Dr. Victor Kalvin, PhD
Assistant Professor, Mathematics and Statistics
Ph.D.: University of Jyväskylä, Finland 2004
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-regularizations for the determinant of the Laplace operator on non-compact/singular manifolds), related Numerical Methods and mathematical analysis of their stability and convergence.
- ENGR 213: Applied Ordinary Differential Equations
- MATH 354/MAST 334: Numerical Analysis (Approximation Theory)
- MATH 208: Fundamental Mathematics I
- ENGR 233: Applied Advanced Calculus
- On Determinants of Laplacians on Compact Riemann Surfaces equipped with Pullbacks of Conical Metrics by Meromorphic Functions, J. Geom. Anal. (2018) in press, https://doi.org/10.1007/s12220-018-0018-2, ArXiv:1712.05405
- Determinant of Laplacian on tori of constant positive curvature with one conical point, to appear in Canad. Math. Bull. (2018), http://dx.doi.org/10.4153/CMB-2018-036-9, ArXiv:1712.04588 (with A. Kokotov)
- Metrics of curvature 1 with conical singularities, Hurwitz spaces, and determinants of Laplacians, Intern. Math. Research Notices (2017) in press, DOI: 10.1093/imrn/rnx224, ArXiv:1612.08660 (with A. Kokotov)
- Moduli spaces of meromorphic functions and determinant of Laplacian, Trans. Amer. Math. Soc. 370 (2018) 4559-4599, DOI: https://doi.org/10.1090/tran/7430, ArXiv:1410.3106
(with L. Hillairet and A. Kokotov).
- Spectral determinants on Mandelstam diagrams, Comm. Math. Phys. 343 (2016), no. 2, pp. 563-600, https://doi.org/10.1007/s00220-015-2506-6 (with L. Hillairet and A. Kokotov).
- Spectral deformations and exponential decay of eigenfunctions for the Neumann Laplacian on manifolds with quasicylindrical ends, J. Math. Anal. Appl. 432 (2015), pp. 749-760. https://doi.org/10.1016/j.jmaa.2015.07.008
- Analysis of perfectly matched layer operators for acoustic scattering on manifolds with quasicylindrical ends, J. Math. Pures Appl. 100 (2013), pp. 204-219. https://doi.org/10.1016/j.matpur.2012.12.001
- Spectral deformations for quasicylindrical domains, 15 pages, Commun. Contemp. Math., Article ID 1250065, 15 p. (2013). https://doi.org/10.1142/S0219199712500654
- Limiting Absorption Principle and Perfectly Matched Layer Method for Dirichlet Laplacians in Quasi-Cylindrical Domains, SIAM J. Math. Anal. 44 (2012), pp. 355-382. https://doi.org/10.1137/110834287
- Perfectly Matched Layers for diffraction gratings in inhomogeneous media. Stability and error estimates, SIAM J. Numer. Anal. 49 (2011), pp. 309-330. https://doi.org/10.1137/08073442X