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Gregory Berkolaiko

Gregory Berkolaiko

D-Index & Metrics

Mathematics

D-Index
33
Citations
3814
World Ranking
3070
National Ranking
1230

Overview

Gregory Berkolaiko is affiliated with Texas A&M University in the United States. Their research primarily focuses on mathematics, with significant contributions across several subfields including mathematical physics, geometry and topology, computational theory and mathematics, applied mathematics, and statistical and nonlinear physics.

The scientist's work spans several main topics, notably:

  • Spectral theory in mathematical physics
  • Graph theory and applications
  • Quantum chaos and dynamical systems
  • Topological and geometric data analysis
  • Matrix theory and algorithms
  • Nonlinear partial differential equations
  • Numerical methods in inverse problems

Gregory Berkolaiko has published extensively, with a substantial number of publications found on arXiv (Cornell University), accounting for 13 papers. Other notable publication venues include:

  • Annales de l Institut Henri Poincaré C Analyse Non Linéaire
  • Pure and Applied Analysis
  • Experimental Mathematics
  • Journal of Spectral Theory

Examples of recent papers by the scientist include:

  • Edge-localized states on quantum graphs in the limit of large mass (2020), published in Annales de l Institut Henri Poincaré C Analyse Non Linéaire
  • A local test for global extrema in the dispersion relation of a periodic graph (2022), published in Pure and Applied Analysis
  • Universality of Nodal Count Distribution in Large Metric Graphs (2022), published in Experimental Mathematics
  • Spectral shift via "lateral" perturbation (2022), published in Journal of Spectral Theory
  • Stability of spectral partitions and the Dirichlet-to-Neumann map (2022), published in Calculus of Variations and Partial Differential Equations

They have frequently collaborated with several coauthors, including:

  • Graham Cox
  • Jeremy L. Marzuola
  • Yaiza Canzani
  • Lior Alon
  • Ram Band

The research output of Gregory Berkolaiko reflects a diverse interest in the theoretical aspects of mathematical physics and applied mathematics, with particular emphasis on spectral theory and graph-theoretic approaches related to quantum systems, as well as numerical and topological methods. The scientist continues to contribute in these areas through peer-reviewed journals and open access platforms.

Best Publications

  • Introduction to Quantum Graphs

    Gregory Berkolaiko;Peter Kuchment

  • Quantum Graphs and Their Applications

    Gregory Berkolaiko;Robert Carlson;Stephen A. Fulling;Peter Kuchment

  • 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

    Gregory Berkolaiko

  • Two-point spectral correlations for star graphs

    G Berkolaiko;Jon P Keating

  • Star graphs and Seba billiards

    Gregory Berkolaiko;Eugene Bogomolny;J.P. Keating;J.P. Keating

  • Surgery principles for the spectral analysis of quantum graphs

    Gregory Berkolaiko;James B. Kennedy;Pavel Kurasov;Delio Mugnolo

  • Dependence of the spectrum of a quantum graph on vertex conditions and edge lengths

    Gregory Berkolaiko;Peter Kuchment

  • Leading off-diagonal correction to the form factor of large graphs.

    Gregory Berkolaiko;Holger Schanz;Robert S. Whitney

  • No Quantum Ergodicity for Star Graphs

    G Berkolaiko;G Berkolaiko;Jon P Keating;B Winn;B Winn

  • NON-EXPONENTIAL STABILITY AND DECAY RATES IN NONLINEAR STOCHASTIC DIFFERENCE EQUATION WITH UNBOUNDED NOISES

    John A. D. Appleby;Gregory Berkolaiko;Alexandra Rodkina

  • A Lower Bound for Nodal Count on Discrete and Metric Graphs

    Gregory Berkolaiko

  • Edge connectivity and the spectral gap of combinatorial and quantum graphs

    Gregory Berkolaiko;James B Kennedy;James B Kennedy;Pavel Kurasov;Delio Mugnolo

  • The Number of Nodal Domains on Quantum Graphs as a Stability Index of Graph Partitions

    Rami Band;Rami Band;Gregory Berkolaiko;Hillel Moshe Raz;Uzy Smilansky;Uzy Smilansky

  • Simplicity of eigenvalues and non-vanishing of eigenfunctions of a quantum graph

    Gregory Berkolaiko;Wen Liu

  • Symmetry and Dirac points in graphene spectrum

    Gregory Berkolaiko;Andrew Comech

  • Limits of quantum graph operators with shrinking edges

    Gregory Berkolaiko;Yuri Latushkin;Selim Sukhtaiev

  • On Spectral Stability of Solitary Waves of Nonlinear Dirac Equation in 1D

    G. Berkolaiko;A. Comech

  • On the connection between the number of nodal domains on quantum graphs and the stability of graph partitions

    Ram Band;Gregory Berkolaiko;Hillel Raz;Uzy Smilansky

  • Universality in chaotic quantum transport: the concordance between random-matrix and semiclassical theories.

    Gregory Berkolaiko;Jack Kuipers

  • Surgery principles for the spectral analysis of quantum graphs

    Gregory Berkolaiko;James B. Kennedy;Pavel Kurasov;Delio Mugnolo

  • An elementary introduction to quantum graphs

    Gregory Berkolaiko

  • Star graphs and Seba billiards

    G.Berkolaiko;E.B.Bogomolny;J.P.Keating;J.P.Keating

Frequent Co-Authors

Peter Kuchment
Peter Kuchment Texas A&M University
Jon P Keating
Jon P Keating University of Oxford
Shlomo Havlin
Shlomo Havlin Bar-Ilan University
Pavel Kurasov
Pavel Kurasov Stockholm University
Nick Duffield
Nick Duffield Texas A&M University
Sergey V. Buldyrev
Sergey V. Buldyrev Yeshiva University
Dmitry E. Pelinovsky
Dmitry E. Pelinovsky McMaster University
George H. Weiss
George H. Weiss National Institutes of Health

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