Algebra, Arithmetic and their Geometries

We plan to make progress in important problems of Number Theory, Algebra, Geometry and Mathematical Physics.

These include the Beilinson conjecture, arithmetic and analytic properties of Hilbert modular forms, the arithmetic of non-congruence subgroups, the Birch-Swinnerton-Dyer and the Iwasawa Main Conjecture, conjectures on motives and the Standard Conjectures on Algebraic Cycles (Grothendieck),  classifications of algebraic torsors, of Fano varieties, of non-associative algebras, and of cohomological operations, the Standard Conjectures on one-relator groups, construction of quantum field theories using geometric and algebraic methods, categorification of invariants, furthering the development of non-commutative geometry, and space-time block codes.