Tuesday 29th June 2021, 9h00 - 9h45 GMT (10h00 - 10h45 Lisbon)
On the top weight cohomology of the moduli space of abelian varieties
In the last few years, tropical methods have been applied quite successfully in understanding several aspects of the geometry of classical algebro-geometric moduli spaces. In particular, in several situations the combinatorics behind compactifications of moduli spaces have been given a tropical modular interpretation. Consequently, one can study different properties of these (compactified) spaces by studying their tropical counterparts.
In this talk, which is based in joint work with Madeleine Brandt, Juliette Bruce, Melody Chan, Gwyneth Moreland and Corey Wolfe, I will illustrate this phenomena for the moduli space Ag of abelian varities of dimension g. In particular, I will show how to apply the tropical understanding of the classical toroidal compactifications of Ag to compute, for small values of g, the top weight cohomology of Ag.
The techniques we use follow the breakthrough results and techniques recently developed by Chan-Galatius-Payne in understanding the topology of the moduli space of curves via tropical geometry.
Zoom meeting: 87103115640
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