About the Laboratory
The International Laboratory of Mirror Symmetry and Automorphic Forms was created in December 2016 in the framework of the Russian Government megagrants program. The head of the Laboratory is the American-Bulgarian mathematician Ludmil Katzarkov.
We are planning to create a new global research platform that combines the efforts of mathematicians from different domains of mathematics and theoretical physics working on the problems related to mirror symmetry, derived and non-commutative geometry, automorphic forms, and number theory.
During the project implementation we will focus on establishing a solid, highly promising generation of young Russian mathematicians as well as on scientific collaboration with leading foreign scientists.
Scientific goal of the Laboratory is to establish applications of Homological Mirror Symmetry to classical questions in geometry with decades long history:
- The categorical Donaldson, Uhlenbeck, Yau–Hitchin, Kobayashi correspondence.
- The existence of Kähler–Einstein metrics on manifolds. This question has its origin in the dawn of General Relativity.
- The question of rationality. This question goes back to the XIX century Italian geometry school.
- Description of Lorentz Kac-Moody algebras that is needed for completion of the classification originated by Cartan in the beginning of XX century.
- Automorphic generalization of the main topological invariants in the framework of the theory of superconformal indices and Mirror Symmetry.
- Creating new symplectic invariants.
- Looking for new applications to symplectic geometry, algebraic geometry, and number theory.
The Laboratory is planned to collaborate with a variety of Russian and foreign scientific centers such as Faculty of Mathematics of HSE, Laboratory of algebraic geometry and applications of HSE, Steklov Mathematical Institute, Joint Institute for Nuclear Research (Dubna), IITP, Independent University of Moscow, IHÉS, Institut e for Advanced study (Princeton), The Courant Institute of Mathematical Sciences (New York), IPMU (Tokyo), Max Planck Institute for Mathematics, Max Planck Institute for Gravitational Physics, Theoretical Division of CERN, ICTP (Trieste), and other centers in Russia, France, Germany, Great Britain, Japan, USA, as well as with other international grants such as Simons Collaboration on Homological Mirror Symmetry and British grant ‘Classification, Computation, and Construction: New Methods in Geometry’.
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