Ambar Sengupta

Ambar Niel Sengupta is an American mathematician. He is a professor of mathematics at the University of Connecticut. He has made contributions to a wide range of areas in mathematics, mostly centered in mathematical physics.

Education and career
Ambar Sengupta attended  Presidency College, Calcutta,  receiving a bachelor's degree, and  Cornell University, where he obtained his PhD in Mathematics in 1990, working under the supervision of Leonard Gross. His doctoral dissertation was titled The Yang-Mills Measure for the Two-Sphere.

Sengupta held a post-doctoral appointment (1990-1991) at Princeton University in the Physics Department, where he also served as an Instructor. In 1991 Sengupta joined the Mathematics Faculty of Louisiana State University as Assistant Professor. He was promoted to Professor in 2003 and named Hubert Butts Alumni Professor in 2011. In 2016 Sengupta joined the Mathematics faculty of the University of Connecticut as Professor and Head of the Department. He retains the title of Hubert Butts Professor Emeritus at Louisiana State University.

Ambar Sengupta has served as doctoral advisor or co-advisor to 8 PhD students. He has also supervised several Master's theses.

Scholarly work
Sengupta's scientific work has been inspired mostly by questions from quantum field theory. Much of his work in mathematics physics has focused on Yang-Mills theory. He gave the first rigorous construction of the Yang-Mills measure for compact surfaces, with or without boundary and for bundles of specified topology. Using this theory he computed Wilson loop  expectation values, providing a mathematically rigorous proof of formulas that had been used in the physics literature and extending these formulas to the case of non-trivial bundles. Sengupta also gave a mathematically rigorous proof of Edward Witten's formula for the volume of the moduli space of flat connections on a compact oriented surface, and proved that the Yang-Mills measure converges to this limiting measure in a suitable sense. Sengupta was also one of the initiators of the rigorous study of the large-N limit of Yang-Mills theory in two dimensions. Along with Michael Anshelevich, he showed that the limit of the $$U(N)$$ Yang-Mills measure for the plane is described by free probability theory, confirming ideas initiated by I. M. Singer.

Working with Sergio Albeverio and Atle Hahn, Sengupta gave a mathematical construction of the Chern-Simons functional integral.

Sengupta has also done extensive work on infinite-dimensional geometry and measure theory, as well as higher gauge theory. Along with Saikat Chatterjee and Amitabha Lahiri, Sengupta  developed a categorical geometric theory for bundles over (higher) path spaces.

Sengupta is the author of Representing Finite Groups: A Semisimple Introduction, an introduction to the theory of representations of finite groups that is inspired by the original works of Frobenius. Sengupta is the editor of several volumes and research monographs.

Outside of pure mathematics and mathematical physics, Sengupta has also worked extensively in financial mathematics. His book Pricing Derivatives presents a conceptual mathematical framework for the notion of risk-neutral measure in pricing and derives the Black-Scholes formula from the abstract framework with minimal additional machinery such as stochastic analysis.

Professional work
Ambar Sengupta is the founding Managing Editor of the Journal of Stochastic Analysis, a journal founded in 2020 by Hui-Hsiung Kuo. He has served on the editorial board of the journal Infinite Dimensional Analysis, Quantum Probability, and Related Topics. Sengupta has organized or co-organized numerous professional events. He is a founding Council Member of the New England Statistical Society.

Awards and visiting positions
Ambar Sengupta was awarded a Humboldt fellowship in 1995. He spent the year 1995–1996 at the Ruhr University in Bochum, Germany, working with Sergio Albeverio. In 2011 he was awarded a Mercator Fellows Visiting Professorship by the Deutsche Forschungsgemeinschaft, and was a visiting faculty at the University of Bonn with this award. Sengupta has held several other visiting positions, including at the University of Paris, the École normale supérieure (Paris), the Indian Statistical Institute, and the S. N. Bose National Centre for Basic Sciences in Kolkata, India.