Contemporary Research in Mathematics from India
Description
This volume brings together fourteen essays authored by distinguished mathematicians from India, offering a panoramic view of current research directions as well as recent historical developments in mathematics in India. The articles cover diverse topics-number theory, operator algebra, operator theory, harmonic analysis, quantum learning, noncommutative geometry and random matrices-showcasing the breadth and depth of contemporary mathematical research. The book provides a vivid snapshot of mathematical thought as it evolves today, connecting tradition with innovation and offering both insight and inspiration to the next generation of mathematicians.
The volume opens with an illuminating essay by M. S. Raghunathan, "Some Highlights of Indian Contributions to Mathematics in the 20th Century", a comprehensive historical account of post-Independence mathematical research in India that will inspire young readers and scholars alike. A special inclusion is the research article "Symmetric Products and Moduli Spaces of Vector Bundles on Curves" by Kyoung-Seog Lee and the late M. S. Narasimhan, completed shortly before Narasimhan's passing in 2021. This paper, which has already attracted wide attention in the research community, stands as a fitting tribute to his enduring influence in algebraic geometry.
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Gadadhar Misra
is currently Visiting Professor in the Department of Mathematics at the Indian Institute of Technology Gandhinagar, Gujarat. He previously served as Professor and Chair of the Department of Mathematics at the Indian Institute of Science (IISc), Bengaluru, and as Head of the Indian Statistical Institute, Bangalore Centre. A distinguished mathematician, inspiring teacher and active researcher, he is a Fellow of the Indian Academy of Sciences, the Indian National Science Academy (where he served as Vice President, 2018-2020), and the National Academy of Sciences, India. He was also a recipient of the J. C. Bose Fellowship (2008-2023). Besides, he received the Shanti Swarup Bhatnagar Prize (2001) and the Biju Patnaik Award for Scientific Excellence (2013), awarded by the Odisha Bigyan Academy in recognition of his outstanding research and academic contributions.
His research interests lie in operator theory, functional analysis and Hilbert modules, and he has played a major role in promoting collaborative research and strengthening mathematics education in India. After completing his master's degree from Sambalpur University, he earned his Ph.D. under the supervision of Prof. Ronald G. Douglas at Stony Brook University, USA. His dissertation, "Curvature Inequalities and External Properties of Bundle Shifts", set the course for a career devoted to deep mathematical inquiry. He has collaborated with several eminent mathematicians and young researchers alike, contributing notably to the study of homogeneous operators, Hilbert modules and geometric invariants of quotient modules. He has published extensively in leading national and international journals and has supervised numerous doctoral students.
Content
Some Highlights of Indian Contributions to Mathematics in the 20th Century.- Convex Analysis-Statistical Theory of Decisions and of Machine Learning Classical and Quantum.- Symmetric Products and Moduli Spaces of Vector Bundles of Curves.- Classification of C algebras, Spaces of Operators and Function Spaces using the Geometry of Banach Spaces.- Contribution to Random Matrices by Indian statisticians and Probabilists: A Brief Survey.- Normalisation of Scores, Multiple Choice Questions, over Multi-phase Tests.- Recent Developments in Analytic Number Theory.- A brief history of Noncommutative Geometry in India.- A Compendium of Research in Operator Theory and Operator Algebra.- Hardy-Hilbert Spaces for General Domains.- The Geometry of Bruhat-Tits Groups.- A Survey of Fourier Analysis on Riemannian Symmetric Spaces: Contribution of Indian Mathematicians (2000-2025).- Positivity and Negativity Preservers under the Entrywise Calculus.- A Survey and a Result on Inhomogeneous Quadratic Forms.