Dr. Deepam Patel – Noviembre 22 de 2022 – 10:30 am
The Hodge conjecture is one of the central problems in Algebraic Geometry. The first part of this talk will
serve as a general introduction to the Hodge conjecture. The conjecture says roughly that certain cohomology classes
as `algebraic’ in the setting of smooth projective varieties. In the second part, I’ll discuss some recent joint work with
M. Nori and V. Srinivas on an enrichment of Hodge structures which would allow one to understand analogs of the Hodge
conjecture in the singular or non-projective cases. I will try to make the talk as self-contained as possible, and in particular, will not assume a background in algebraic geometry.