November 2022
Assistant Professor
School of Physical Sciences
Jawaharlal Nehru University
New Delhi 110067
vedgupta AT mail.jnu.ac.in, ved.math AT gmail.com
Ph: +91 11 2673 8818
Research interests
Operator Algebras : Subfactors, Planar Algebras, Subalgebras of C*-algebras, Operator Systems, Operator Spaces
Banach Algebras: Certain algebraic aspects of Banach algebras coming from various tensor products of C*-algebras/Banach algebras
Collaborators till date: Shamindra Kumar Ghosh (ISI Kolkata), Paramita Das (ISI Kolkata), Preeti Luthra ( when a PhD student at DU), Ranjana Jain (University of Delhi), Keshab Chandra Bakshi (IIT Kanpur), Bharat Talwar (when a PhD student at DU), Lav Kumar Singh (when a PhD student at JNU), Deepika Sharma (when a PhD student at JNU), Sumit Kumar (PhD student at JNU)
Book(s)
The Functional Analysis of Quantum Information Theory (with P. Mandayam and V. S. Sunder), Lecture Notes in Physics 902, Springer, 2015.
Expository article(s)
On the topology of certain matrix groups (with Mukund Madhav Mishra), The Mathematics Student, 87 (3-4), July-December 2018, 61 - 71. For B.Sc. and M.Sc. students.
Research articles
Regular inclusions of simple unital C*-algebras (with Keshab Chandra Bakshi). Preprint available at arXiv:2404.06959.
On various notions of distance between subalgebras of operator algebras (with Sumit Kumar). Preprint available at arXiv:2403.05967
On possible values of the interior angle between intermediate subalgebras (with Deepika Sharma), J. Aust. Math. Soc. (2023 online). Preprint available at arxiv:2211.07291
On strong Arens irregularity of projective tensor product of Hilbert-Schmidt space (with Lav Kumar Singh), Houston J. Mathematics 48 (2) (2022), 337-351. Preprint available at arXiv:2108.13946 (2022)
A few remarks on Pimsner-Popa bases and regular subfactors of depth 2 (with Keshab Chandra Bakshi), Glasgow Math. J. 64 (3) (2022), 586-602.
Lattice of intermediate subalgebras (with Keshab Chandra Bakshi), J. London Math. Soc. 104 (5) (2021), 2082-2127.
On closed Lie ideals and center of generalized group algebras (with Ranjana Jain and Bharat Talwar), J. Math. Anal. Appl. 502 (1) (2021), 125228.
On orthogonal systems, two-sided bases and regular subfactors (with Keshab Chandra Bakshi), New York J. Math., 26 (2020), 817-835.
A note on irreducible quadrilaterals of $II_1$-factors (with Keshab Chandra Bakshi), Internat. J. Math., 30 (12), 1950061, 2019.
On closed Lie ideals of certain tensor products of C*-algebras II (with Ranjana Jain and Bharat Talwar), Math. Nachr., 293 (1), 101-114, 2020.
On Banach space projective tensor product of C*-algebras (with Ranjana Jain), Banach J. Math. Anal. 14, 524 - 538, 2020.
On closed Lie ideals of certain tensor products of C*-algebras (with Ranjana Jain), Math. Nachr., 291 (8-9), 1297-1309, 2018.
Operator system nuclearity via C*-envelopes (with Preeti Luthra), J. Aust. Math. Soc., 101, 356 - 375, 2016.
Drinfeld center of planar algebra (with Paramita Das and Shamindra Ghosh), Internat. J. Math., 25(8), 43 pages, 2014.
Affine modules and the Drinfeld center (with Paramita Das and Shamindra Ghosh), Math. Scand., 118(1), 119-151, 2016.
Perturbations of Planar Algebras (with Paramita Das and Shamindra Ghosh), Math. Scand., 114(1), 38-85, 2014.
Planar Algebra of the Subgroup-Subfactor, Proc. Ind. Acad. Sci. (Math. Sci.). 118 (4), 583-612, 2008.
Academic Experience
Assistant Professor, School of Physical Sciences, Jawaharlal Nehru University (JNU), New Delhi (May 2013 - present)
Assistant Professor, Dept. of Mathematics, School of Natural Sciences, Shiv Nadar University (SNU), Gautam Buddh Nagar, UP (August 2011 - May 2013)
Postdoctoral Fellow, Institute of Mathematical Sciences, Chennai (August 2010 - August 2011)
Postdoctoral Fellow, Dept. of Mathematics, Katholieke Universiteit, Leuven, Belgium (November 2008- July 2010)
Visiting Scientist, Indian Statistical Institute, Delhi Center, New Delhi (June 2008 - November 2008)
Research Scholar, Institute of Mathematical Sciences, Chennai (August 2003 - June 2008)
Courses taught at JNU (August 2013 - present)
Pre Ph.D./Course Work (Ph.D.):
Analysis, Functional Analysis and Operator Theory, Topology, Research Course on "Basics of Operator Algebras"
M.Sc.: Complex Analysis, Functional Analysis, Ordinary Differential Equations, Real Analysis, Discrete Mathematics, Harmonic Analysis, Banach Algebras and Operator Algebras
Courses taught at SNU (August 2011 - May 2013)
MS: Advanced Linear Algebra, Functional Analysis
BS: Precalculus, Real Analysis I
B.Tech: ODEs, Probability and Statistics, Calculus II
Ph.D. students
Kislay Kishor (Started in August 2014, took up a teaching job in 2017 -- pursuing from distance)
Lav Kumar Singh (Started in August 2018 - Defended in November 2022). At present, a PDF at IISER Bhopal.
Deepika Sharma (Started in July 2020, took up a teaching job in December 2022 -- pursuing from distance)
Sumit Kumar (Pursuing: Started in September 2021)
A list of books on Banach algebras and operator algebras
oa-books.docxA (partial) list of operator theorists and operator algebraists in India.
op-algebraists-n-op-theorists.docxOperator Algebras Miscellany
Operator Algebras on arXiv .
Operator Algebra Searchable Information Website (Directory, Journals and Opportunities)
A very useful list of editors in operator algebras is maintained by Hannes Theil at http://hannesthiel.org/oa-editors
Some important open problems in Operator Algebras : List maintained by Jesse Peterson
Operator Algebras events across the world:
Lists maintained by Narutaka Ozawa and Paulo R. Pinto.
Some online notes on Operator Algebras
Notes on Operator Algebras by Jesse Peterson.
A good collection of notes on different topics of Operator Algebras by Paul Skoufranis.
Notes on von Neumann algebras by (Late) Vaughan Jones.
Notes by L. W. Marcoux
Notes on von Neumann algebras by Brent Nelson.
Notes on von Neumann algebras by Ronaldo de Santiago and Brent Nelson.
Miscellaneous
Some useful articles:
A treasure of expository mathematical articles by Keith Conrad.
Some funding agencies in India for (present and prospective) mathematicians:
MATRICS: Financial support for research in mathematics by Science and Engineering Research Board.
Financial supports provided by National Board for Higher Mathematics .