Research

Research

My research interest is in complex analysis, more specifically, Several Complex Variables. So far, my primary focus has been the study of various metrics and other biholomorphic invariants in complex analysis by investigating their boundary behaviour using the scaling principle.

• Current projects:

  • Union problem

  • Narasimhan-Simha type metrics

  • Squeezing function and Fridman invariant

• Past projects:

  • Caratheodory and Kobayashi-Eisenman volume elements

  • Multidimensional Suita conjecture

  • Arakelov's Green function for Modular curves

  • Capacity metric

  • Robin metric

Publications

• (With G. Bharali, S. Gorai) The Squeezing function: exact computations, optimal estimates, and a new application, Submitted for publication.

• (With G.P. Balakumar, P. Mahajan, and K. Verma) Limits of an increasing sequence of complex manifolds, Annali di Matematica Pura ed Applicata, 202(2023), 1381-1410.

• (With D. Kar) Some remarks on the Kobayashi-Fuks metric on strongly pseudoconvex domains, accepted for publication in the Journal of Mathematical Analysis and Applications, 512(2022), 2022, 24pp.

• (With K. Verma) Narasimhan--Simha type metrics on strongly pseudoconvex domains in C^n, Complex Variables and Elliptic Equations, 2022, 27pp.

• (With G.P. Balakumar, P. Mahajan, and K. Verma) Further remarks on the higher dimensional Suita conjecture, Ann. Poln. Math. 125 (2020), no. 2, 101-115. 

• (With D. Banerjee and C. Chaudhuri) Arakelov self-intersection numbers of minimal regular models of modular curves  X_0(p^2), Math. Z. 296 (2020), no. 3-4, 1287-1329.

• (With D. Kar) Boundary behaviour of the Carathéodory and Kobayashi-Eisenman volume elements, Illinois J. Math. 64 (2020), no 2, 151-168.

• (With G.P. Balakumar, P. Mahajan, and K. Verma) Remarks on the higher dimensional Suita conjecture, Proceedings of the AMS 147 (2019), 3401-3411

• (With P. Haridas and K. Verma) Comments on the Green's function of a planar domain, Anal. Math. Phys. 8 (2018), 383–414.

• Remarks on the metric induced by the Robin function III, JRMS. 32 (2017), 17-42.

• Remarks on the metric induced by the Robin function II, Michigan Math. J. 62 (2013), 581-630.

• (With K. Verma) Remarks on the metric induced by the Robin function, Indiana Univ. Math. J. 60 (2011), no. 3, 751-801.