Department of Mathematics
Hill Center - Busch Campus
Piscataway, NJ 08854

Email: purvi.gupta (at) rutgers (dot) edu

Office: Hill 205

• Postdoc., Univ. of Western Ontario, 2015-2017
(Mentor: Rasul Shafikov)
• Ph.D., Univ. of Michigan, 2015
• M.S. (Math), Indian Institute of Science, 2010
• B.A. (Math. Hons.) St. Stephen's College, Delhi, 2007

I am a Hill Assistant Professor (postdoc) in the Department of Mathematics at Rutgers University, New Jersey.

My primary area of research is several complex variables. I study its connections to convex geometry, approximation theory and symplectic geometry.

Since Fall 2018, I have co-organized the Rutgers Complex Analysis and Geometry Seminar with Xiaojun Huang.

### Publications & Preprints

Papers

• Polynomially convex embedddings of even-dimensional compact manifolds (with R. Shafikov). arXiv
Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), to appear.
• The rational hull of Rudin's Klein bottle (with J. T. Anderson & E. L. Stout). arXiv
Proc. Amer. Math. Soc., to appear.
• A real-analytic nonpolynomially convex isotropic torus with no attached discs. PDF
Canad. Math. Bull. 61 (2018), No. 2, 289-291.
• Rational and polynomial density on compact real manifolds (with R. Shafikov). PDF
Internat. J. Math. 28 (2017), No. 5, 17pp.
• Convex floating bodies as approximations of Bergman sublevel sets on tube domains. PDF
Proc. Amer. Math. Soc. 145 (2017), No. 10, 4385-4396.
• Volume approximations of strongly pseudoconvex domains. PDF
J. Geom. Anal. 27 (2017), Issue 2, 1029–1064.
• Lower-dimensional Fefferman measures via the Bergman kernel. PDF
Contemp. Math. 681 (2017), 137-152.
• Two extension theorems of Hartogs-Chirka type involving continuous multifunctions. PDF
Mich. Math. J. 60 (2011), Issue 3, 675-685.

Theses

• Fefferman's hypersurface measure and volume approximation problems. PDF
Ph.D. Thesis, University of Michigan, Ann Arbor.
• Some descriptions of the envelopes of holomorphy of domains in $\mathbb{C}^n$ . PDF
M.S. Thesis, Indian Institute of Science, Bangalore.

### Teaching

TBA

#### Past

Rutgers University: Math 311 (Introduction to Real Analysis I), 477 (Mathematical Theory of Probability), Math 152 (Calc II for Math/Phy).

Uniersity of Western Ontario: Calculus 1000A, Math 0110A (Introduction to Calculus) and 1600B (Linear Algebra).

University of Michigan: Math 105 (Pre-Calculus), Math 115 (Calculus I) and Math 116 (Calculus II).

### Upcoming Travel

• Midwest Several Complex Variables , University of Michigan - Dearborn, Oct. 11 - 13, 2019.
• Centro Internazionale per la Ricerca Matematica (for Research in Pairs), Trento, Jan. 6 - 16, 2020.
• AMS-AWM Special Session on Women in Several Complex Variables, JMM, Denver, Jan. 17-18, 2020.