Ilya V. Schurov

Mathematics, ML & AI

Radboud University

About me

I’m a mathematician and technology enthusiast. I love pure mathematics and I equally love to code and solve applied problems. Currently I work at Radboud University in the Theory of Condensed Matter group. Previously I worked as an associate professor at HSE University, where I participated in various research projects with topics ranging from differential equations and physics to game theory to linguistics. My teaching experience include courses on calculus, machine learning, differential equations and data science. I prepared several online courses for Coursera devoted to foundations of machine learning and wrote free interactive textbooks on calculus and ordinary differential equations that are used by thousands Russian-speaking students.

Download my CV.

Interests

Machine Learning
Differential Equations
Dynamical Systems

Education

Ph.D. in Mathematics, 2010

Moscow State University
M.S. in Mathematics, 2006

Moscow State University

Research Projects

Data science journey to highland Daghestan

How machine learning helps sociolinguists to assess their data

Textbooks

I want to reinvent mathematical textbooks: make them accessible, friendly, full of illustrations and in-depth explanations of the essence of mathematical concepts. To achieve this goal, I even developed my own publishing platform that leverages modern web-technologies and allows to include interactive elements to mathematical texts.

Calculus

Friendly introduction to rigorous one-dimensional calculus. We have precise epsilon-delta definitions and all the proofs, carefully explained, with examples, motivations and illustrations. Batteries included!

Ordinary differential equations

Introductory textbook with focus on important geometrical and dynamical phenomena like conservation laws, stability and bifurcations.

Featured Publications

Yu. Ilyashenko, Yu. Kudryashov, I. Schurov

March, 2018 Inventiones mathematicae, 213 (2), 461–506

Global bifurcations in the two-sphere: a new perspective

We construct an open set of structurally unstable three parameter families whose weak and so called moderate topological classification has a numerical invariant that may take an arbitrary positive value. Here and below “families” are “families of vector fields in the two-sphere”. This result disproves an Arnold’s conjecture of 1985. Then we construct an open set of six parameter families whose moderate topological classification has a functional invariant. This invariant is an arbitrary germ of a smooth map $(ℝ_+, a)→(ℝ_+, b)$. More generally, for any positive integers $d$ and $d’$, we construct an open set of families whose topological classification has a germ of a smooth map $\left(ℝ_+^d, a\right)→\left(ℝ_+^{d’}, b\right)$ as an invariant. Any smooth germ of this kind may be realized as such an invariant. These results open a new perspective of the global bifurcation theory in the two sphere.

Research Papers

Michael Daniel, Alexey Koshevoy, Ilya Schurov, Nina Dobrushina (2022). Can Recall Data Be Trusted?. Field Methods, 34 (4), 2022.

Cite Project DOI Code

Dmitry Dagaev, Ilya Schurov (2020). Bachet’s game with lottery moves. Discrete Mathematics, 343 (4), 111704.

Cite DOI arXiv

Michael Daniel, Ruprecht von Waldenfels, Aleksandra Ter-Avanesova, Polina Kazakova, Ilya Schurov, Ekaterina Gerasimenko, Daria Ignatenko, Ekaterina Makhlina, Maria Tsfasman, Samira Verhees, Aleksei Vinyar, Vasilisa Zhigulaskaja, Maria Ovsjannikova, Sergey Say, Nina Dobrushina (2019). Dialect loss in the Russian North: Modeling change across variables. Language Variation and Change, 31 (3), 353–376.

Cite DOI Code

Yu. Ilyashenko, Yu. Kudryashov, I. Schurov (2018). Global bifurcations in the two-sphere: a new perspective. Inventiones mathematicae, 213 (2), 461–506.