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]
                       Advisors: Fritz Gesztesy and Yuri Latushkin

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,
  • Weyl-type asymptotic formulas,
  • Ergodic quantum graph models
Papers and preprints:

Upcoming/Recent travel:

  1. June 24--27, 2019, University of Hagen, On mathematical aspects of interacting systems in low dimension, Hagen, Germany
    Talk: "Localization for Anderson Models on Tree Graphs"
  2. July 1-5, 2019, Institut Henri Poincaré, Stability of Nonlinear Waves: Analysis and Computation, Paris, France
  3. August 4-9, 2019, Lake Como School of Advanced Studies, Quantum Graphs and Quantum Random Walks in Mathematics, Computer Science and Physics, Italy
    Talk: TBA
  4. September 5-8, 2019, University of Missouri, Analysis in Missouri: a Midwestern symposium, Columbia, MO
    Talk: "Localization for Anderson Models on Tree Graphs"
  5. September 15-20, 2019, BIRS, Workshop on Random Matrix Products and Anderson Localization, Banff, Canada
    Talk: TBA
  6. November 9-10, 2019, University of California, Riverside, AMS Fall Western Sectional Meeting.
    Talk: "Localization for Anderson Models on Tree Graphs"
Past Talks/Conferences:
  1. November 8, 2018, Analysis and Geometry seminar, UC Santa Cruz,
         Talk: "The Maslov Index and the Spectra of Second Order Elliptic Operators"

  2. 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"
  3. June 17-24, 2018, BIRS FRG Workshop, Stability Indices for Nonlinear Waves and Patterns in Many Space Dimensions, Banff, Canada
  4. June 11-14 2018,  SIAM Conference, Anaheim, CA,
    Talk: "On Limits of Quantum Graph Operators with Shrinking Edges "
  5. March 23, 2018, PDE Seminar, University of Houston, 
              Talk: "The Maslov Index and the Spectra of Second Order Elliptic Operators"
  6. March 5-9, 2018, Arizona School of Analysis and Mathematical Physics, University of Arizona, Tucson.
              Talk: "The Maslov Index and the Spectra of Second Order Elliptic Operators"
  7. February 18-19, 2018, 36th Western States meeting of Mathematical Physics, UC Irvine.
              Talk: "The Maslov Index and the Spectra of Second Order Elliptic Operators"
  8. SIAM Conference on Analysis of Partial Differential Equations, Baltimore MD
              
    Talk:"The Maslov Index and the Spectra of Second Order Elliptic Operators"
  9. Texas Analysis and Mathematical Physics Symposium 2017, Austin, TX
              
    Talk:"The Maslov Index and the Spectra of Second Order Elliptic Operators"
  10. Waves, Spectral Theory and Applications – Part 2, University of North Carolina, Chapel Hill, NC.
  11. Geometry-Analysis Seminar, Rice University, Houston, TX.
             
    Talk:"The Maslov Index and the Spectra of Second Order Elliptic Operators"
  12. Mathematical Physics and Harmonic Analysis Seminar, Texas A&M, College Station, TX. 
              Talk:"The Maslov Index and the Spectra of Second Order Elliptic Operators"
  13. SIAM Conference on Applications of Dynamical Systems, Snowbird, UT, USA
    Talk:"The Maslov Index and the Spectra of Second Order Elliptic Operators"    
  14. KUMUNU Conference on PDE, Dynamical Systems and Applications 2017, Lincoln, NE, USA  
  15. Baylor University, Analysis Seminar, Waco, TX, USA
              Talk :"The Maslov Index and the Spectra of Second Order Elliptic Operators" 
  16. The Tenth IMACS Conference on Nonlinear Waves, Athens, GA, USA      
              Talk :"The Maslov Index and the Spectra of Second Order Elliptic Operators"
  17. Conference on Methods of Modern Mathematical Physics, The Fields Institute, Toronto, Canada
  18. Frontiers in Mathematical Physics. In honor of Barry Simon's 70th birthday,University of Montreal, Canada
  19. SIAM Conference on Nonlinear Waves and Coherent Structures, Philadelphia, PA, USA
    Talk: "Counting spectrum via the  Maslov index for Schrödinger operators"
  20.  Applications of the Maslov index to multidimensional stability problems, AIM SQuaRE, San Jose, CA, USA
  21.  Mathematical Physics and Harmonic Analysis Seminar, Texas A&M University, College Station, TX, USA
    Talk: "A Bound for the Eigenvalue Counting Function for Higher-Order Krein Laplacians on Open Sets"
  22. Computational & Applied Mathematics Seminar, University Kansas, Lawrence, KS, USA
    Talk:"Counting spectrum via the  Maslov index for Schrödinger operators"
  23.  Geometric and Computational Spectral Theory, University of Montreal, Canada
  24.  KUMU PDE, Dynamical Systems and Applications, University of Kansas, Lawrence, KS, USA
    Talk:"The Morse and Maslov Indices for Schrödinger Operators"
  25.  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"
  26.  University of North Carolina, Chapel Hill, research visit by invitation of Prof. C. K. R. T. Jones
  27.  Differential Equations Seminar, University of Missouri, Columbia, MO, USA
    Talk:"The Morse and Maslov Indices for Schrödinger Operators"
  28.  The 34th Southeastern-Atlantic Regional Conference on Differential Equations, University of Memphis, TN, USA
    Talk:"The Morse and Maslov Indices for Periodic Schrödinger Operators"
  29.  Differential Equations Seminar, University of Missouri, Columbia, MO, USA
    Talk:"A Bound for the Eigenvalue Counting Function for Higher-Order Krein Laplacians on Open Sets"
  30.  Stability of Solitary waves, Pisa, Italy
  31.  Operator Semigroups and Dispersive Equations, Heinrich-Fabri 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

  1. Math 212, Multivariable calculus, Spring 2019
  2. Math 424/514, Topics in PDE II, Spring 2019
  3. Math 499, (research with undergraduate students)  Spring 2019
  4. Math 321, Introduction to analysis, Fall 2018
  5. Math 211, Differential equations and linear algebra, Spring 2018
  6. Math 211, Differential equations and linear algebra,  Fall 2017 
  7. 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.