Appointment: 2017 Evans Instructor, Rice University
Education: 2017 PhD in Mathematics, University of Missouri, Columbia. Thesis title "Topics In Spectral Theory of Differential Operators"
2012 B.Sc. in Mathematics (degree with honors), Taras Shevchenko National University of Kyiv, Ukraine
Research My research interests are in mathematical physics, partial differential equations, spectral theory, and infinite dimensional dynamical systems. Specifically, my work concerns the following topics:
 asymptotic distribution of eigenvalues of elliptic operators on bounded domains: Weyltype asymptotic formulas, bounds for the eigenvalue counting function,
 (in)stability of nonlinear waves: evaluation of the Morse index via the Maslov index,
 spectral theory of differential operators with nonlocal boundary conditions,
 computation of the spectral flow via the Maslov index.
Papers and preprints:
 A bound for the eigenvalue counting function for Kreinvon Neumann and Friedrichs extensions.
Joint with M.S. Ashbaugh, F. Gesztesy, A. Laptev, and M. Mitrea, Advances in Mathematics 304, 1108–1155 (2017). [PDF, 48 pages]
 Counting spectrum via the Maslov index for one dimensional θperiodic Schrödinger operators.
Joint with C. K. R. T. Jones and Y. Latushkin, Proceedings of the AMS 145, 363377 (2017). [PDF, 15 pages]
 The Morse and Maslov indices for Schrödinger operators.
Joint with Y. Latushkin and A. Sukhtayev, Accepted for publication in Journal d'Analyse Mathematique. arXiv:1411.1656 [PDF, 36 pages]
 A bound for the eigenvalue counting function for higherorder Krein Laplacians on open sets.
Joint with F. Gesztesy, A. Laptev, and M. Mitrea, Mathematical Results in Quantum Mechanics, Proceedings of the QMath12 Conference P. Exner, W. König, and H. Neidhardt (eds), World Scientific, Singapore, 2015, pp. 329. [PDF, 27 pages]
 The Maslov index and the spectra of second order elliptic operators.
Joint with Y. Latushkin. Preprint available on the ArXiv [PDF, 48 pages].
Upcoming Talks/Conferences:  September 1, 2017, Mathematical Physics and Harmonic Analysis Seminar, Texas A&M, College Station, TX.
Talk:"The Maslov Index and the Spectra of Second Order Elliptic Operators"  September 6, 2017, GeometryAnalysis Seminar, Rice University, Houston, TX.
Talk:"The Maslov Index and the Spectra of Second Order Elliptic Operators"  October 2022, 2017 Waves, Spectral Theory and Applications – Part 2, University of North Carolina, Chapel Hill, NC.
 November 35, 2017, Texas Analysis and Mathematical Physics Symposium, University of Texas, Austin, TX
 December 912, 2017, SIAM Conference on Analysis of Partial Differential Equations, Baltimore, MD.
Past Talks/Conferences:
SIAM Conference on Applications of Dynamical Systems, Snowbird, UT, USA Talk:"The Maslov Index and the Spectra of Second Order Elliptic Operators"
 KUMUNU Conference on PDE, Dynamical Systems and Applications 2017, Lincoln, NE, USA
Baylor University, Analysis Seminar, Waco, TX, USA Talk :"The Maslov Index and the Spectra of Second Order Elliptic Operators"  The Tenth IMACS Conference on Nonlinear Waves, Athens, GA, USA
Talk :"The Maslov Index and the Spectra of Second Order Elliptic Operators"  Conference on Methods of Modern Mathematical Physics, The Fields Institute, Toronto, Canada
 Frontiers in Mathematical Physics. In honor of Barry Simon's 70th birthday,University of Montreal, Canada
 SIAM Conference on Nonlinear Waves and Coherent Structures, Philadelphia, PA, USA
Talk: "Counting spectrum via the Maslov index for Schrödinger operators"
 Applications of the Maslov index to multidimensional stability problems, AIM SQuaRE, San Jose, CA, USA
 Mathematical Physics and Harmonic Analysis Seminar, Texas A&M University, College Station, TX, USA
Talk: "A Bound for the Eigenvalue Counting Function for HigherOrder Krein Laplacians on Open Sets"
 Computational & Applied Mathematics Seminar, University Kansas, Lawrence, KS, USA
Talk:"Counting spectrum via the Maslov index for Schrödinger operators"
 Geometric and Computational Spectral Theory, University of Montreal, Canada
 KUMU PDE, Dynamical Systems and Applications, University of Kansas, Lawrence, KS, USA
Talk:"The Morse and Maslov Indices for Schrödinger Operators"
 The 1st Annual Meeting of SIAM Central States Section, Missouri University of Science and Technology, Rolla, MO, USA
Talk:"The Morse and Maslov Indices for Schrödinger Operators"
 University of North Carolina, Chapel Hill, research visit by invitation of Prof. C. K. R. T. Jones
 Differential Equations Seminar, University of Missouri, Columbia, MO, USA
Talk:"The Morse and Maslov Indices for Schrödinger Operators"
 The 34th SoutheasternAtlantic Regional Conference on Differential Equations, University of Memphis, TN, USA
Talk:"The Morse and Maslov Indices for Periodic Schrödinger Operators"
 Differential Equations Seminar, University of Missouri, Columbia, MO, USA
Talk:"A Bound for the Eigenvalue Counting Function for HigherOrder Krein Laplacians on Open Sets"
 Stability of Solitary waves, Pisa, Italy
 Operator Semigroups and Dispersive Equations, HeinrichFabri Institut, Blaubeuren, Germany
Talk:"A Spectral Mapping Theorem for Nonlinear Schrodinger Equation"
Teaching
Past teaching:  [TA] Advanced Calculus of One Real Variable I: Spring 2014, Fall 2016, Spring 2017.
 [TA] Analytic Geometry and Calculus I: Fall 2013, Spring 2014, Fall 2014, Fall 2015, Spring 2017.
 [TA] Calculus II: Spring 2015, Spring 2016, Fall 2016.

