Faculty Fellows

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, combinatorics, and quantum computing.

In number theory, he 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. He is also interested in the areas of classical number theory influenced by the work of Ramanujan, such as Partitions, and q-series identities. 

Professor Shukla has a keen research interest in quantum computing and its applications. He is interested in applications of quantum computing for the solution of nonlinear ordinary and partial differential equations. He has used a Walsh-Hadamard basis functions-based approach to discover a hybrid classical-quantum algorithm for solving nonlinear ordinary differential equations. He has also applied a similar approach to obtain a hybrid classical-quantum algorithm for digital image processing applications. 

• A generalization of Bernstein–Vazirani algorithm with multiple secret keys and a probabilistic oracle, (with Prakash Vedula), Quantum Information Processing, 22, 244 (2023). https://doi.org/10.1007/s11128-023-03978-3. (Preprint: https://arxiv.org/pdf/2301.10014)
• A hybrid classical-quantum algorithm for digital image processing, (with Prakash Vedula), Quantum Information Processing, 22, 3 (2023). https://doi.org/10.1007/s11128-022-03755-8. (Preprint: https://arxiv.org/pdf/2208.09714.pdf)
• A hybrid classical-quantum algorithm for solution of nonlinear ordinary differential equations, (with Prakash Vedula), Applied Mathematics and Computation, Volume 442, 2023, 127708, ISSN 0096-3003, https://doi.org/10.1016/j.amc.2022.127708. (Preprint: https://arxiv.org/pdf/2112.00602.pdf)
• Tiling proofs of Jacobi triple product and Rogers-Ramanujan identities, to appear in the Journal of the Ramanujan Mathematical Society. (Preprint: https://arxiv.org/pdf/2006.03878.pdf)
• When do we have 1 + 1 = 11 and 2 + 2 = 5? (with R. Padmanabhan), The Mathematical Gazette, 106(566), 319-323. doi:10.1017/mag.2022.74  (Preprint: https://arxiv.org/pdf/1906.02324.pdf)
• Pullback of Klingen Eisenstein series and certain critical L-values identities. Ramanujan Journal, 55, 471–495 (2021). https://doi.org/10.1007/s11139-019-00246-w.  (Preprint: https://arxiv.org/pdf/2006.05273)
• 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  (Preprint: https://arxiv.org/pdf/2003.07172.pdf)
• Trajectory optimization using quantum computing, (with Prakash Vedula), Journal of Global Optimization, 75, 199-225 (2019). https://doi.org/10.1007/s10898-019-00754-5  (Preprint: https://arxiv.org/pdf/1901.04123.pdf)
• On Klingen Eisenstein series, (with Ralf Schmidt), Journal of the Ramanujan Mathematical Society, 34 (2019), 373-388.
• Means Compatible with Semigroup Laws, (with R. Padmanabhan), Quasigroups and Related Systems, 27 (2019), 317 - 324 (Preprint: https://arxiv.org/pdf/1902.10809)
• A short proof of Cayley's Tree Formula. The American Mathematical Monthly, 125(2018), no.~1,65-68. (Preprint: https://arxiv.org/pdf/0908.2324.pdf)
• 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.
• On Klingen Eisenstein series with levels, (PhD Dissertation), https://shareok.org/bitstream/handle/11244/299326/2018_Shukla_Alok_Dissertation.pdf

Preprint:

• A quantum algorithm for counting zero-crossings,  https://arxiv.org/abs/2212.11814
• An efficient quantum algorithm for preparation of uniform quantum superposition states, https://arxiv.org/pdf/2306.11747.pdf 

Monsoon 2024

• MAT256 - Differential Equations
• MAT485 / MAT585 - Introduction to Quantum Computing

Winter 2023

• MAT248 - Applied Linear Algebra
• MAT334 - Introductory Real Analysis

Monsoon 2022

• MAT142 - Introductory Calculus
• MAT465 / MAT565 - Fourier Analysis and Its Applications
• PHY798 Research Project - II

Winter 2022

• MAT248 - Applied Linear Algebra
• MAT442 - Complex Analysis
• MAT485 / MAT585 - Introduction to Quantum Computing

Monsoon 2021

• MAT256 - Differential Equations

Winter 2021

• MAT246 - Introduction to Linear Algebra