Appointment: 2017 G. C. Evans Instructor, Rice University
Education: 2017 PhD in Mathematics, University of Missouri, Columbia. Thesis title: "Topics In Spectral Theory of Differential Operators", [Thesis]
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 dynamical systems:  Maslov index and symplectic functional analysis in spectral theory and PDE,
 Anderson localization for quantum graphs,
 Weyltype asymptotic formulas,
 Ergodic quantum graph models
Papers and preprints:
 Zero measure and singular continuous spectra for quantum graphs
Joint with D. Damanik, L. Fang [Preprint, (2019) 22 pages]
 Localization for Anderson models on metric and discrete tree graphs
Joint with D. Damanik and J. Fillman, [Preprint, (2019) 52 pages]
 Limits of quantum graph operators with shrinking edges
Joint with G. Berkolaiko and Y. Latushkin, Advances in Mathematics 352, 632–669 (2019), 38 pages
 Anderson localization for radial tree graphs with random branching numbers
Joint with D. Damanik, Journal of Functional Analysis 277, 418–433 (2019), 16 pages
 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), 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, 363–377 (2017), 15 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. 3–29, 27 pages
Upcoming/Recent travel:  June 2427, 2019, University of Hagen, On mathematical aspects of interacting systems in low dimension, Hagen, Germany
Talk: "Localization for Anderson Models on Tree Graphs"
 July 15, 2019, Institut Henri Poincaré, Stability of Nonlinear Waves: Analysis and Computation, Paris, France
 August 49, 2019, Lake Como School of Advanced Studies, Quantum Graphs and Quantum Random Walks in Mathematics, Computer Science and Physics, Italy
Talk: TBA
 September 58, 2019, University of Missouri, Analysis in Missouri: a Midwestern symposium, Columbia, MO
Talk: "Localization for Anderson Models on Tree Graphs"  September 1520, 2019, BIRS, Workshop on Random Matrix Products and Anderson Localization, Banff, Canada
Talk: TBA  November 910, 2019, University of California, Riverside, AMS Fall Western Sectional Meeting.
Talk: "Localization for Anderson Models on Tree Graphs"
Past Talks/Conferences:  November 8, 2018, Analysis and Geometry seminar, UC Santa Cruz,
Talk: "The Maslov Index and the Spectra of Second Order Elliptic Operators"
 July 23–27, 2018, Conference on Mathematics of Wave Phenomena, Karlsruhe Institute of Technology, Germany
Talk: "The Maslov Index and the Spectra of Second Order Elliptic Operators"  June 1724, 2018, BIRS FRG Workshop, Stability Indices for Nonlinear Waves and Patterns in Many Space Dimensions, Banff, Canada
 June 1114 2018, SIAM Conference, Anaheim, CA,
Talk: "On Limits of Quantum Graph Operators with Shrinking Edges "  March 23, 2018, PDE Seminar, University of Houston,
Talk: "The Maslov Index and the Spectra of Second Order Elliptic Operators"  March 59, 2018, Arizona School of Analysis and Mathematical Physics, University of Arizona, Tucson.
Talk: "The Maslov Index and the Spectra of Second Order Elliptic Operators"  February 1819, 2018, 36th Western States meeting of Mathematical Physics, UC Irvine.
Talk: "The Maslov Index and the Spectra of Second Order Elliptic Operators"  SIAM Conference on Analysis of Partial Differential Equations, Baltimore MD
Talk:"The Maslov Index and the Spectra of Second Order Elliptic Operators"  Texas Analysis and Mathematical Physics Symposium 2017, Austin, TX
Talk:"The Maslov Index and the Spectra of Second Order Elliptic Operators"  Waves, Spectral Theory and Applications – Part 2, University of North Carolina, Chapel Hill, NC.
 GeometryAnalysis Seminar, Rice University, Houston, TX.
Talk:"The Maslov Index and the Spectra of Second Order Elliptic Operators"  Mathematical Physics and Harmonic Analysis Seminar, Texas A&M, College Station, TX.
Talk:"The Maslov Index and the Spectra of Second Order Elliptic Operators" 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 Upcoming teaching:
 Math 381, Introduction to partial differential equations, Fall 2019
 Math 499, (research with undergraduate students) Fall 2019
Past teaching:At Rice University Math 212, Multivariable calculus, Spring 2019 Math 424/514, Topics in PDE II, Spring 2019 Math 499, (research with undergraduate students) Spring 2019 Math 321, Introduction to analysis, Fall 2018 Math 211, Differential equations and linear algebra, Spring 2018 Math 211, Differential equations and linear algebra, Fall 2017 Math 321, Introduction to analysis, Fall 2017
At the University of Missouri as Teaching Assistant (duties: leading recitation sessions, grading exams and quizzes, holding office hours):  Advanced Calculus of One Real Variable I: Spring 2014, Fall 2016, Spring 2017.
 Analytic Geometry and Calculus I: Fall 2013(2 sections), Spring 2014, Fall 2014 (2 sections), Fall 2015(2 sections), Spring 2017.
 Calculus II: Spring 2015(2 sections), Spring 2016, Fall 2016.

