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Prof. Shukla commenced his research career under the supervision of Prof. K. K. Azad, with a focus on Wavelet Analysis, particularly Multiresolution Analysis, Scaling Sets, Wavelet Sets, Non-MSF Wavelets, and their topological properties. He was awarded the Doctor of Philosophy (D.Phil.) degree in Mathematics by the University of Allahabad in 2010. His doctoral research was supported by CSIR Junior Research Fellowship (JRF) and Senior Research Fellowship (SRF).
Following the completion of his doctoral studies, Prof. Shukla served as a Guest Faculty member in the Department of Mathematics, University of Allahabad, during 2010–2011 session. From February 2011 to March 2012, he taught Mathematics at the undergraduate and postgraduate levels at several institutions, including RKGIT, Ghaziabad; Galgotias University; UCER, Prayagraj; and the Central University of Bihar, Patna.
In April 2012, Prof. Shukla joined the IIT Indore as an Assistant Professor. Since then, he has made significant contributions to teaching and research at both the undergraduate and postgraduate levels. His research interests encompass Harmonic Analysis, Sampling Theory, and Frame and Wavelet Analysis. Since October 2023, Prof. Shukla has been serving as a Professor at IIT Indore.
Prof. Shukla has actively participated in academic programmes, conferences, and research activities at various institutions in India and abroad. His international academic engagements have included visits to Argentina, Israel, Italy, Switzerland, Germany, Austria, France, Belgium and other countries. He has established research collaborations with scholars from India, Canada, Denmark, Germany, and other countries. He has also supervised several Ph.D. scholars and M.Sc. students in diverse areas of Mathematics.
Prof. Shukla served as Head of the Department of Mathematics at IIT Indore from September 17, 2021, to December 31, 2024, providing academic and administrative leadership to the Department. In addition to his academic, research, and administrative responsibilities, he has been actively engaged in institutional and societal outreach initiatives aligned with various programmes of the Government of India. Since January 2020, in his capacity as Convener of Ek Bharat Shreshtha Bharat at IIT Indore, he has been associated with initiatives including Ek Bharat Shreshtha Bharat, Rashtriya Avishkar Abhiyan, Unnat Bharat Abhiyan, Swachh Bharat Abhiyan, and RuTAG.
Since September 2025, Prof. Shukla has also been serving as the Convener of the Rajbhasha Hindi Samiti at IIT Indore. Through his sustained contributions to teaching, research, academic administration, and societal outreach, Prof. Shukla continues to contribute significantly to the advancement of Mathematics and higher education, while supporting initiatives aimed at social welfare and national development.