Research Interest

  • Number Theory
  • Automorphic Forms
  • Combinatorics
  • Optimization
  • My research interests primarily lie in modular forms, automorphic forms and automorphic representations . I am especially interested in the rich interplay between the classical methods and the autmorphic representation theoretic methods, that often provides deep insights. We have developed a complete theory of Klingen Eisenstein series using automorphic representations, both with respect to paramodular and Siegel congruence subgroups. I am also interested in the paramodular conjecture, which predicts a connection between abelian surfaces and Siegel modular forms with respect to the paramodular subgroups.

    I am also interested in optimization, especially using randomized algorithms and quantum computation.

    Publicatons & preprints

    1. Co-dimensions of the spaces of cusp forms for Siegel congruence subgroups in degree two, Pacific Journal of Mathematics 293(2018), no. 1, 207–244.
    2. A short proof of Cayley's Tree Formula, The American Mathematical Monthly, 125(2018), no.~1,65-68.
    3. On Klingen Eisenstein series. (Submitted, with Ralf Schmidt.)
    4. Some interesting connections. (Submitted.)