# 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.

# keywords[]
4903 Numerical And Computational Mathematics

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Parametric Families Of Self-adjoint Matrices

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Schroedinger Operator With Honeycomb Potential

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4903 Numerical And Computational Mathematics

# educationAndTraining[].organization.label
University of Strathclyde - (Glasgow, United Kingdom)

# educationAndTraining[].organization.label
Voronezh State University - (Voronezh, Russia)

# educationAndTraining[].organization.label
University of Bristol - (Bristol, United Kingdom)

# publications[].label
Dynamics of piecewise linear interval maps with hysteresis

# publications[].label
The Duistermaat index and eigenvalue interlacing for self-adjoint extensions of a symmetric operator

# publications[].label
Nodal deficiency, spectral flow, and the Dirichlet-to-Neumann map

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LOCATING CONICAL DEGENERACIES IN THE SPECTRA OF PARAMETRIC SELF-ADJOINT MATRICES

# publications[].publisher
Society for Industrial & Applied Mathematics (SIAM)

# publications[].label
Optimizing Consistent Merging and Pruning of Subgraphs in Network   Tomography

# publications[].label
RELATIONSHIP BETWEEN SCATTERING MATRIX AND SPECTRUM OF QUANTUM GRAPHS

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

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Eigenspaces of symmetric graphs are not typically irreducible

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An elementary introduction to quantum graphs

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ON THE ASYMPTOTIC BEHAVIOR OF THE MOMENTS OF SOLUTIONS OF STOCHASTIC DIFFERENCE EQUATIONS

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Limits of quantum graph operators with shrinking edges

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

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Analytical solution of the logistic equation

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Universality of Nodal Count Distribution in Large Metric Graphs

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Structural properties of self-attracting walks.

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Graph reconstruction from path correlation data

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Analysis of Carleman representation of analytical recursions

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Form factor for large quantum graphs: evaluating orbits with time reversal

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Form factor for a family of quantum graphs: an expansion to third order

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

# publications[].label
SHARP PATHWISE ASYMPTOTIC STABILITY CRITERIA FOR PLANAR SYSTEMS OF LINEAR STOCHASTIC DIFFERENCE EQUATIONS

# publications[].label
Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs

# publications[].label
Almost sure asymptotic stability analysis of the -Maruyama method applied to a test system with stabilising and destabilising stochastic perturbations

# publications[].label
Vakhitov-Kolokolov and energy vanishing conditions for linear instability of solitary waves in models of classical self-interacting spinor fields

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Combinatorial theory of the semiclassical evaluation of transport moments II: Algorithmic approach for moment generating functions

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On inequivalent factorizations of a cycle

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Non-Exponential Stability and Decay Rates in Nonlinear Stochastic Homogeneous Difference Equations

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Edge-localized states on quantum graphs in the limit of large mass

# publications[].publisher
European Mathematical Society - EMS - Publishing House GmbH

# publications[].label
Number of distinct sites visited by Levy flights injected into a d-dimensional lattice

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Spectral shift via "lateral" perturbation

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Form factor expansion for large graphs: a diagrammatic approach

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Transport moments beyond the leading order

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Almost sure convergence of solutions to non-homogeneous stochastic difference equation

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Spectral shift via "lateral" perturbation

# publications[].publisher
European Mathematical Society - EMS - Publishing House GmbH

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Semiclassical gaps in the density of states of chaotic Andreev billiards.

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Multiplicity of periodic solutions in bistable equations

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Two-point spectral correlations for star graphs

# publications[].label
SHARP PATHWISE ASYMPTOTIC STABILITY CRITERIA FOR PLANAR SYSTEMS OF LINEAR STOCHASTIC DIFFERENCE EQUATIONS

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Territory covered by N Levy flights on d-dimensional lattices

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Dynamics of Nodal Points and the Nodal Count on a Family of Quantum Graphs

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SURGERY PRINCIPLES FOR THE SPECTRAL ANALYSIS OF QUANTUM GRAPHS

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Stability of spectral partitions and the Dirichlet-to-Neumann map

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Edge connectivity and the spectral gap of combinatorial and quantum graphs

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Combinatorial theory of the semiclassical evaluation of transport moments. I. Equivalence with the random matrix approach

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Expected number of distinct sites visited by N Lvy flights on a one-dimensional lattice.

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Maximal scarring for eigenfunctions of quantum graphs

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

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Expected number of distinct sites visited by N Lvy flights on a one-dimensional lattice

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NODAL COUNT OF GRAPH EIGENFUNCTIONS VIA MAGNETIC PERTURBATION

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Exotic eigenvalues and analytic resolvent for a graph with a shrinking edge

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Degenerate band edges in periodic quantum graphs

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Impediments to diffusion in quantum graphs: geometry-based upper bounds on the spectral gap

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Exotic eigenvalues of shrinking metric graphs

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Stability of nodal structures in graph eigenfunctions and its relation to the nodal domain count

# publications[].label
Number of distinct sites visited by Lvy flights injected into a d-dimensional lattice

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Two constructions of quantum graphs and two types of spectral statistics

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Quotients of graph operators by symmetry representations

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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)

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Mathematical aspects of vacuum energy on quantum graphs

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CRITICAL PARTITIONS AND NODAL DEFICIENCY OF BILLIARD EIGENFUNCTIONS

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Symmetry and Dirac points in graphene spectrum

# publications[].publisher
European Mathematical Society - EMS - Publishing House GmbH

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Quantum ergodicity for graphs related to interval maps

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Stability of eigenvalues of quantum graphs with respect to magnetic perturbation and the nodal count of the eigenfunctions.

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Type of dynamic phase transition in bistable equations.

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Morse inequalities for ordered eigenvalues of generic self-adjoint families

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A local test for global extrema in the dispersion relation of a periodic graph

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

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Three-dimensional elastic beam frames: Rigid joint conditions in variational and differential formulation

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Computing Nodal Deficiency with a Refined Dirichlet-to-Neumann Map

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Convergence of moments of twisted COE matrices

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Full counting statistics of chaotic cavities from classical action correlations

# publications[].label
VakhitovKolokolov and energy vanishing conditions for linear instability of solitary waves in models of classical self-interacting spinor fields

# publications[].label
Dynamics of piecewise linear interval maps with hysteresis

# publications[].label
Exotic eigenvalues and analytic resolvent for a graph with a shrinking edge

# publications[].label
Dynamics of piecewise linear interval maps with hysteresis

# publications[].label
Exotic eigenvalues of shrinking metric graphs

# publications[].label
On Spectral Stability of Solitary Waves of Nonlinear Dirac Equation in 1D

# editorOf[].label
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

# researcherOn[].label
Spectral analysis of Schrödinger operators on metric graphs

# researcherOn[].awardedBy.label
United States-Israel Binational Science Foundation - (Jerusalem, Israel)

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
Nodal Count, Magnetic Potentials and Dirac Cones: Exploring The Connections-

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# researcherOn[].label
Zeros of Eigenfunctions of Metric Graphs and Their Applications to Spectral Gap Estimates and to Buckling of Structures

# researcherOn[].awardedBy.label
National Science Foundation - (Arlington, Virginia, United States)

# streetAddress
Texas A&M University; Mathematics; 3368 TAMU

# etdChairOf[].label
Liu, Wen (2016-06). Degeneracies in the Eigenvalue Spectrum of Quantum Graphs. Doctoral Dissertation.

# etdChairOf[].label
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.