Algebraic Geometry Seminar | The Kodaira dimension of the moduli space of curves: geometric and tropical aspects

Abstract：

It is one of the landmark results in algebraic geometry of the 20th century that the moduli space M_g of curves of genus g is a variety of general type when g>23. I will discuss joint work with Jensen and Payne proving that both moduli spaces M_22 and M_23 are of general type, highlighting both the geometrical and the novel tropical aspects related to this circle of ideas.

About the Speaker:

My field of work is algebraic geometry. A significant part of my research is concerned with the study of the geometry and topology of various moduli spaces. Among other things, I am interested in moduli of curves, enumerative geometry, syzygies of algebraic varieties and commutative algebra aspects, vector bundles on curves, abelian varieties and theta functions, Prym varieties, K3 surfaces and Brill-Noether type problems, geometric group theory and resonance varieties.