My research has been supported in part by the National Science Foundation through grants DMS-2510344, DMS-2418900, DMS-2243027, by the U.S. -Israel Binational Science Foundation through grant 2024154, by the Simons Foundation through grant MP-TSM-000028, and by the Office of Senior Vice President for Research & Economic Development (OVPRED, Auburn University) through an RSP grant. 

My research profiles: MathSciNet, GoogleScholar, ArXiv

Papers and preprints:

• Duistarmaat's triple index and the difference of Hermitian matrices
  Joint with G. Berkolaiko, G. Cox, Y. Latushkin
  [arxiv:2412.20825]

• Some Remarks On Krein--von Neumann Extensions
  Joint with F. Gesztesy
  [arxiv:2504.11718]

• First-order asymptotic perturbation theory for extensions of symmetric operators
  Joint with Y. Latushkin
  Journal of the London Mathematical Society, 110 (5), 2024, e13005 [arXiv:2012.00247] 

• Well-posedness of Keller-Segel systems on compact metric graphs
  Joint with H. Shemtaga, W. Shen
  Journal of Evolution Equations, 25 (7), 2025 [arXiv:2403.19747]

• The Duistermaat index and eigenvalue interlacing for self-adjoint extensions of a symmetric operator
  Joint with G. Berkolaiko, G. Cox, Y. Latushkin
  [arXiv:2311.06701, 35 pages]

• Stability and bifurcation for logistic Keller--Segel models on compact graphs
  Pure and Applied Functional Analysis, 9 (5),  2024 H. Shamtaga, W. Shen
  [arXiv:2310.00756, 25 pages]

• Spectral properties of Schrödinger operators with locally $H^{−1}$ potentials
  Joint with M. Lukic, X. Wang
  Journal of Spectral Theory, 14 (1), 59-120 (2024)

• Resolvent expansions for self-adjoint operators via boundary triplets
  Joint with Y. Latushkin 
  Bulletin of the London Mathematical Society, 54 (6), 2022

• Random Hamiltonians with arbitrary point interactions
  Joint with D. Damanik, J. Fillman, M. Helman, J. Kesten  
  Journal of Differential Equations, 282, 104-126 (2021)

• Zero measure and singular continuous spectra for quantum graphs
  Joint with D. Damanik, L. Fang 
  Annales Henri Poincaré,  21, 2167--2191 (2020) 

• Localization for Anderson models on metric and discrete tree graphs
  Joint with D. Damanik, J. Fillman,
  Mathematische Annalen,  376, 1337-1393 (2020)

• Limits of quantum graph operators with shrinking edges
  Joint with G. Berkolaiko, Y. Latushkin,
  Advances in Mathematics 352, 632–669 (2019) 

• Anderson localization for radial tree graphs with random branching numbers
  Joint with D. Damanik,
  Journal of Functional Analysis 277, 418–433 (2019) 

• The Maslov index and the spectra of second order elliptic operators
  Joint with Y. Latushkin,
  Advances in Mathematics 329, 422–486 (2018) 

• The Morse and Maslov indices for Schrödinger operators
  Joint with Y. Latushkin, A. Sukhtayev,
  Journal d'Analyse Mathematique 135, 345–387 (2018), 

• An index theorem for Schrödinger operators on metric graphs
  Joint with Y. Latushkin,
  Analytic trends in mathematical physics, Contemp. Math. 741, 105-119 (2020)  

• A bound for the eigenvalue counting function for Krein--von Neumann and Friedrichs extensions
  Joint with M.S. Ashbaugh, F. Gesztesy, A. Laptev, M. Mitrea,
  Advances in Mathematics 304, 1108–1155 (2017) 

• Counting spectrum via the Maslov index for one dimensional θ-periodic Schrödinger operators
  Joint with C. K. R. T. Jones, Y. Latushkin,
  Proceedings of the AMS 145, 363–377 (2017) 

• A bound for the eigenvalue counting function for higher-order Krein Laplacians on open sets
  Joint with F. Gesztesy, A. Laptev, M. Mitrea, Mathematical  Results in Quantum Mechanics,   Proceedings of the QMath12 Conference, P.Exner, W. Knig, H. Neidhardt (eds), World Scientific, Singapore, 2015, pp. 3–29