∙ Integrable systems in relation with differential, algebraic and symplectic geometry, as well as with the theory of random matrices, special functions and nonlinear waves, Frobenius manifolds
• Deformation theory, moduli spaces of sheaves and of curves, in relation with supersymmetric gauge theories, strings, Gromov-Witten invariants, orbifolds and automorphisms
• Quantum groups, noncommutative Riemannian and spin geometry, applications to models in mathematical physics
• Mathematical methods of quantum mechanics
• Mathematical aspects of quantum Field Theory and String
Theory
• Symplectic geometry, sub-riemannian geometry
• Geometry of quantum fields and strings
The Boris Dubrovin medal, in memory of Boris Anatolievich Dubrovin, Professor at SISSA from 1993 to 2019, is awarded by SISSA, with the support of the Moscow Mathematical Society, the “Gruppo Nazionale per la Fisica Matematica” (GNFM) and the “Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni” (GNSAGA), which are part of the Istituto Nazionale di Alta Matematica (INDAM).
Boris Dubrovin made several groundbreaking contributions to mathematical physics, with far-reaching influences in various areas of mathematics. Possibly one of his best known inventions is the definition of Frobenius manifolds (which we ought now to refer to as "Dubrovin-Frobenius manifolds"). Their formalization built a surprising bridge between mathematical physics and differential, algebraic and symplectic geometry.
The medal recognizes exceptionally promising young researchers who have already made outstanding contributions to the fields of mathematical physics and geometry.
The Dubrovin medal will be awarded every two years starting from 2020.