Skip to content
Texas A&M University

Events for 12/04/2023 from all calendars

Geometry Seminar

iCal  iCal

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

iCal  iCal

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.