Arakelov geometry combines algebraic geometry of schemes over Z, with refinements of Hodge theory on the associated complex varieties, in a unified formalism. While a detailed description of the theory requires heavy preliminaries, some of its consequences are quite concrete and pleasant to explain. In this talk, I will focus on old and new such results, which capture the essence of modern Arakelov geometry. Notably, I will discuss some applications in the context of modular curves (Kronecker limit formula, volumes of lattices of cusps forms), as well as a recent application to a mirror symmetry conjecture for Calabi-Yau varieties.
An introduction to Arakelov geometry: from the geometry of numbers to mirror symmetry.
10.12.2019 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: