Field of Science

Scientific interests 

In the late 80s and 90s, my main publications concerned the connection between the hierarchical Dyson model and p-adic quantum field theory, the theory of renormalizations of Feynman amplitudes from p-adic argument and adelic amplitudes. In the 2000s, the main publications dealt with various Arnold conjectures, problems of combinatorics and number theory. In the 2010s, the main publications are related to mathematical models of Zipf's law and other power laws. Currently, a series of papers on stable matchings has been submitted for publication (formerly I was the scientific editor of Donald Knuth's book 'Stable matchings and other combinatorial problems' in Russian).  In 2017, next topic was staked in the Electronic Journal of Combinatorics, and now a deeper study of the generalization of flow and chromatic as Feynman amplitudes over finite fields is planned. It is also planned to study continuous statistical-physical models over unusual (but natural) algebraic structures.