Vortrag
Non-archimedean Gromov-Witten invariants and Mirror symmetry
Vortrag von Dr. Mauro Porta
Sprecher eingeladen von: Prof. Dr. Joseph Ayoub
Datum: 27.03.23 Zeit: 13.15 - 14.45 Raum: Y27H25
Mirror symmetry is a subject at the crossroad of symplectic geometry, complex analytic geometry and mathematical physics. Informally, it is a conjectural duality between Calabi-Yau varieties: given such a variety X (or, rather, a family of such objects), there should be a second variety (or family) Y, called the "mirror" of X. The pair (X,Y) should be characterised by the fact that symplectic invariants of X should correspond to holomorphic invariants of Y. Nevertheless, the construction of Y out of X stays an open major problem of the theory: it has been solved in countless many examples, but not in general. In 2006 Kontsevich and Soibelman proposed an attack strategy based on non-archimedean geometry. In this exposé I will survey the history of this program, focusing on the key moments and the recent advances dues to S. Keel, J. Nicaise, C. Xu, T. Y. Yu and myself.