Mirror Symmetry was discovered by physicists in 90-th. It originated as a physical duality between superconformal field theories. The mathematical theory of mirror symmetry is actively developing in the 21st century. 

Recent progress in studying mirror symmetry  discovered a deep relation between Mirror Symmetry Conjecture and birational and symplectic invariants of algebraic varieties. A big role in the research in this direction played Russian and Chinese mathematicians. The multidisciplinary of the nature of mirror symmetry explains this fact, that our joint project is designed for cooperation with two laboratories of BIMSA: Algebraic Geometry (Prof. Artan Sheshmani) and Theoretical Physics and General Relativity (Prof. Babak Haghighat, Prof. Nicolai Reshetikhin) with Prof. S.-T. Yau (president of BIMSA) being the head of BIMSA team. The main direction of the project is the development of approaches that combine various branches of mathematics and mathematical physics for the construction of new birational invariants of algebraic varieties and the study of various automorphic generating functions associated with varieties and physical theories. 

The main goal of the project is to explore a new research direction: applications of ideas of Homological Mirror Symmetry  to birational geometry in which the strong potentials of Russian and Chinese groups will be combined.

We shall work on a new theory of singularities of Landau Ginzburg models, which leads to new birational invariants. As an application we are planning to make progress on and, we hope, fully answer long standing problems of classical algebraic geometry.  Mirror Symmetry and the theory of automorphic forms are an instrumental bridge between geometry and representation theory, geometry and physics, between geometric, analytical and representational constructions.

• Derived Geometry, Mirror Symmetry and Enumerative Geometry

• Birational geometry of Fano and close to Fano varieties

• Applications of automorphic forms to geometry, mathematical physics and number theory

Beijing Institute of Mathematical Sciences and Applications (BIMSA) is the youngest  mathematical institute in China, established and operating with the support of Tsinghua University and the Chinese Academy of Sciences. The president of the institute is the world-famous scientist Shing-Tung Yau (winner of the 1982 Fields Medal and other major world scientific awards).

BIMSA is engaged in cutting-edge research in all areas of mathematics, theoretical physics, computer science and related disciplines. Today, the institute is one of the leading mathematical institutions in China, which significantly influences the international mathematical agenda.

Our joint project is designed as a collaboration between the International Laboratory for Mirror Symmetry and Automorphic Forms and Laboratories of Algebraic Geometry and Theoretical Physics and General Relativity.