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Department of Mathematics
Neha Gupta
Assistant Professor,
Department of Mathematics,
School of Natural Sciences
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Education Qualifications
Ph.D. in Mathematics from University of Warwick, Coventry, UK.Supervisor: Asst Professor Dmitriy Rumynin, University of Warwick, UK. (2007 – 2011)
M.Sc. in Mathematics, scoring 86.25%, from University of Delhi, Delhi, India. (2004 – 2006)
Bachelor in Education, scoring 80.7%, from GGS Indraprastha University, Delhi, India. (2003 – 2004)
P.G. Diploma in Educational Planning and Management, scoring 79%, from Amity Institute of Education, Amity University, Noida, India. (2003 – 2004)
B.Sc. (Hons) in Mathematics, scoring 82%, from University of Delhi, Delhi, India. (2000 – 2003)
eDiploma in Advanced Software Technology (eDAST), obtaining grade A, from CMC Ltd., New Delhi, India. Ph.D. from University of Warwick , U.K. (2000 – 2002)
Professional/Teaching Experience
Assistant Professor in Mathematics at Amity University, Noida. I was teaching maths to B.Tech. Students and Computers to M.Sc. (Computer Maths)(2011 – 2012)
Teaching Assistance for Groups and Representations, University of Warwick, UK. Supervisions for the 1st year, Undergraduate, Discrete Maths, University of Warwick, UK.(2010)
Assistance in Fundamental Tools for Financial Mathematics, University of Warwick, UK.(2010)
Assistance in Further Mathematics, University of Warwick, UK.(2008)
Supervisions for the 1st year, Undergraduate, MMaths, University of Warwick, UK.(2007 – 2011)
Teaching Maths and Physics to A-level (Sr. Secondary), Summer Field School, Gurgaon, India.(2007)
Select Publications
Book titled "Quantum Groups and Homotopy Quantum Field Theory" with ISBN-13: 978-3847338574
Executive Summary
I have done Ph.D. from University of Warwick, under the supervision of Dr. Dmitriy Rumynin. I am working in Homotopy Quantum Field Theory (HQFT) in dimension 2 and dimension 3. Here is an abstract for my work:
Abstract for my work:
There are basically two parts one for dimension 2 and the other for dimension 3. In dimension one there is a generalisation of the definition of an $n$-dimensional HQFT in terms of a monoidal functor from a rigid symmetric monoidal category $X_n$ to any monoidal category $A$. In particular, 2-dimensional HQFTs with target $K(G,1)$ taking values in $A$ are generated from any Turaev $G$-crossed system in $A$ and vice versa. This is the generalisation of the theory given by Turaev into a purely categorical set-up.

In dimension two there is a generalisation of the concept of a group-coalgebra, Hopf group- coalgebra, crossed Hopf group-coalgebra and quasitriangular Hopf group-coalgebra in the case of a group scheme. Quantum double of a crossed Hopf group-scheme coalgebra is constructed in the affine case and conjectured for the more general non-affine case. We can construct 3-dimensional HQFTs from modular crossed $G$-categories. The category of representations of a quantum double of a crossed Hopf group-coalgebra is a ribbon (quasitriangular) crossed group-category, and hence can generate 3-dimensional HQFTs under certain conditions if the category becomes modular. However, the problem of systematic finding of modular crossed $G$-categories is largely open.
Professional traits
Programming Languages: C, C++, Visual Basic 6.0, Fortran, FlashOperating systems: Windows, Mac,
Linux. Database: MS-Access, OracleMathematical Applications & Software:
  • Image Processing using Linear Algebra (Singular Value Decomposition)
  • MuPad
  • Latex
  • MatLab
  • Developed a mathematical software which provides solution to various mathematicalproblems, using MuPad, Flash.
  • Developed a project named ‘Payroll Management System’ using C++.
  • Developed a project named ‘Game Show’ using Visual Basic 6.0 and Oracle 7.0. The FrontEnd – Back End connectivity was provided by using ADODB.
Honours and Awards
Vice chancellors scholarship, awarded by University of Warwick, UK. (2007)
Post Graduate Scholarship awarded by University of Delhi, India. (2005)
Merit Scholarship awarded by Laxman Public School, Delhi, India. (1999)
Merit Scholarship awarded by Laxman Public School, Delhi, India. (1998)
National Mathematics Olympiad, level B Certificate, First Division. (1997)
Non scientific academic awards
Senior United Nation Information Test Certificate, securing 64%, conducted by The Council for the United Nation Information. (1998)
Certificate by Erehwon Programme for thinking & to expand “field of exploration”. (1997)
Pre-Senior UNESCO Information Test, securing 75%, conducted by The Council for the United Nation Information. (1995)
Conferences/Workshops attended
Geometric Langlands Correspondence, LMS, Oxford, England. (April 2007)
British Mathematical Colloquium, University of Swansea, Wales. (April 2007)
Cherednik Algebras, University of Edinburgh, Scotland. (June 2007)
Quantum Groups and non commutative geometry, MPIM, Bonn, Germany. (August 2007)
Liegrits, Lie Representation Theory, at University of Oxford, England. (January 2008)
23rd Annual Conference of Ramanujan Mathematical Society, IIT Kanpur, India.(May 2008)
A short Instructional course on ”Linear Algebraic Groups” at University of Birmingham, England. (September 2008)
Talks delivered
Decomposition of cuspidal characters and Hecke algebras, University of Warwick, UK. (2008)
Representations of Frobenius Kernels, University of Warwick, UK. (2009)
Frobenius Algebras and monoidal category, University of Warwick, UK. (2010)
From Frobenius Algebras to 2-dim TQFTs to 2-dim HQFTs, Shiv Nadar University, Dadri, UP, India. (2012)
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