Professor Eugene Lytvynov

Research Highlights

1. Schiavo, L. & Lytvynov, E. (2023). A Mecke-type characterization of the Dirichlet–Ferguson measure. Electronic Communications in Probability, 28(none)

   https://doi.org/10.1214/23-ecp528, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa63328

   http://dx.doi.org/10.1214/23-ecp528
2. Alshehri, M. & Lytvynov, E. (2022). Hafnian point processes and quasi-free states on the CCR algebra. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 25(1)

   https://doi.org/10.1142/s0219025722500023, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa58782
3. Finkelshtein, D., Kondratiev, Y., Lytvynov, E., & Oliveira, M. (2022). Stirling operators in spatial combinatorics. Journal of Functional Analysis, 282(2), 109285

   https://doi.org/10.1016/j.jfa.2021.109285, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa58358
4. Daletskii, A., Kalyuzhny, A., Lytvynov, E., Proskurin, D., & Lytvynov, E. (2020). Fock representations of multicomponent (particularly non-Abelian anyon) commutation relations. Reviews in Mathematical Physics, 32(05), 2030004

   https://doi.org/10.1142/s0129055x20300046, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa54446
5. Finkelshtein, D., Kondratiev, Y., Lytvynov, E., Oliveira, M., & Streit, L. (2019). Sheffer homeomorphisms of spaces of entire functions in infinite dimensional analysis. Journal of Mathematical Analysis and Applications, 479(1), 162-184.

   https://doi.org/10.1016/j.jmaa.2019.06.021, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa50766
6. Lytvynov, E. (2019). Representations of the Anyon Commutation Relations. In Geometric Methods in Physics XXXVI-327).

   https://doi.org/10.1007/978-3-030-01156-7_33, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa50118
7. Finkelshtein, D., Kondratiev, Y., Lytvynov, E., & Oliveira, M. (2019). An infinite dimensional umbral calculus. Journal of Functional Analysis, 276(12), 3714-3766.

   https://doi.org/10.1016/j.jfa.2019.03.006, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa49896
8. Litvinov, W. & Lytvynov, E. (2019). Construction of solutions to parabolic and hyperbolic initial–boundary value problems. Applicable Analysis, 99(14), 2381-2413.

   https://doi.org/10.1080/00036811.2019.1566528, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa48055
9. Bożejko, M., da Silva, J., Kuna, T., & Lytvynov, E. (2018). Approximation of a free Poisson process by systems of freely independent particles. Infinite Dimensional Analysis, Quantum Probability and Related Topics, 21(3), 1850020-1-1850020-25.

   https://doi.org/10.1142/S0219025718500200, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa43227
10. Ibraheem, H. & Lytvynov, E. (2018). Quasi-invariance of completely random measures. Methods of Functional Analysis and Topology, 24(3), 207-239.

    SU Repository: https://cronfa.swan.ac.uk/Record/cronfa38956

    http://mfat.imath.kiev.ua/article/?id=1083

All Research

• Untitled (current)

  PhD

  Other supervisor: Prof Chenggui Yuan

• Umbral calculus over a Hilbert space. (current)

  PhD

  Other supervisor: Dr Dmitri Finkelshtein

• Generalised Stirling operators, with Applications (current)

  PhD

  Other supervisor: Dr Dmitri Finkelshtein

• Convergence of approximate solutions of SDEs (current)

  PhD

  Other supervisor: Prof Feng-Yu Wang

  Other supervisor: Prof Chenggui Yuan

• Quasi-free states on algebra of multicomponent commutation relations (awarded 2023)

  PhD

  Other supervisor: Dr Dmitri Finkelshtein

• MA-359 Financial Mathematics in Continuous Time

  This module will introduce students to sections 3, 4 and 6 of the Institute and Faculty of Actuaries CM2 syllabus. This module serves as an introduction to the Black-Scholes model for the continuous-time dynamics of a financial market containing a bank account and several kinds of stocks. This theory is based on stochastic (Itô) calculus for Brownian motion. Special attention is paid to the applications of stochastic calculus to the absence of arbitrage in a financial market and pricing and hedging of the options.

• MA-384 Fourier Analysis

  The module serves as an introduction to the main concepts, results and examples related to Fourier series of a function. The students will study in depth how, for a given periodic function, one finds its Fourier series and studies convergence of this series ¿ pointwise convergence, uniform convergence, absolute convergence, convergence in the L^1 space. The concept of the Schwartz space of smooth, rapidly decreasing functions will be introduced and the students will learn how the Fourier transform acts on this space. Finally, the students will study how Fourier series and Fourier transform is applicable for solving ordinary and partial differential equations.

• MA-M59 Financial Mathematics in Continuous Time

  This module will introduce students to sections 3, 4 and 6 of the Institute and Faculty of Actuaries CM2 syllabus. This module serves as an introduction to the Black-Scholes model for the continuous-time dynamics of a financial market containing a bank account and several kinds of stocks. This theory is based on stochastic (Itô) calculus for Brownian motion. Special attention is paid to the applications of stochastic calculus to the absence of arbitrage in a financial market and pricing and hedging of the options.

• MA-M84 Fourier Analysis

  An introduction to Fourier Analysis

• MARM02 Stochastic Processes (MRes Thesis)

  A research project selected from an area of expertise of a member of staff in the Department of Mathematics. It will enable the students to develop an enquiring, analytical critical and creative approach to problem identification and solution. The project will typically focus on a subject area covered within one of the taught modules in the MRes scheme.