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.
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.
Researchers have conducted a study on tournaments using the playoff system, which is one of the most popular forms of sporting competitions. The results of the study were published in the Journal of Combinatorial Optimization.
Carlos Cortez, a bronze medallist of the International Mathematical Olympiad (2011, 2012, 2013) and a Mathematics graduate of MIT, recently completed a two-month research internship at the HSE Faculty of Mathematics under the supervision of Professor Sergei Lando. He will soon be pursuing a Master’s degree at University Paris-Sud in France followed by a PhD at Northwestern University (USA). The research internship was made possible through a cooperation agreement between MIT International Science and Technology Initiatives (MISTI) and HSE.
‘Mirror Symmetry Was Discovered by Physicists, But Very Quickly Got the Attention of Mathematicians…’
The HSE International Laboratory for Mirror Symmetry and Automorphic Forms, which is among several international laboratories to recently open within the Higher School of Economics, was created in December 2016 as part of the Russian government’s mega-grants program. Below, the lab’s academic supervisor, Ludmil Katzarkov, along with deputy heads Valery Gritsenko and Viktor Przyjalkowski, explain why the laboratory is fully capable of becoming a unique multidisciplinary unit dedicated to the study of mirror symmetry, automorphic forms, and number theory.
HSE researchers have used computer modelling to demonstrate the varying manipulability of decision-making procedures and to identify those least susceptible to manipulation. Their findings are published in the paper 'Manipulability of Majority Relation-based Collective Decision Rules'.
Three HSE students from the Faculty of Mathematics and the Faculty of Computer Science won medals at the Vojtěch Jarník International Mathematical Competition held in the Czech Republic. Nikita Gladkov, a mathematics student, scored maximum points and was recognized as the outright winner in his category.
On December 23, 2016, the HSE Academic Council approved the creation of four new laboratories: the International Laboratory for the Study of Russian and European Intellectual Dialogue, the International Laboratory for Population and Health Studies, the International Laboratory of Deep Learning and Bayesian Methods, and the International Laboratory for Supercomputer Atomistic Modelling and Multi-scale Analysis.
This summer, the HSE Faculty of Mathematics moved into a new building on Usacheva Street. As part of the Open House project, two HSE students – Petr Ogarok, a second-year student in the Mathematics programme, and Anastasia Matveeva, a first-year master’s student in the Mathematics and Mathematical Physics programme – gave an excursion around the new building.
In 2015 Alexey Bufetov graduated from HSE Doctoral School of Mathematics, and is now working at MIT. He has talked to HSE News Site about his research and his career as a mathematician.
Jonathan Gerhard from James Madison University spent one semester studying in Math in Moscow programme run jointly by HSE, Moscow Center for Continuous Mathematical Education, and Independent University of Moscow. During his time in Russia Jonathan took intensive maths courses, studied the Russian language and traveled to several Russian cities.