Frontiers in Mathematical Sciences
7th Conference University of Isfahan  January 13, 2020 
Title:
Approximability of tropical currents
Speaker:
Farhad Babaee, University of Bristol
Date, Time, and Venue: Thursday, January 2  09:4510:30  Hall 1
Abstract:
Demailly in 2012 showed that the Hodge conjecture is
equivalent to the statement that any $(p,p)$dimensional closed current
with rational cohomology class can be approximated by linear
combinations of integration currents; Moreover, the statement that all
strongly positive currents with rational cohomology class can be
approximated by positive linear combinations of integration currents,
can be viewed as a strong version of the Hodge conjecture (1982).
In this talk, I will explain a few basic notions in the theory of
currents and in tropical geometry, and discuss how ideas from tropical
geometry can be used to refute the latter statement. The talk is based
on joint works with June Huh and Karim Adiprasito.
