My main research interests are in theory of complex systems and, therefore, they are in the interplay of mathematical physics, functional analysis, PDE, and probability theory. In particular, I have worked on problems dealing with infinite-dimensional analysis, applications of methods of functional analysis and probability theory to mathematical physics, Gibbs measures, point processes, stochastic dynamics and scaling limits, mathematical biology. Currently, I am actively working in the study of non-local evolution equations arising as (mesoscopics) limits for dynamics of the considered complex systems.

Areas of Expertise

  • Interacting Particle Systems
  • Stochastic Dynamics
  • Infinite-dimensional Analysis
  • Markov Evolutions
  • Complex Systems
  • Nonlocal PDE
  • Front propagation
  • Travelling waves

Publications

  1. Finkelshtein, D., Kondratiev, Y., Lytvynov, E., Oliveira, M. An infinite dimensional umbral calculus Journal of Functional Analysis 276 12 3714 3766
  2. Finkelshtein, D., Kondratiev, Y., Lytvynov, E., Oliveira, M., Streit, L. Sheffer homeomorphisms of spaces of entire functions in infinite dimensional analysis Journal of Mathematical Analysis and Applications
  3. Cornell, S., Suprunenko, Y., Finkelshtein, D., Somervuo, P., Ovaskainen, O. A unified framework for analysis of individual-based models in ecology and beyond Nature Communications 10 1
  4. Finkelshtein, D., Kondratiev, Y., Tkachov, P. Doubly nonlocal Fisher–KPP equation: front propagation Applicable Analysis 1 24
  5. Finkelshtein, D., Tkachov, P. An Ikehara-type theorem for functions convergent to zero Comptes Rendus Mathematique 357 4 333 338

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Teaching

  • MA-142 Classical Mechanics (of Particles)

    An introduction to the concepts and principles of classical mechanics. The course covers the use of vectors to model physical problems and various quantities from physics. It then introduces Newton¿s laws of motion and considers some of the fundamental examples such as rocket motion and planetary motion.

Supervision

  • (tentative)«br /»«br /» Space-time correlations for interacting particle systems (current)

    Student name:
    PhD
    Other supervisor: Prof Eugene Lytvynov
  • Untitled (current)

    Student name:
    PhD
    Other supervisor: Prof Eugene Lytvynov
  • Untitled (current)

    Student name:
    PhD
    Other supervisor: Prof Vitaly Moroz

Administrative Responsibilities

  • First Year Tutor

    2017 - Present

  • Foundation Year Tutor

    2014 - 2016

Career History

Start Date End Date Position Held Location
March 2017 Present Senior Lecturer Swansea University
September 2013 February 2017 Lecturer Swansea University
March 2013 August 2013 Scientific Fellow Faculty of Mathematics, Bielefeld University, Germany
December 2003 August 2013 Senior Researcher Institute of Mathematics, Kiev, Ukraine
September 2008 June 2013 Associate Professor Dragomanov Pedagogical University, Kiev, Ukraine

Academic History

Date Qualification Location
June 2014 D.Sc. (Habilitation) Institute of Mathematics, Kiev, Ukraine
November 2004 PhD Institute of Mathematics, Kiev, Ukraine
June 2000 MSc with distinction Kiev National Taras Shevchenko University