Thursday, March 5, 2020
03/05/2020 - 3:00pm
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.
Phelps Hall Room 207, 344 College St
03/05/2020 - 4:15pm
Lorentzian polynomials link continuous convex analysis and discrete convex analysis via tropical geometry. The tropical connection is used to produce Lorentzian polynomials from discrete convex functions. Although no specific background beyond linear algebra and multivariable calculus will be needed to enjoy the presentation, I advertise the talk to people with interests in at least one of the following topics: graphs, convex bodies, stable polynomials, projective varieties, Potts model partition functions, tropicalizations, Schur polynomials, highest weight representations. Based on joint works with Petter Brändén, Christopher Eur, Jacob Matherne, Karola Mészáros, and Avery St. Dizier. The first talk on March 4 will focus on the theory of Lorentzian polynomials, and the second talk on March 5 will cover applications.