The moduli space M_{g,n} of smooth algebraic curves of genus g with n distinct marked points is not compact. However, it admits many compactifications that are themselves moduli spaces, and it remains an outstanding problem in algebraic geometry to classify these modular compactifications. An important family of examples is that of the moduli spaces of "weighted pointed" curves constructed by Hassett, in which a vector of real numbers determines which of the n marked points are permitted to come together. In this talk, I will present joint work with Vance Blankers that constructs modular compactifications of M_{g,n} using a simplicial complex rather than vector of weights as an input. Not only do the resulting "simplicial" moduli spaces generalize Hassett's, but they also classify the modular compactifications coming from colliding markings.

On modular compactifications of M_g,n with colliding points

Dec. 01, 2022 2:30pm (MATH 3…

Functional Analysis

Andrew Stocker (CU Boulder)

X

This talk will for the most part be an expository talk about the relationships between inverse semigroups, groupoids, and dynamical systems. Inverse semigroups are semigroups with the property that for every element x there is a unique element x* such that xx*x = x and x*xx* = x*. I will present a construction of a shift space, given a finite graph with edges labeled in an inverse semigroup. I will discuss how one can construct, from the labeled graph, a groupoid which contains the stable synchronizing algebra of the shift space as a sub-groupoid.

Dynamical Systems from Inverse Semigroups

Dec. 01, 2022 3:35pm (Online)

Probability

Jiaming Chen (ETH Zurich)

X

How do we simulate a singular stochastic diffusion with high efficiency? In the context of Schramm- Loewner evolution, we study the approximation of its traces via the Ninomiya-Victoir Splitting Scheme. We prove a strong convergence in probability with respect to the sup-norm to the distance between the SLE trace and the output of the Ninomiya-Victoir Splitting Scheme when applied in the context of the Loewner differential equation.