MenuEvents for 12/04/2023 from all calendars
Geometry Seminar
Time: 3:00PM - 4:00PM
Location: BLOC 302
Speaker: Jake Levinson, Université de Montréal
Title: Minimal degree fibrations in curves and asymptotic degrees of irrationality
Abstract: A basic question about an algebraic variety X is how similar it is to projective space. One measure of similarity is the minimum degree of a rational map from X to projective space, called the degree of irrationality. This number, and the corresponding minimal-degree maps, are in general challenging to compute, but capture special features of the geometry of X. I will discuss some recent joint work with David Stapleton and Brooke Ullery on asymptotic bounds for degrees of irrationality for divisors X on projective varieties Y. Here, the minimal-degree rational maps $X \dashrightarrow \mathbb{P}^n$ turn out to "know" about Y and factor through rational maps $Y \dashrightarrow \mathbb{P}^n$ fibered in curves. This leads to the useful notion of "minimal fibering degree in curves".
Colloquium: Title: Metric geometric aspects of Einstein manifolds
Time: 4:00PM - 5:00PM
Location: BLOC 117
Speaker: Ruobing Zhang
Description: Title: Metric geometric aspects of Einstein manifolds Abstract: This lecture concerns the metric Riemannian geometry of Einstein manifolds, which is a central theme in modern differential geometry and is deeply connected to a large variety of fundamental problems in algebraic geometry, geometric topology, analysis of nonlinear PDEs, and mathematical physics. We will exhibit the rich geometric/topological structures of Einstein manifolds and specifically focus on the structure theory of moduli spaces of Einstein metrics. My recent works center around the intriguing problems regarding the compactification of the moduli space of Einstein metrics, which tells us how Einstein manifolds can degenerate. Such problems constitute the most challenging part in the metric geometry of Einstein manifolds. We will introduce recent major progress in the field. If time permits, I will propose several important open questions.
