Research

You can find my papers on arXiv.

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. arXiv: 2509.09861.

We define a ring of motivic classes of stacks suitable for symmetric powers in finite characteristic. Let $X$ be a smooth projective curve over a field of arbitrary characteristic. We calculate the motivic classes of the moduli stacks of semistable Higgs bundles on $X$. This recovers results of Fedorov, A. Soibelman and Y. Soibelman in characteristic zero, as well as those of Mozgovoy and Schiffmann for finite fields. We also obtain a simpler formula for the motivic classes of Higgs bundles in the universal $\lambda$-ring quotient using Mellit’s results.

3. Motives of moduli spaces of stable quiver representations (with Sergey Mozgovoy, Markus Reineke and Rahul Singh). In progress.

4. Motivic classes of stacks of bundles with connections (with Roman Fedorov). In progress.