Ambar N. Sengupta
| Ambar N. Sengupta | |
|---|---|
 Ambar Sengupta.jpg Sengupta in 2016 | |
| Born | 20 July 1963 Calcutta, India |
| 🏳️ Nationality | American |
| 🎓 Alma mater |
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| 💼 Occupation | |
| 🌐 Website | math |
Ambar Niel Sengupta is an American mathematician. He is a professor of mathematics at the University of Connecticut. He has made contributions to different areas in mathematics and its applications.
Education and Career[edit]
Ambar Sengupta attended Presidency College, Calcutta and stood first class first in the B.Sc. (Mathematics Honours) examination of the University of Calcutta in 1984. He joined Cornell University, where he obtained an M.S. and then a Ph.D. 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 Professor of Mathematics in 2003 and 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.
Professional Activities[edit]
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.
Sengupta is the author of several scholarly volumes including Representing Finite Groups: A Semisimple Introduction[7] on the theory of representations of finite groups and Pricing Derivatives[8] in financial mathematics.
He has served as doctoral advisor or co-advisor to 8 PhD students[9].
Ambar Sengupta is the founding Managing Editor of the Journal of Stochastic Analysis.[10] He is a Council Member of the New England Statistical Society.[11] Besides serving on editorial boards, he has organized many professional conferences including several American Mathematical Society meetings.
Honors[edit]
Ambar Sengupta was awarded a Humboldt fellowship in 1995.[12] 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.[13][14] He has held visiting scholar positions at the Max Planck Institute in Bonn, 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.
Selected Publications[edit]
- Gross, Leonard; King, Christopher; Sengupta, Ambar. Two dimensional Yang-Mills theory via stochastic differential equations. Annals of Physics 194(1), 1989, 65-112.[15]
- Sengupta, Ambar: Quantum Gauge Theory on Compact Surfaces. Annals of Physics 221(1), 1993, 17-52.[16]
- Sengupta, Ambar: Gauge Theory on Compact Surfaces. Memoirs of the American Mathematical Society. 126(600), 1997, 1-85.[17]
- Albeverio, Sergio; Sengupta, Ambar: A Mathematical Construction of the Non-Abelian Chern-Simons Functional Integral. Communications in Mathematical Physics 186, 1997, 563–579.[18]
- Cochran, W. G.; Kuo, H.-H.; Sengupta, A.: A New Class of White Noise Generalized Functions. Infinite Dimensional Analysis, Quantum Probability and Related Topics 1(1), 1998, 43-67.[19]
- King, Christopher; Sengupta, Ambar: The semiclassical limit of the two‐dimensional quantum Yang–Mills model. Journal of Mathematical Physics 35, 1994, 5354-5361.[20]
- Sengupta, Ambar N.: The Volume Measure for Flat Connections as Limit of the Yang-Mills measure. Journal of Geometry and Physics 47(4), 2003, 398-426.[21]
- Sengupta, Ambar N.: Yang-Mills on Surfaces with Boundary: Quantum Theory and Symplectic Limit. Communications in Mathematical Physics 183, 1997, 661-705.[22]
- Anshelevich, Michael; Sengupta, Ambar N.: Quantum free Yang–Mills on the plane. Journal of Geometry and Physics 62(2), 2012, 330-343.[23]
- Sengupta, Ambar N.: Representing Finite Groups: A Semisimple Introduction. Springer, 2012.[24]
- Sengupta, Ambar N.: Pricing Derivatives: The financial concepts underlying the mathematics of pricing derivatives. McGraw-Hill, 2005.[25]
References[edit]
- ↑ "Ambar Sengupta Cornell PhD Dissertation".
- ↑ "LSU College of Science News".
- ↑ Lévy, Thierry (2003). "Yang-Mills Measure on Compact Surfaces". Memoirs of the American Mathematical Society. 166 (790).
- ↑ 4.0 4.1 Driver, Bruce; Gabriel, Franck; Hall, Brian C.; Kemp, Todd (2017). "The Makeenko-Migdal equation for Yang-Mills theory on compact surfaces". Communications in Mathematical Physics. 352 (3): 967?978.
- ↑ Lévy, Thierry; Norris, James R. (2006). "Large deviations for the Yang-Mills measure on a compact surface". Communications in Mathematical Physics. 261 (2): 405–450.
- ↑ Sengupta, Ambar N. (2003). "The Volume Measure for Flat Connections as Limit of the Yang-Mills measure". Journal of Geometry and Physics. 47 (4): 398–426.
- ↑ "Representing Finite Groups: A Semimsimple Introduction".
- ↑ "Pricing Derivatives: The financial concepts underlying the mathematics of pricing derivatives".
- ↑ "Mathematics Genealogy".
- ↑ "Journal of Stochastic Analysis".
- ↑ "New England Statistical Society Council Members".
- ↑ "Alexander von Humboldt".
- ↑ "New England Statistical Society Council Members Bios".
- ↑ "Mercator Fellows program".
- ↑ "Two dimensional Yang-Mills theory via stochastic differential equations". Annals of Physics. 194(1): 65–112.
- ↑ "Quantum Gauge Theory on Compact Surfaces". Annals of Physics. 221(1): 17–52.
- ↑ Sengupta, Ambar (1997). Gauge Theory on Compact Surfaces. American Mathematical Society. ISBN 9780821804841. Search this book on
- ↑ "A Mathematical Construction of the Non-Abelian Chern-Simons Functional Integral". Communications in Mathematical Physics. 186: 563–579. 1997.
- ↑ "A New Class of White Noise Generalized Functions". Infinite Dimensional Analysis, Quantum Probability and Related Topics. 1(1): 43–67. 1998.
- ↑ "The semiclassical limit of the two‐dimensional quantum Yang–Mills model". Journal of Mathematical Physics. 35: 5354–5361. 1994.
- ↑ "The volume measure for flat connections as limit of the Yang–Mills measure". Journal of Geometry and Physics. Volume 47, Issue 4: 398–426. 2003.
- ↑ "Yang-Mills on Surfaces with Boundary: Quantum Theory and Symplectic Limit". Communications in Mathematical Physics. 183: 661–705. 1997.
- ↑ "Quantum free Yang–Mills on the plane". Journal of Geometry and Physics. 62(2): 330–343. 2012.
- ↑ Sengupta, Ambar (2012). Representing Finite Groups: A Semisimple Introduction. Springer. pp. 1–371. ISBN 978-1-4614-1231-1. Search this book on
- ↑ Sengupta, Ambar (2005). Pricing Derivatives. USA: McGraw-Hill. pp. 1–282. ISBN 9780071445887. Search this book on
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