International Laboratory for Mirror Symmetry and Automorphic Forms
The new International Laboratory for Mirror Symmetry and Automorphic Forms will open at HSE’s Faculty of Mathematics in 2017. This project, overseen by Ludmil Katzarkov (Professor at the University of Miami), won the Fifth Mega-Grants Competition of the Government of the Russian Federation.
HSE Faculty of Mathematics is the only one of its kind in the country. In 2017, it will be operating three laboratories focused on fundamental mathematics, two of which have been developed as part of a global scientific programme with federal support for scientific research.
Katzarkov’s project aims at developing a new cutting edge area of mathematics — Mirror Symmetry and Categorical Kähler Geometry. Mirror Symmetry, as a foundational attribute of models used in elementary particles theory, was discovered by physicists in 1990s. The starting point of this project is Homological Mirror Symmetry. This was conjectured by Kontsevich and originated in physics as a duality between superconformal quantum field theories. Furthermore, Homological Mirror Symmetry was studied by Katzarkov along with mathematicians of the Moscow School of Algebraic Geometry. Therefore, the new laboratory will collaborate with the Laboratory of Algebraic Geometry (Fedor Bogomolov and Alexandr Kuznetzov). Categorical Kähler Geometry is deeply related to the physical theories of Mirror Symmetry, which, in turn, are closely related to those developed by the Laboratory of Representation Theory and Mathematical Physics (under Andrey Okounkov and Boris Feigin).
The need for convergence of ideas from mathematics and physics is driven by the fact that physics of elementary particles stands on the verge of a major breakthrough thanks to new experimental data obtained on the Large Hadron Collider. This data should help experts to identify which quantum field theories best address the issues posed by high energy physics. Furthermore, basic mathematical research is necessary for developing the technical framework of modern physical theories. The major aim of this project consists of creating a new centre for combining mathematics and physics at the HSE Faculty of Mathematics.
Mathematicians at the Higher School of Economics have developed a model that explains how cell specialization arises in the context of resource constraints. The results are published in PLOS One journal.
An international group of researchers (the first author is Nikita Kalinin, HSE Saint-Petersburg, the last author is Ernesto Lupercio, CINVESTAV, Mexico) has presented the first continuous model describing self-organised criticality. The proposed solution is simpler and more universal than the classical sandpile model: it integrates areas as remote from one another as economics, developmental biology and gravity in the context of tropical geometry. The paper was published in PNAS.
Graduates of the Faculty of Mathematics at HSE, Andrey Ionov and Lera Starichkova, who have since enrolled in educational programmes at leading international universities, spoke about their love for mathematics, the level of the Bachelor programme at HSE, and admission to foreign PhD programmes.
The HSE Summer University is off to a strong start this year, and one of its programmes – the Research Experience for Undergraduates (REU) in Mathematics – has already been met with considerable enthusiasm by participating students. Designed for undergraduate students majoring in Mathematics or related areas, participants work on research projects under the supervision of distinguished mathematicians.
Moscow Lectures, a new series of books in English, is set to be published by Springer Nature. The series is issued jointly by HSE and Skoltech, and its Editor-in-Chief is Alexey Gorodentsev, Professor at the HSE Faculty of Mathematics. Twelve volumes are currently in preparation and the first volume will be published at the beginning of June 2018. The series builds on the outstanding research and education in the field of mathematics in Moscow. It is aimed at graduate and undergraduate students, as well as lecturers and researchers, across the globe.
A team of HSE students has sucessfully returned after taking part in the 28th Vojtěch Jarník International Mathematical Competition, held in the Czech Republic. The competition has been held annually since 1991 by the University of Ostrava in the Czech Republic. Students compete in two age groups: category I (junior group) is for first and second-year students under 22 years and category II (senior group) is for older students.
On March 24, a mathematics test 'Q.E.D.' (quod erat demonstrandum, meaning 'which was to be proved') will take place, organized by Yandex. It is open to anyone who is interested. As on previous occasions, HSE will be one of the test sites.
The recipients of the annual Web of Science Awards are the most influential scientists, scientific organizations and publications of the year. The Moscow Mathematical Journal has made it into the top quartile in the subject area of mathematics and was announced by jury members to be the most influential Russian scientific journal of 2017.
Mirror symmetry is a relatively new field of mathematics which came into being in the 1990s. In 2017, HSE opened the International Laboratory for Mirror Symmetry and Automorphic Forms. The December conference, ‘Mirror Symmetry and Applications’, was a commemoration of its first year of operation.