Dr. Victor Kalvin

Assistant Professor, Mathematics and Statistics


Office: S-LB 916 
J.W. McConnell Building,
1400 De Maisonneuve Blvd. W.
Phone: (514) 848-2424 ext. 3223
Email: victor.kalvin@concordia.ca
Website(s): ResearchGate

Education

Ph.D.: University of Jyväskylä, Finland 2004

Research Interests

Geometric/Global/Applied Analysis, Analysis on Non-compact and Singular Manifolds, Partial Differential Equations, Pseudo-Differential Operators, Mathematical Physics, and Scientific Computing. 

These include: General Elliptic Boundary Value Problems, Asymptotic Theory, Spectral Theory (for selfadjoint and non-selfadjoint operators), Theory of Analytic and Singular Perturbations, Scattering Theory,  Spectral Determinants (zeta-regularized determinants of Laplacians on non-compact/singular manifolds), related Numerical Methods and mathematical analysis of their stability and convergence.

 
 


Recent Publications



CIRGET CRM Geometry and Topology Seminar, Invited talk

Title: Determinants of Laplacians on compact surfaces with conical singularities. (Video)
Date: Nov 18, 2022

Abstract: In this talk I will discuss new anomaly formulae for the zeta regularized spectral determinants of Laplacians on compact Riemann surfaces. These formulae are valid for the metrics with conical singularities and, in particular, show how the determinants of Laplacians depend on the orders (angles) of conical singularities. With a simple  example I will show that the extremal properties of the determinants of Laplacians on singular metrics are very different from the classical results of Osgood, Phillips, and Sarnak for the smooth metrics. If time permits, I will also discuss how this is related to Kaehler potentials of metrics on moduli spaces, the famous accessory parameters, and the celebrated DOZZ formula from the Liouville conformal field theory. The talk is based on a series of recent papers of mine. 

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