PhD (University of Oklahoma)
Research Interests: Modular Forms, Automorphic Forms And Representations.
Alok Shukla is an Assistant Professor in the Mathematical and Physical Sciences division of the School of Arts and Sciences at Ahmedabad University. He received a Bachelor of Engineering degree in Electrical and Electronics Engineering from Birla Institute of Technology, Ranchi, and a MA and PhD in Mathematics from the University of Oklahoma, USA. He was selected for several scholarship awards by the Department of Mathematics at Oklahoma during his PhD, including the John Clark Brixey Graduate Scholarship award in 2015, and the Richard V. Andree Memorial Scholarship awards for academic excellence in 2016 and 2017. After receiving his PhD in 2018, Professor Shukla joined the Department of Mathematics at the University of Manitoba, Canada, as a Postdoctoral Fellow.
Prior to pursuing his doctoral studies in Mathematics, Professor Shukla worked for HAL (Hindustan Aeronautical Limited) for several years, first on the Avionics system of MiG-27 fighter aircraft, and later in the final assembly section of ALH (Advanced Light Helicopter), Dhruv. He learned the basics of Aeronautical Engineering in a special one-semester programme at IIT, Madras in 2004. He has also worked as a software engineer for IBM and TCS, for about a year in each organisation. In addition to research in Mathematics, he enjoys teaching the subject to students. Professor Shukla has organised several maths-popularisation and community outreach events to spread the ‘Joy of Mathematics’ among young students.
Professor Shukla has research interests in number theory, and is primarily interested in classical and adelic modular forms, automorphic forms and representations.
He has worked on a representation theoretic approach to the Klingen lift in degree two, and generalize the classical construction of the Klingen-Eisenstein series to arbitrary levels for both paramodular and Siegel congruence subgroups.
Professor Shukla’s research interests come under the general umbrella of the ‘Langlands program’, which has emerged in recent years as a kind of ‘grand unified theory’ of Mathematics.
Professor Shukla is also interested in the areas of classical number theory influenced by the work of Ramanujan, such as Partitions, and q-series identities.
Besides his primary research interests in number theory, he has broad research interests in several other areas of Mathematics including combinatorics and quantum computational algorithms.
A fun fact: Professor Shukla’s Erdős number is 3.
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. Orchards in elliptic curves over finite fields, (with R. Padmanabhan), Finite Fields and Their Applications, Volume 68, 2020, 101756, ISSN 1071-5797, https://doi.org/10.1016/j.ffa.2020.101756.
8. When do we have 1 + 1 = 11 and 2 + 2 =5?, (with R. Padmanabhan),To appear in The Mathematical Gazette. (Preprint - https://arxiv.org/pdf/1906.02324.pdf)