The main aim of our research is to develop mathematical framework for the study of a class of stochastic systems of a large number of elements (called "particles") described by their "positions" and "marks" (representing internal structure of the corresponding particles). The particles are coupled via (random) interaction potentials. Examples of systems of such type can be found in a wide variety of sciences, including quantum physics, astrophysics, chemical physics, biology, ecology, computer science, economics, finance, etc.

**Participating institutions:** University of York, University of Wales-Swansea, University of Reading, University of Durham

**Participating researchers:** Dr Alex Daletskii, Dr Kasia Rejzner (York), Professor Eugene Lytvynov, Dr Dmitri Finkelshtein (Swansea), Dr Tobias Kuna (Reading), Dr Ostap Hryniv (Durham).

**PhD students:** Tayfun Kok, Georgy Chargazia, Habeebat Ibraheem, Maryam Alshehri, Adam Barker, Joey McMillan

**International collaboration:** Professor Yuri Kondratiev, Dr Tanja Pasurek, Dr Oles Kutovyi (Bielefeld), Dr Maria Infusino (Konstanz), Professor Yuri Kozitsky (Lublin), Dr Diana Conache (Muenchen)

**Recent selected publications:**

D. Conache, Y. Kondratiev, E. Lytvynov: Equilibrium diffusion on the cone of discrete Radon measures, arXiv:1503.04166, to appear in Potential Analysis

Y. Kondratiev, E. Lytvynov, A. Vershik: Laplace operators on the cone of Radon measures, arXiv:1503.00750, to appear in J. Funct. Anal.

Y. Kondratiev, T. Kuna, E. Lytvynov: A moment problem for random discrete measures, Stochastic Process. Appl. 125 (2015), 3541-3569

D. Conache, A. Daletskii, Yu. Kondratiev, T. Pasurek: Gibbs Measures on Marked Configuration Spaces: Existence and Uniqueness, arXiv:1503.06349 [math-ph] (2015).

A. Daletskii, Yu. Kondratiev, Yu. Kozitsky: Phase Transitions in Continuum Ferromagnets with Unbounded Spins, arXiv:1503.07010 [math-ph] (2015).

A. Daletskii, Yu. Kondratiev, Yu. Kozitsky, T. Pasurek: Phase Transitions in a quenched amorphous ferromagnet, *J. Stat. Phys*. (2014) 156:156—176.

A. Daletskii, Yu. Kondratiev, Yu. Kozitsky, T. Pasurek: Gibbs states on random configurations (with Yu. Kondratiev, Yu. Kozitsky, T. Pasurek), *J. Math. Phys*. 55, 083513 (2014).

Finkelshtein, D. Around Ovsyannikov's method. Methods of Functional Analysis and Topology, (2015) 21(2), 134-150.

Finkelshtein, D., Kondratiev, Y., Kozitsky, Y. Kutoviy, O. The statistical dynamics of a spatial logistic model and the related kinetic equation. Mathematical Models and Methods in Applied Sciences, (2015) 25(02), 343-370, doi:10.1142/S0218202515500128

Finkelshtein, D., Kondratiev, Y., Kutoviy, O. Oliveira, M. Dynamical Widom–Rowlinson Model and its Mesoscopic Limit. Journal of Statistical Physics, (2015) 158(1), 57-86, doi:10.1007/s10955-014-1124-6

D. Finkelshtein: International Conference "Micro and Macro Systems in Life Sciences", Bedlewo, Poland, April 8-13, 2015. Talk: "Nonlocal Kinetic Equations derived from Stochastic Dynamics ofComplex Systems"

Wales Mathematics Colloquium, Gregynog, U.K., May 18-20, 2015 Talk: "Self-Aggregation and Expansion in a Spatial Stochastic Evolution"

International Conference "Probability, Reliability and Stochastic Optimization", Kyiv, Ukraine, April 7-10, 2015. Plenary Talk: "Statistical Description for Spatial Stochastic Dynamics: an Overview"

E. Lytvynov: Analysis on the cone of discrete Radon measures, Mini-course within the International Programme for Studies in Computer Science and Mathematics Applied to Business, Wroclaw University, May 2015

**Events: - **the following meetings are partly funded by an LMS Joint Research Groups in the UK - Scheme 3 grant.

MMRMS Workshop 1 - December 2015

MMRMS Workshop 2 - February 2016

MMRMS Workshop 3 - June 2016

MMRMS Workshop 4 - September 2016

MMRMS Workshop 5 - March 2017

MMRMS Workshop 6 - November 2017

MMRMS Workshop 7 - May 2018