International laboratory for Mirror Symmetry and Automorphic Forms

The new international laboratory 'Mirror Symmetry and Automorphic Forms' will open at the Faculty of Mathematics of HSE in 2017. The project of Ludmil Katzarkov (Professor of the University of Miami) won the fifth Mega-grants competition of the Government of the Russian Federation. Our faculty is the only one in the country, where in 2017 will run three laboratories in fundamental mathematics, and two of them are in the framework of this global scientific program of the federal support of scientific research.

The project of Katzarkov is aimed to developing of a new cutting edge direction in mathematics — Mirror Symmetry and Categorical Kähler Geometry. Mirror Symmetry, as a foundational attribute of models in elementary particles theory was discovered by physicists in 90th. The starting point of this project is Homological Mirror Symmetry. It was conjectured by Kontsevich and has originated in physics as a duality between superconformal quantum field theories. Important parts of Homological Mirror Symmetry were studied by Katzarkov with mathematicians of the Moscow school in algebraic geometry. Due to this the new Laboratory will collaborate with the Laboratory of Algebraic Geometry (Fedor Bogomolov and Alexandr Kuznetzov). Categorical Kähler geometry is deeply related to physical theories of Mirror Symmetry. Methods of Mirror symmetry are closely related to ones that are developed by the Laboratory of Representation Theory and Mathematical Physics (Andrey Okounkov and Boris Feigin).

The need for convergence of ideas from mathematics and physics is explained by the fact that physics of elementary particles stands on the edge of a profound revolution expected from new experimental data obtained on the Large Hadron Collider. These data should help to identify which quantum field theories best address the high energy physics. Basic mathematical research is needed for developing the technical framework of modern physical theories. The major aim of the present project consists of creating a new centre for bringing together mathematics and physics at the HSE Faculty of Mathematics.