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

- 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.** - A short proof of Cayley's Tree Formula.
**The American Mathematical Monthly, 125(2018), no.~1,65-68.** - On Klingen Eisenstein series. ( withJournal of the Ramanujan Mathematical Society, 34 (2019), 373-388.
**Ralf Schmidt.**) - Trajectory optimization using quantum computing. ( withShukla, A. & Vedula, P., Journal of Global Optimization (2019). https://doi.org/10.1007/s10898-019-00754-5.
**Prakash Vedula.**) - Means Compatible with Semigroup Laws. ( withQuasigroups and Related Systems, 27 (2019), 317 - 324.
**R. Padmanabhan.**) - Pullback of Klingen Eisenstein series and certain critical L-values identities.Ramanujan J (2020). https://doi.org/10.1007/s11139-019-00246-w.
- Tiling proofs of Jacobi triple product and Rogers-Ramanujan identitiesPdf.
- When do we have 1 + 1 = 11 and 2 + 2 =5? ( withPdf.
**R. Padmanabhan.**) - Machine learning based trajectory optimization. ( withPdf.
**Prakash Vedula.**) - Orchards in elliptic curves over finite fields ( withPdf.
**R. Padmanabhan.**) - My thesis: On Klingen Eisenstein series.

### Preprints

**Pdf.**