Research Interest

  1. Number Theory
  2. Quantum Computation
  3. Optimization
  4. Machine Learning
  5. Combinatorics

I am an Assistant Professor in the Mathematical and Physical Sciences division at Ahmedabad University.

I received my PhD in mathematics in May 2018, from the University of Oklahoma, under the supervision of Dr. Ralf Schmidt. Subsequently, I joined the Department of Mathematics at the University of Manitoba as a Postdoctoral Fellow, and stayed there for the next two years.



Research

My research interests primarily lie in modular forms, automorphic forms and automorphic representations. I am interested in exploring the rich interplay between the classical methods and the automorphic representation theoretic methods, that often provides deep insights in number theory.

I am also interested in optimization, especially using randomized algorithms, quantum computational methods and machine learning tools.

        Publicatons

  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. ( with Ralf Schmidt. )
    Journal of the Ramanujan Mathematical Society, 34 (2019), 373-388.


  4. Trajectory optimization using quantum computing. ( with Prakash Vedula. )
    Shukla, A. & Vedula, P., Journal of Global Optimization (2019). https://doi.org/10.1007/s10898-019-00754-5.


  5. Means Compatible with Semigroup Laws. ( with R. Padmanabhan. )
    Quasigroups and Related Systems, 27 (2019), 317 - 324.


  6. Pullback of Klingen Eisenstein series and certain critical L-values identities.
    Ramanujan J (2020). https://doi.org/10.1007/s11139-019-00246-w.


  7. Preprints

  8. Tiling proofs of Jacobi triple product and Rogers-Ramanujan identities
    Pdf.


  9. When do we have 1 + 1 = 11 and 2 + 2 =5? ( with R. Padmanabhan. )
    Pdf.


  10. Machine learning based trajectory optimization. ( with Prakash Vedula. )
    Pdf.


  11. Orchards in elliptic curves over finite fields ( with R. Padmanabhan. )
    Pdf.


  12. My thesis: On Klingen Eisenstein series.
  13. Pdf.


Math Education

  1. On teaching mathematics to gifted students.
    Pdf.