HR job title
- Professor
- Contact Info
- 1 979 845 3261
- Websites
- ORCiD
- 0000-0002-3335-8901
Berkolaiko, Gregory Professor
Positions
- Professor, Mathematics, College of Arts and Sciences
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.
- Overview
- Publications
- Research
- Teaching
- Works By Students
- Background
- Contact
- Other
- View All
Overview
Publications
selected publications
-
academic article
-
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.
-
Alon, L., Band, R., & Berkolaiko, G.
(2022).
Universality of Nodal Count Distribution in Large Metric Graphs. 1-35.
-
Berkolaiko, G., & Ettehad, M.
(2022).
Three-dimensional elastic beam frames: Rigid joint conditions in variational and differential formulation. 148(4), 1586-1623.
-
Berkolaiko, G., & Kuchment, P.
(2022).
Spectral shift via "lateral" perturbation. Journal of Spectral Theory.
12(1), 83-104.
-
Berkolaiko, G., & Booton, L.
(2021).
Convergence of moments of twisted COE matrices. 62(6), 063502.
-
Berkolaiko, G., & Parulekar, A.
(2021).
LOCATING CONICAL DEGENERACIES IN THE SPECTRA OF PARAMETRIC SELF-ADJOINT MATRICES. SIAM Journal on Matrix Analysis and Applications.
42(1), 224-242.
-
Berkolaiko, G., Marzuola, J. L., & Pelinovsky, D. E.
(2021).
Edge-localized states on quantum graphs in the limit of large mass. Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire.
38(5), 1295-1335.
-
Berkolaiko, G., & Kuchment, P.
(2020).
Spectral shift via "lateral" perturbation. 12(1), 83-104.
-
Berkolaiko, G., & Kha, M.
(2020).
Degenerate band edges in periodic quantum graphs. Letters in Mathematical Physics.
110(11), 2965-2982.
-
Ettehad, M., Duffield, N., & Berkolaiko, G.
(2019).
Optimizing Consistent Merging and Pruning of Subgraphs in Network Tomography. abs/1908.03519.
-
Berkolaiko, G., Cox, G., & Marzuola, J. L.
(2019).
Nodal deficiency, spectral flow, and the Dirichlet-to-Neumann map. Letters in Mathematical Physics.
109(7), 1611-1623.
-
Berkolaiko, G., Latushkin, Y., & Sukhtaiev, S.
(2019).
Limits of quantum graph operators with shrinking edges. Advances in Mathematics.
352, 632-669.
-
Berkolaiko, G., Kennedy, J. B., Kurasov, P., & Mugnolo, D.
(2019).
SURGERY PRINCIPLES FOR THE SPECTRAL ANALYSIS OF QUANTUM GRAPHS. Transactions of the American Mathematical Society.
372(7), 5153-5197.
-
Berkolaiko, G., Duffield, N., Ettehad, M., & Manousakis, K.
(2019).
Graph reconstruction from path correlation data. Inverse Problems.
35(1), 015001-015001.
-
Alon, L., Band, R., & Berkolaiko, G.
(2018).
Nodal Statistics on Quantum Graphs. Communications in Mathematical Physics.
362(3), 909-948.
-
Berkolaiko, G., & Liu, W.
(2018).
Eigenspaces of symmetric graphs are not typically irreducible. Letters in Mathematical Physics.
108(8), 1825-1835.
-
Berkolaiko, G., & Comech, A.
(2018).
Symmetry and Dirac points in graphene spectrum. 8(3), 1099-1147.
-
Berkolaiko, G., & Winn, B.
(2018).
Maximal scarring for eigenfunctions of quantum graphs. NONLINEARITY.
31(10), 4812-4850.
-
Band, R., Berkolaiko, G., Joyner, C. H., & Liu, W.
(2017).
Quotients of graph operators by symmetry representations
-
Berkolaiko, G., Kennedy, J. B., Kurasov, P., & Mugnolo, D.
(2017).
Edge connectivity and the spectral gap of combinatorial and quantum graphs. Journal of Physics A: Mathematical and Theoretical.
50(36), 365201-365201.
-
Berkolaiko, G.
(2017).
An elementary introduction to quantum graphs. Contemporary Mathematics.
700, 41-72.
-
Berkolaiko, G., & Liu, W.
(2017).
Simplicity of eigenvalues and non-vanishing of eigenfunctions of a quantum graph. Journal of Mathematical Analysis and Applications.
445(1), 803-818.
-
Berkolaiko, G., & Irving, J.
(2016).
Inequivalent factorizations of permutations. Journal of Combinatorial Theory Series A.
140, 1-37.
-
Band, R., Berkolaiko, G., & Weyand, T.
(2015).
Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs. Journal of Mathematical Physics.
56(12), 122111.
-
Berkolaiko, G., Comech, A., & Sukhtayev, A.
(2015).
VakhitovKolokolov and energy vanishing conditions for linear instability of solitary waves in models of classical self-interacting spinor fields. NONLINEARITY.
28(3), 577-592.
-
Berkolaiko, G., Comech, A., & Sukhtayev, A.
(2015).
Vakhitov-Kolokolov and energy vanishing conditions for linear instability of solitary waves in models of classical self-interacting spinor fields. NONLINEARITY.
28(3), 577-592.
-
Berkolaiko, G., & Weyand, T.
(2014).
Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.
372(2007), 20120522-20120522.
-
Berkolaiko, G., & Kuipers, J.
(2013).
Combinatorial theory of the semiclassical evaluation of transport moments II: Algorithmic approach for moment generating functions. 54(12), 123505.
-
Berkolaiko, G.
(2013).
NODAL COUNT OF GRAPH EIGENFUNCTIONS VIA MAGNETIC PERTURBATION. 6(5), 1213-1233.
-
Berkolaiko, G., & Kuipers, J.
(2013).
Combinatorial theory of the semiclassical evaluation of transport moments. I. Equivalence with the random matrix approach. 54(11), 112103.
-
Berkolaiko, G., Buckwar, E., Kelly, C., & Rodkina, A.
(2013).
On the use of a discrete form of the Ito formula in the article 'Almost sure asymptotic stability analysis of the -Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations' (vol 15, pg 71, 2012). 16, 366-372.
-
Berkolaiko, G., Kuchment, P., & Smilansky, U.
(2012).
CRITICAL PARTITIONS AND NODAL DEFICIENCY OF BILLIARD EIGENFUNCTIONS. GEOMETRIC AND FUNCTIONAL ANALYSIS.
22(6), 1517-1540.
-
Berkolaiko, G., & Kuchment, P.
(2012).
Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths. 84, 117-137.
-
Berkolaiko, G., Buckwar, E., Kelly, C., & Rodkina, A.
(2012).
Almost sure asymptotic stability analysis of the -Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations. LMS Journal of Computation and Mathematics.
15, 71-83.
-
Band, R., Berkolaiko, G., Raz, H., & Smilansky, U.
(2012).
The Number of Nodal Domains on Quantum Graphs as a Stability Index of Graph Partitions. Communications in Mathematical Physics.
311(3), 815-838.
-
Berkolaiko, G., & Kuipers, J.
(2012).
Universality in chaotic quantum transport: the concordance between random-matrix and semiclassical theories. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics.
85(4 Pt 2), 045201.
-
Berkolaiko, G., Raz, H., & Smilansky, U.
(2012).
Stability of nodal structures in graph eigenfunctions and its relation to the nodal domain count. 45(16), 165203-165203.
-
Berkolaiko, G., & Comech, A.
(2012).
On Spectral Stability of Solitary Waves of Nonlinear Dirac Equation in 1D. Mathematical Modelling of Natural Phenomena (MMNP).
7(2), 13-31.
-
Band, R., Berkolaiko, G., & Smilansky, U.
(2012).
Dynamics of Nodal Points and the Nodal Count on a Family of Quantum Graphs. Annales Henri Poincaré.
13(1), 145-184.
-
Berkolaiko, G., Kelly, C., & Rodkina, A.
(2011).
SHARP PATHWISE ASYMPTOTIC STABILITY CRITERIA FOR PLANAR SYSTEMS OF LINEAR STOCHASTIC DIFFERENCE EQUATIONS. Discrete and Continuous Dynamical Systems Series A.
163-173.
-
Berkolaiko, G., Kelly, C., & Rodkina, A.
(2011).
SHARP PATHWISE ASYMPTOTIC STABILITY CRITERIA FOR PLANAR SYSTEMS OF LINEAR STOCHASTIC DIFFERENCE EQUATIONS. Discrete and Continuous Dynamical Systems Series A.
31, 163-173.
-
Berkolaiko, G., & Kuipers, J.
(2011).
Transport moments beyond the leading order. New Journal of Physics.
13(6), 063020-063020.
-
Berkolaiko, G., & Winn, B.
(2010).
RELATIONSHIP BETWEEN SCATTERING MATRIX AND SPECTRUM OF QUANTUM GRAPHS. Transactions of the American Mathematical Society.
362(12), 6261-6277.
-
Berkolaiko, G., & Kuipers, J.
(2010).
Moments of the Wigner delay times. Journal of Physics A: Mathematical and Theoretical.
43(3), 035101-035101.
-
Kuipers, J., Waltner, D., Petitjean, C., Berkolaiko, G., & Richter, K.
(2010).
Semiclassical gaps in the density of states of chaotic Andreev billiards. Physical Review Letters.
104(2), 027001.
-
Berkolaiko, G., Harrison, J. M., & Wilson, J. H.
(2009).
Mathematical aspects of vacuum energy on quantum graphs. Journal of Physics A: Mathematical and Theoretical.
42(2), 025204-025204.
-
Berkolaiko, G., Harrison, J. M., & Novaes, M.
(2008).
Full counting statistics of chaotic cavities from classical action correlations. Journal of Physics A: Mathematical and Theoretical.
41(36), 365102-365102.
-
Berkolaiko, G., Harrison, J. M., & Novaes, M.
(2008).
On inequivalent factorizations of a cycle
-
Berkolaiko, G., & Grinfeld, M.
(2007).
Type of dynamic phase transition in bistable equations. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics.
76(6 Pt 1), 061110.
-
Berkolaiko, G., Keating, J. P., & Smilansky, U.
(2007).
Quantum ergodicity for graphs related to interval maps. Communications in Mathematical Physics.
273(1), 137-159.
-
Berkolaiko, G., & Rodkina, A.
(2006).
Almost sure convergence of solutions to non-homogeneous stochastic difference equation. 12(6), 535-553.
-
Berkolaiko, G.
(2006).
Form factor expansion for large graphs: a diagrammatic approach. Contemporary Mathematics.
415, 35-49.
-
Berkolaiko, G., & Grinfeld, M.
(2006).
Multiplicity of periodic solutions in bistable equations. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
462(2067), 1001-1019.
-
Berkolaiko, G., Keating, J. P., & Winn, B.
(2004).
No quantum ergodicity for star graphs. Communications in Mathematical Physics.
250(2), 259-285.
-
Berkolaiko, G.
(2004).
Form factor for large quantum graphs: evaluating orbits with time reversal. 14(1), S7-S27.
-
Berkolaiko, G., Keating, J. P., & Winn, B.
(2003).
Intermediate wave function statistics. Physical Review Letters.
91(13), 134103.
-
Berkolaiko, G., Schanz, H., & Whitney, R. S.
(2003).
Form factor for a family of quantum graphs: an expansion to third order. Journal of Physics A: Mathematical and General.
36(31), 8373-8392.
-
Berkolaiko, G., Schanz, H., & Whitney, R. S.
(2002).
Leading off-diagonal correction to the form factor of large graphs. Physical Review Letters.
88(10), 104101-1041014.
-
Ordemann, A., Tomer, E., Berkolaiko, G., Havlin, S., & Bunde, A.
(2001).
Structural properties of self-attracting walks. Physical Review E: Statistical, Nonlinear, and Soft Matter Physics.
64(4 Pt 2), 046117-461179.
-
Berkolaiko, G., Bogomolny, E. B., & Keating, J. P.
(2000).
Star graphs and eba billiards. BRIMS(22),
-
Berkolaiko, G.
(1999).
Dynamics of piecewise linear interval maps with hysteresis. Dynamical Systems.
14(1), 56-70.
-
Berkolaiko, G., & Keating, J. P.
(1999).
Two-point spectral correlations for star graphs. BRIMS(10),
-
Berkolaiko, G.
(1999).
Dynamics of piecewise linear interval maps with hysteresis. Dynamics and Stability of Systems.
14(1), 57-70.
-
Berkolaiko, G., Rabinovich, S., & Havlin, S.
(1998).
Analysis of Carleman representation of analytical recursions. Journal of Mathematical Analysis and Applications.
224(1), 81-90.
-
Berkolaiko, G., & Havlin, S.
(1998).
Number of distinct sites visited by Lvy flights injected into a d-dimensional lattice. 57(3), 2549-2552.
-
Berkolaiko, G., & Havlin, S.
(1998).
Number of distinct sites visited by Levy flights injected into a d-dimensional lattice. Physical Review E.
57(3), 2549-2552.
-
Berkolaiko, G., & Havlin, S.
(1997).
Territory covered by N Levy flights on d-dimensional lattices. Physical Review E.
55(2), 1395-1400.
-
Berkolaiko, G. M.
(1997).
On a Peetre functional. Mathematical Notes.
61(1), 22-28.
-
, ., & Berkolaiko, G. M.
(1997).
On a Peetre functional. Mathematical Notes.
61(1), 26-33.
-
Rabinovich, S., Berkolaiko, G., & Havlin, S.
(1996).
Solving nonlinear recursions. Journal of Mathematical Physics.
37(11), 5828-5836.
-
Berkolaiko, G., Havlin, S., Larralde, H., & Weiss, G. H.
(1996).
Expected number of distinct sites visited by N Lvy flights on a one-dimensional lattice. Physical Review E.
53(6), 5774-5778.
-
Berkolaiko, G., Havlin, S., Larralde, H., & Weiss, G. H.
(1996).
Expected number of distinct sites visited by N Lvy flights on a one-dimensional lattice. Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.
53(6), 5774-5778.
-
RABINOVICH, S., BERKOLAIKO, G., BULDYREV, S., & SHEHTER, A.
(1995).
LOGISTIC MAP - AN ANALYTICAL SOLUTION. Physica A: Statistical Mechanics and its Applications.
218(3-4), 457-460.
-
Rabinovich, S., Berkolaiko, G., Buldyrev, S., Shehter, A., & Havlin, S.
(1995).
Logistic map: an analytical solution. 218(3), 457-460.
-
Berkolaiko, G., & de Verdiere, Y. C.
(2024).
Exotic eigenvalues of shrinking metric graphs. 534(1), 128040-128040.
-
book
-
Berkolaiko, G., & Kuchment, P.
(2013).
Introduction to Quantum Graphs. American Mathematical Soc..
-
Berkolaiko, G., & Kuchment, P.
(2012).
Introduction to Quantum Graphs. Ed. 186.
American Mathematical Society (AMS).
-
Berkolaiko, G., & Kuchment, P.
(2013).
Introduction to Quantum Graphs. American Mathematical Soc..
-
conference paper
-
Appleby, J., Berkolaiko, G., & Rodkina, A.
(2010).
Non-Exponential Stability and Decay Rates in Nonlinear Stochastic Homogeneous Difference Equations. 155-162.
-
Engl, T., Kuipers, J., Berkolaiko, G., Petitjean, C., Waltner, D., & Richter, K.
(2010).
Semiclassics of Andreev billiards. 03009.
-
Berkolaiko, G.
(2008).
Two constructions of quantum graphs and two types of spectral statistics. 315-329.
-
Appleby, J., Berkolaiko, G., & Rodkina, A.
(2007).
ON THE ASYMPTOTIC BEHAVIOR OF THE MOMENTS OF SOLUTIONS OF STOCHASTIC DIFFERENCE EQUATIONS. 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.
837-838.
-
Appleby, J., Berkolaiko, G., & Rodkina, A.
(2010).
Non-Exponential Stability and Decay Rates in Nonlinear Stochastic Homogeneous Difference Equations. 155-162.
-
institutional repository document
-
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., & de Verdire, Y. C.
(2023).
Exotic eigenvalues of shrinking metric graphs
-
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
-
Berkolaiko, G., Cox, G., Latushkin, Y., & Sukhtaiev, S.
(2023).
The Duistermaat index and eigenvalue interlacing for self-adjoint extensions of a symmetric operator
-
report
-
Berkolaiko, G.
(1998).
Dynamics of piecewise linear interval maps with hysteresis. 1-18.
-
Berkolaiko, G.
(1998).
Dynamics of piecewise linear interval maps with hysteresis. 1-18.
editor of
-
book
-
Berkolaiko, G.
Quantum Graphs and Their Applications Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Quantum Graphs and Their Applications, June 19-23, 2005, Snowbird, Utah
Berkolaiko, G. (Eds.),
American Mathematical Soc..
-
Berkolaiko, G.
Quantum Graphs and Their Applications Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Quantum Graphs and Their Applications, June 19-23, 2005, Snowbird, Utah
Berkolaiko, G. (Eds.),
American Mathematical Soc..
Research
principal investigator on
- Zeros of Eigenfunctions of Metric Graphs and Their Applications to Spectral Gap Estimates and to Buckling of Structures awarded by National Science Foundation - (Arlington, Virginia, United States) 2018 - 2021
- Nodal Count, Magnetic Potentials and Dirac Cones: Exploring The Connections- awarded by National Science Foundation - (Arlington, Virginia, United States) 2014 - 2018
- Spectral analysis of Schrödinger operators on metric graphs awarded by United States-Israel Binational Science Foundation - (Jerusalem, Israel) 2016
- Inverse Problems and Spectral Theory awarded by National Science Foundation - (Arlington, Virginia, United States) 2014 - 2015
Teaching
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
- MATH485 Directed Studies Instructor
- MATH491 Hnr-research Instructor
- MATH628 Mathematical Tools In Finance Instructor
- MATH685 Directed Studies Instructor
- MATH689 Sptp:math Tools For Risk Analy Instructor
- MATH689 Sptp:math Tools Of Finance Instructor
- MATH691 Research Instructor
Works By Students
chaired theses and dissertations
-
Liu, Wen (2016-06). Degeneracies in the Eigenvalue Spectrum of Quantum Graphs.
-
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.
Background
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
Contact
first name
- Gregory
has last name
- Berkolaiko
mailing address
-
Texas A&M University
Mathematics
3368 TAMU
College Station, TX 77843-3368
USA
Other
- gberkolaiko@tamu.edu