Dr. Leonid Zerkalov

Corporate Relations

Dr. Leonid Zerkalov graduated from the Peoples' Friendship University of Russia (PFUR) with bachelor’s and master’s degrees in Mathematics. He has also received his Ph.D. in Physics and Mathematics after defending his dissertation in Geometry and Topology. Leonid worked as a professor of mathematics for 20 years at various universities in Russia, Spain, and Mexico.


A significant part of Dr. Zerkalov’s research papers is devoted to problems of creating AI and DSS using innovative pattern recognition models. As a renowned specialist in mathematic modeling and pattern recognition, Dr. Zerkalov has created an invariant pattern recognition theory based on the synthesis of algebraic topology and classical pattern recognition methods. This approach is unique in the field of mathematic modeling as it allows to precisely describe (frame) the features (specificities) of an image (pattern form) based on its homotopic invariants, thus making recognition of fuzzy (unsharp) patterns much more efficient when solving problems dealing with uncertainty.

Methods of pattern recognition, created by Dr. Zerkalov and based on the concept of combinatorial homotopic equivalence, allow one to structure data on invariants of object forms, thus creating a single concept of the form for sharp and unsharp patterns.

Dr. Zerkalov received international recognition for his research works. Throughout his career, he received multiple high international awards, including the National Researcher and Professor of the Patrimonial Cathedra of Excellence in Mexico, as well as various international research grants for conducting his research projects in a number of universities in various countries, such as State University  Paulista (San Jose do Rio Preto, Brazil), University Jaume I (Valencia, Spain), Benemerita Universidad Autonoma de Puebla (Puebla, Mexico), and Moscow State University (Moscow, Russia).

Later in his career, Dr. Zerkalov worked as the head of the R&D Group and the Technical Director of the Scientific and Technical Centre. He was also actively engaged in scientific practices working as a Consulting Professor at Optimisation and Nonlinear Analysis Department of People’s Friendship University of Russia (PFUR). He also served as the head of the University’s Inter-disciplinary Centre for Mathematic Modelling run in collaboration with Mexico’sBenemerita Universidad Autonoma de Puebla.

The research group led by Dr.Zerkalov developed a methodology enabling recognition of unsharp photography duplicates which involves preliminary pattern processing by means of segmenting the duplicates through clusterization of image pixels’ brightness.

Currently, Dr. Zerkalov works as the Managing Partner of Elumee LLC where he leads the development of an interactive platform, Elumee Learn, helping automate the process of professional development of teaching staff based on PIFMA program, also developed by Elumee LLC.