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Ambar N. Sengupta | |
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 Sengupta in 2016 | |
| Born | July 20, 1963 Calcutta, India |
| Nationality | American |
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| Scientific career | |
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| Doctoral advisor | Leonard Gross |
| Website | math |
Ambar Niel Sengupta is an Indian-American mathematician. He is a professor of mathematics at the University of Connecticut.
Ambar Sengupta attended Presidency College, Calcutta and stood first class first in the BSc (Mathematics Honours) examination of the University of Calcutta in 1984.[ citation needed ] He then joined Cornell University, where he obtained an MS and then a PhD under the supervision of Leonard Gross in 1990. [1]
After a post-doctoral appointment in the Physics Department of Princeton University, he joined Louisiana State University. He became a professor of mathematics in 2003, and he was awarded the Hubert Butts Alumni Professorship in 2011. [2] Sengupta joined the Mathematics faculty of the University of Connecticut as Professor and Head of the Department in 2016.[ citation needed ]
Sengupta's contributions have been in the fields of pure mathematics, mathematical physics, and financial mathematics.
In quantum field theory, Sengupta gave the first rigorous construction of the Yang-Mills measure for compact surfaces, with or without boundary and for bundles of specified topology. He used this to mathematically prove formulas that had been used in the physics literature and discovered new formulas for non-trivial bundles. [3] [4] He gave a 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. [5] [6] He is an initiator of the rigorous study of the large-N limit of Yang-Mills theory in two dimensions. He and Michael Anshelevich 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. [4] He has published extensively in infinite-dimensional geometry and measure theory, as well as higher gauge theory.
He has served as doctoral advisor or co-advisor to 8 PhD students. [7]
Ambar Sengupta is the founding Managing Editor of the Journal of Stochastic Analysis. [8] He is a Council Member of the New England Statistical Society. [9]
Ambar Sengupta was awarded a Humboldt fellowship in 1995. [10] He was named a Mercator Fellow by the Deutsche Forschungsgemeinschaft (German Research Foundation) in 2011; he was invited to a visiting professorship at the University of Bonn with this award. [11] [12]
In theoretical physics, twistor theory was proposed by Roger Penrose in 1967 as a possible path to quantum gravity and has evolved into a widely studied branch of theoretical and mathematical physics. Penrose's idea was that twistor space should be the basic arena for physics from which space-time itself should emerge. It has led to powerful mathematical tools that have applications to differential and integral geometry, nonlinear differential equations and representation theory, and in physics to general relativity, quantum field theory, and the theory of scattering amplitudes. Twistor theory arose in the context of the rapidly expanding mathematical developments in Einstein's theory of general relativity in the late 1950s and in the 1960s and carries a number of influences from that period. In particular, Roger Penrose has credited Ivor Robinson as an important early influence in the development of twistor theory, through his construction of so-called Robinson congruences.
In probability theory, the Schramm–Loewner evolution with parameter κ, also known as stochastic Loewner evolution (SLEκ), is a family of random planar curves that have been proven to be the scaling limit of a variety of two-dimensional lattice models in statistical mechanics. Given a parameter κ and a domain in the complex plane U, it gives a family of random curves in U, with κ controlling how much the curve turns. There are two main variants of SLE, chordal SLE which gives a family of random curves from two fixed boundary points, and radial SLE, which gives a family of random curves from a fixed boundary point to a fixed interior point. These curves are defined to satisfy conformal invariance and a domain Markov property.
In theoretical particle physics, maximally helicity violating amplitudes (MHV) are amplitudes with massless external gauge bosons, where gauge bosons have a particular helicity and the other two have the opposite helicity. These amplitudes are called MHV amplitudes, because at tree level, they violate helicity conservation to the maximum extent possible. The tree amplitudes in which all gauge bosons have the same helicity or all but one have the same helicity vanish.
Kalyanapuram Rangachari Parthasarathy was an Indian statistician who was professor emeritus at the Indian Statistical Institute and a pioneer of quantum stochastic calculus. Parthasarathy was the recipient the Shanti Swarup Bhatnagar Prize for Science and Technology in Mathematical Science in 1977 and the TWAS Prize in 1996.
Igor Rivin is a Russian-Canadian mathematician, working in various fields of pure and applied mathematics, computer science, and materials science. He was the Regius Professor of Mathematics at the University of St. Andrews from 2015 to 2017, and was the chief research officer at Cryptos Fund until 2019. He is doing research for Edgestream LP, in addition to his academic work.
In differential geometry, algebraic geometry, and gauge theory, the Kobayashi–Hitchin correspondence relates stable vector bundles over a complex manifold to Einstein–Hermitian vector bundles. The correspondence is named after Shoshichi Kobayashi and Nigel Hitchin, who independently conjectured in the 1980s that the moduli spaces of stable vector bundles and Einstein–Hermitian vector bundles over a complex manifold were essentially the same.
Twistor string theory is an equivalence between N = 4 supersymmetric Yang–Mills theory and the perturbative topological B model string theory in twistor space.
In theoretical physics, the AGT correspondence is a relationship between Liouville field theory on a punctured Riemann surface and a certain four-dimensional SU(2) gauge theory obtained by compactifying the 6D (2,0) superconformal field theory on the surface. The relationship was discovered by Luis Alday, Davide Gaiotto, and Yuji Tachikawa in 2009. It was soon extended to a more general relationship between AN-1 Toda field theory and SU(N) gauge theories. The idea of the AGT correspondence has also been extended to describe relationships between three-dimensional theories.
In theoretical physics, the six-dimensional (2,0)-superconformal field theory is a quantum field theory whose existence is predicted by arguments in string theory. It is still poorly understood because there is no known description of the theory in terms of an action functional. Despite the inherent difficulty in studying this theory, it is considered to be an interesting object for a variety of reasons, both physical and mathematical.
Gérard Ben Arous is a French mathematician, specializing in stochastic analysis and its applications to mathematical physics. He served as the director of the Courant Institute of Mathematical Sciences at New York University from 2011 to 2016.
François Ledrappier is a French mathematician.
Roberto Longo is an Italian mathematician, specializing in operator algebras and quantum field theory.
Shen Weixiao is a Chinese mathematician, specializing in dynamical systems.
Leonard Gross is an American mathematician and Professor Emeritus of Mathematics at Cornell University.
Olaf Lechtenfeld is a German mathematical physicist, academic and researcher. He is a full professor at the Institute of Theoretical Physics at Leibniz University, where he founded the Riemann Center for Geometry and Physics.
In mathematical physics, two-dimensional Yang–Mills theory is the special case of Yang–Mills theory in which the dimension of spacetime is taken to be two. This special case allows for a rigorously defined Yang–Mills measure, meaning that the (Euclidean) path integral can be interpreted as a measure on the set of connections modulo gauge transformations. This situation contrasts with the four-dimensional case, where a rigorous construction of the theory as a measure is currently unknown.
Klaus Fredenhagen is a German theoretical physicist who works on the mathematical foundations of quantum field theory.
Alberto Sergio Cattaneo is an Italian mathematician and mathematical physicist, specializing in geometry related to quantum field theory and string theory.
Robert Schrader was a German theoretical and mathematical physicist. He is known for the Osterwalder–Schrader axioms.
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