I am an Assistant Professor at the Department of Mathematics, Indian Institute of Science, Bangalore.
My primary area of research is several complex variables. Within this field, I work on problems that have connections to convex geometry (asymptotics of polytope approximations), harmonic analysis (integral representation formulas and singular kernels) and approximation theory (rational and polynomial approximations). I am a member of the Analysis and Probability Research Group at IISc.
Publications & Preprints
Papers
- Hypersurface convexity and extension of Kähler forms (with B. Boudreaux and R. Shafikov). arXiv Pre-print.
- Volume approximations of strongly \(\mathbb{C}\)-convex domains by random polyhedra (with S. Athreya and D. Yogeshwaran). arXiv Adv. Math., to appear.
- On the dimension of bundle-valued Bergman spaces on compact Riemann surfaces (with A.-K. Gallagher and L. Vivas). arXiv Indiana Univ. Math. J., to appear.
- On the dimension of Bergman spaces on \(\mathbb{P}^1\) (with A.-K. Gallagher and L. Vivas). arXiv La Matematica, 1 (2022), 666--684.
- Stability of the hull(s) of an \(n\)-sphere in \(\mathbb{C}^n\) (with C. U. Wawrzyniak). arXiv Adv. Math., 392, (2021), 107989.
- Hardy spaces for a class of singular domains (with A.-K. Gallagher, L. Lanzani and L. Vivas). arXiv Math. Z., 299, (2021), 2171--2197.
- Polynomially convex embeddings of odd-dimensional closed manifolds (with R. Shafikov). arXiv J. Reine Angew. Math., 777 (2021), 273--299.
- Polynomially convex embedddings of even-dimensional compact manifolds (with R. Shafikov). arXiv Ann. Sc. Norm. Super. Pisa Cl. Sci. (5), Vol.XXI (2020), 1649--1666.
- The rational hull of Rudin's Klein bottle (with J. T. Anderson & E. L. Stout). arXiv Proc. Amer. Math. Soc., 147 (2019), 3859--866.
- 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
Upcoming (Jan.-Apr. 2024)
I will be teaching UM 204 (Introduction to Basic Analysis) in the upcoming semester.Past
IISc: UM 101 (Analysis & Linear Algebra I), Math 324 (Approximation Theory in Complex Analysis), Math 221 (Analysis I - Real Analysis), Math 224 (Complex Analysis), Math 381 (Topics in Several Complex Variables a.k.a. Introduction to CR Geometry).
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).