Ilya V. Schurov

Associate Professor

HSE University

About me

I’m a mathematician and technology enthusiast. Since 2010 I work as an associate professor at HSE University, where I am participating in various research projects with topics ranging from differential equations and physics to game theory to linguistics. I love pure mathematics and I equally love to code and solve applied problems. Currently I’m looking for opportunities to apply my broad mathematical background, including dynamical systems, geometry and topology, to data analysis. 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

Experience and achievements

Research

Received Best young mathematician award from the Dynasty Foundation.
Systematically publish research papers in top journals.
Published in Inventiones Mathematicae, one of the most presitigious mathematical journals.
Received a special 5-year bonus from HSE for academic performance.

Teaching

Taugh more than 20 different courses in mathematics, data science, statistics, game theory and programming to students of different backgrounds, in Russian and English.
Received best teacher award according to a students’ vote for six years in a row.
Received honorary mention from Faculty of Computer Sciences for teaching.
Prepared 3 courses for Coursera on Probability and Statistics and received a special bonus from HSE for their success.

Service

Member of the academic council at HSE/NES Programme in Economics, supervising mathematical and computer science courses.
Member of jury, Russian National Olympiad on Economics for high-schoolers.
Member of jury, Data Analysis National Olympiad for high-schoolers.

Industry

Co-supervising Joint HSE — Tinkoff Bank project group aimed at solving mathematically-demanding data science problems, including graph analysis and data generation.

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, to appear.

Cite Project 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.