Berkolaiko, Gregory
individual record
Professor
Positions:
- Professor, Mathematics, College of Arts and Sciences
overview
My research interests focuses on spectral problems in mathematical physics. In particular, graph models, their use in physics in general and in the theory of quantum chaos in particular. I also have interest in combinatorial problems arising in mathematical physics.
education and training
- Ph.D. in Mathematics, University of Bristol - (Bristol, United Kingdom) 2001
- M.Phil. in Mathematics, University of Strathclyde - (Glasgow, United Kingdom) 1997
- B.Sc. in Mathematics, Voronezh State University - (Voronezh, Russia) 1996
selected publications
Academic Articles78
- Berkolaiko, G., & de Verdiere, Y. C. (2024). Exotic eigenvalues of shrinking metric graphs. 534(1), 128040-128040.
- Berkolaiko, G., Borisov, D. I., & King, M. (2023). Exotic eigenvalues and analytic resolvent for a graph with a shrinking edge. Analysis and Mathematical Physics. 13(6), 90.
- Berkolaiko, G., Canzani, Y., Cox, G., & Marzuola, J. L. (2022). Stability of spectral partitions and the Dirichlet-to-Neumann map. Calculus of Variations and Partial Differential Equations. 61(6), 203.
- Berkolaiko, G., Canzani, Y., Cox, G., & Marzuola, J. L. (2022). A local test for global extrema in the dispersion relation of a periodic graph. 4(2), 257-286.
- Berkolaiko, G., Cox, G., Helffer, B., & Sundqvist, M. P. (2022). Computing Nodal Deficiency with a Refined Dirichlet-to-Neumann Map. 32(10), 246.
Books2
- Berkolaiko, G., & Kuchment, P. (). Introduction to Quantum Graphs. American Mathematical Society (AMS).
Conference Papers5
- Appleby, J., Berkolaiko, G., & Rodkina, A. (2010). Non-Exponential Stability and Decay Rates in Nonlinear Stochastic Homogeneous Difference Equations. Discrete Dynamics and Difference Equations. 155-162.
- Engl, T., Kuipers, J., Berkolaiko, G., Petitjean, C., Waltner, D., & Richter, K. (2010). Semiclassics of Andreev billiards. Mesoscopic Physics in Complex Media. 03009.
- Berkolaiko, G. (2008). Two constructions of quantum graphs and two types of spectral statistics. 77, 315-329.
- Appleby, J., Berkolaiko, G., & Rodkina, A. (2007). ON THE ASYMPTOTIC BEHAVIOR OF THE MOMENTS OF SOLUTIONS OF STOCHASTIC DIFFERENCE EQUATIONS. Difference Equations, Special Functions and Orthogonal Polynomials. 557-+.
- Rabinovich, S., Berkolaiko, G., Buldyrev, S., Shehter, A., & Havlin, S. (1997). Analytical solution of the logistic equation. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering. 7(4), 837-838.
Repository Documents / Preprints5
- Berkolaiko, G., Cox, G., Latushkin, Y., & Sukhtaiev, S. (2023). The Duistermaat index and eigenvalue interlacing for self-adjoint extensions of a symmetric operator.
- Berkolaiko, G., Borisov, D. I., & King, M. (2023). Exotic eigenvalues and analytic resolvent for a graph with a shrinking edge.
- Berkolaiko, G., & Zelenko, I. (2023). Morse inequalities for ordered eigenvalues of generic self-adjoint families.
- Berkolaiko, G., Kennedy, J. B., Kurasov, P., & Mugnolo, D. (2022). Impediments to diffusion in quantum graphs: geometry-based upper bounds on the spectral gap.
Reports1
- Berkolaiko, G. (1998). Dynamics of piecewise linear interval maps with hysteresis. (HPL-BRIMS-98), 1-18.
editor of
researcher on
Principal Investigator4
recent teaching activities
- MATH304 Linear Algebra Instructor
- MATH308 Differential Equations Instructor
- MATH411 Math Probability Instructor
- MATH412 Theory Of Pdes Instructor
- MATH425 Math Of Contingent Claim Instructor
chaired theses and dissertations
- Liu, Wen (2016-06). Degeneracies in the Eigenvalue Spectrum of Quantum Graphs. (Doctoral Dissertation)
- Weyand, Tracy Kathleen (2014-07). Zeros of Eigenfunctions of the Schrodinger Operator on Graphs and Their Relation to the Spectrum of the Magnetic Schrodinger Operator. (Doctoral Dissertation)
Email
gberkolaiko@tamu.edu
First Name
Gregory
Last Name
Berkolaiko
mailing address
Texas A&M University; Mathematics; 3368 TAMU
College Station, TX 77843-3368
USA