‘The Conference Strengthened Our Sense of Belonging to the International Mathematics Community’
From July 13 to 17, 2026, the HSE Faculty of Mathematics hosted the international conference ‘Moduli, Dynamics, and Integrability,’ bringing together leading mathematicians from Russia, the United States, China, the United Kingdom, and other countries.
According to Alexandra Skripchenko, Dean of the Faculty of Mathematics, the conference on moduli spaces provided an excellent opportunity to bring together experts from two rapidly developing fields—geometry and dynamical systems theory. ‘Experience shows that the most significant and insightful results in contemporary mathematics often emerge at the intersection of different disciplines,’ she explained.
Alexandra Skripchenko
In the dean's view, one of the conference's greatest achievements was creating opportunities for early-career mathematicians—undergraduate and postgraduate students alike—to meet internationally renowned researchers, who presented the latest advances in algebraic geometry, topological recursion, and other areas of mathematics. At the same time, young scholars were able to showcase their own research. ‘The conference proved to be a truly inspiring event that will undoubtedly provide a major impetus for the further development of mathematics in Moscow,’ said Alexandra Skripchenko.
Among the distinguished mathematicians who took part in the conference were Andrei Okounkov, Professor at HSE University and Columbia University; Michael Shapiro, Professor at Michigan State University; Andrey Mironov, Acting Director of the Sobolev Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences; and Alexander Veselov, Professor at Loughborough University.
Alexandr Buryak
‘The profound relationship between moduli spaces in algebraic geometry and the theory of integrable systems has remained an active area of research for the past 35 years. At the same time, dynamics is a classical branch of mathematics in which many important questions have remained unresolved for well over a century. More recently, new connections between these two fields have emerged through the geometry of moduli spaces of curves. That is precisely why the conference focused on these two areas, which at first glance might appear only loosely connected,’ explained Alexandr Buryak, Head of the HSE–Skoltech International Laboratory of Representation Theory and Mathematical Physics.
In his assessment, the conference attracted considerable interest and was characterised by a lively atmosphere that encouraged productive scientific discussions.
Vladlen Timorin
‘It was extremely important for me to meet colleagues working in different countries and exchange the latest research developments and ideas with them. The conference strengthened my sense of belonging to the international mathematical community. To preserve that sense of connection, events like this need to take place regularly,’ said Vladlen Timorin, Research Fellow at the Laboratory of Algebraic Geometry and Its Applications and Distinguished Professor at HSE University.
Alexey Basalaev
‘As a researcher whose work in recent years has focused on mirror symmetry and integrable systems, I found the conference to be a genuine catalyst. The discussions with colleagues enabled me to look at long-standing projects from a fresh perspective and discover unexpected links with other branches of mathematics. I believe the conference was important not only because of the outstanding presentations, but also because it identified concrete directions for future collaboration that will help advance several questions that have interested me for many years,’ emphasised Alexey Basalaev, Associate Professor at the HSE Faculty of Mathematics.
Mikhail Zaitsev
‘The conference gave us an opportunity to present our latest findings on braided structures related to the reflection equation algebra. Our research lies at the intersection of representation theory and integrable systems and is somewhat outside the conference's main focus on Gromov–Witten invariants. Nevertheless, many of the talks offered new perspectives on our work. For example, some generating series for generalised Hurwitz numbers appear in our research as averages over certain families of central elements, while their description in terms of topological recursion suggests that these families have an independent significance beyond the framework of the reflection equation algebra,’ said Mikhail Zaitsev, Research Assistant at the HSE Faculty of Mathematics.
He added that informal discussions with senior colleagues during the conference had also proved valuable. For example, Michael Shapiro mentioned that the reflection equation itself appears in work he has been carrying out with his co-authors. ‘It was very encouraging to learn that our results may prove useful for their research as well,’ the research assistant added.
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