Urshita Pal

Research interests

I study the cohomology of arithmetic groups using tools from algebraic topology, combinatorial topology, and homological algebra. Specifically, I study the cohomology of special linear and symplectic groups over a number ring, and their finite index subgroups. My approach to this is via studying certain representations of these groups called Steinberg modules. Steinberg modules can be defined in terms of certain simplicial complexes, thus allowing for combinatorial techniques to come into play. I am also interested in (co)homological stability patterns in families of groups and topological spaces.
Overall, I tend to enjoy any math that involves an interplay of topology, algebra, and combinatorics.

Papers

A projective resolution of the symplectic Steinberg module
  Arxiv preprint Arxiv:2605.06499

The top degree cohomology of principal congruence subgroups of special linear groups over Euclidean domains
  Arxiv preprint Arxiv:2605.05087

Representation stability in the (co)homology of vertical configuration spaces
  with D Baron, C Wang, J Wilson, and C Yang.
  ArXiv preprint ArXiv:2412.01128