Tautological rings and Gorenstein conjectures

Algebraic and Tropical Geometry
Event time: 
Thursday, March 5, 2020 - 3:00pm
Phelps Hall Room 207, 344 College St
Aaron Pixton
Speaker affiliation: 
University of Michigan
Event description: 

Let M_g be the moduli space of smooth curves of genus g. The tautological ring is a subring of the cohomology of M_g that was introduced by Mumford in the 1980s in analogy with the cohomology of Grassmannians. Work of Faber and Faber-Zagier in the 1990s led to two competing conjectural descriptions of the structure of the tautological ring. After reviewing these conjectures, I will discuss some of the evidence in recent years favoring one conjecture over the other.