spaces of stable quiver representations

With Sergey Mozgovoy, Markus Reineke and Rahul Singh. In Progress.

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