Schedule for: 19w5115 - Women in Geometry 2

Arriving in Oaxaca, Mexico on Sunday, June 23 and departing Friday June 28, 2019
Sunday, June 23
14:00 - 23:59 Check-in begins (Front desk at your assigned hotel)
19:30 - 22:00 Dinner (Restaurant Hotel Hacienda Los Laureles)
20:30 - 22:00 Informal gathering (Hotel Hacienda Los Laureles)
Monday, June 24
07:30 - 09:00 Breakfast (Restaurant at your assigned hotel)
09:15 - 09:30 Introduction and Welcome (Conference Room San Felipe)
09:30 - 10:20 Chikako Mese: Harmonic maps in dimension two
We discuss harmonic maps from two dimensional domains including a harmonic maps approach to uniformization and finding minimal surfaces.
(Conference Room San Felipe)
10:30 - 11:00 Coffee Break (Conference Room San Felipe)
11:00 - 11:50 Alina Stancu: Main tools and techniques in curvature flows - a user’s guide
I will outline the main techniques for studying flows of immersed, codi- mension 1, manifolds in Rn evolving with curvature dependent speed. As the field of such flows is very large, I will exemplify these tools on a few of the most known curvature flows on closed convex hypersurfaces.
(Conference Room San Felipe)
12:00 - 13:20 Group Work (Location to be assigned)
13:20 - 13:30 Group Photo (Hotel Hacienda Los Laureles)
13:30 - 15:00 Lunch (Restaurant Hotel Hacienda Los Laureles)
15:00 - 16:00 Group Work (Location to be assigned)
16:00 - 16:30 Coffee Break (Conference Room San Felipe)
16:30 - 19:00 Group Work (Location to be assigned)
19:00 - 21:00 Dinner (Restaurant Hotel Hacienda Los Laureles)
Tuesday, June 25
07:30 - 09:00 Breakfast (Restaurant at your assigned hotel)
09:30 - 10:20 Regina Rotman: Periodic geodesics on Riemannian manifolds
I will discuss the known results of (1) existence of periodic geodesics on Riemannian manifolds; (2) volume and diameter upper bounds for the length of the shortest periodic geodesics. I will also talk about various known techniques that potentially can help establishing the existence and the upper bounds.
(Conference Room San Felipe)
10:30 - 11:00 Coffee Break (Conference Room San Felipe)
11:00 - 11:50 Francesca De Marchis: Prescribing the Gaussian curvature on singular surfaces
I will consider the problem of prescribing the Gaussian curvature (under pointwise conformal change of the metric) on surfaces with conical singularities. This question has been first raised by Troyanov and it is a generalization of the Kazdan-Warner problem for regular surfaces, known as the Nirenberg problem on the sphere. Answer this question amounts to solve a singular differential problem on the surface. This Liouville-type equation has been studied first in the case $K > 0$, where $K$ denotes the Gaussian curvature we want to prescribe. I will review classical results on the regular case, more recent results obtained for positive functions $K$ in presence of singularities and I will present some new results in the sign-changing singular case.
(Conference Room San Felipe)
12:00 - 13:30 Group Work (Location to be assigned)
13:30 - 15:00 Lunch (Restaurant Hotel Hacienda Los Laureles)
15:00 - 16:00 Group Work (Location to be assigned)
16:00 - 16:30 Coffee Break (Conference Room San Felipe)
16:30 - 19:00 Group Work (Location to be assigned)
18:30 - 20:30 Dinner (Restaurant Hotel Hacienda Los Laureles)
20:30 - 21:30 Full Group Discussion: Under-representation of tenured women in PhD granting departments (Conference Room San Felipe)
Wednesday, June 26
07:30 - 09:00 Breakfast (Restaurant at your assigned hotel)
09:00 - 09:50 Mary Sandoval: Using Heat Invariants to distinguish Orbifolds from Manifolds
We will examine the question of whether or not an orbifold (with singular points) can be isospectral to a manifold. The answer is known to be “no” in the case of two-dimensional manifolds/orbifolds with non-negative Euler characteristic. We propose to use heat invariants for functions and the analogous invariants for one- forms to distinguish between manifolds and orbifolds in the three-dimensional case.
(Conference Room San Felipe)
10:00 - 10:30 Group Work (Location to be assigned)
10:30 - 11:00 Coffee Break (Conference Room San Felipe)
11:00 - 12:30 Group Work (Location to be assigned)
12:30 - 13:30 Lunch (Restaurant Hotel Hacienda Los Laureles)
13:30 - 19:00 Free Afternoon (Oaxaca)
19:00 - 21:00 Dinner (Restaurant Hotel Hacienda Los Laureles)
Thursday, June 27
07:30 - 09:00 Breakfast (Restaurant at your assigned hotel)
09:30 - 10:20 Emmy Murphy: Legendrian knots and Lagrangian cobordisms
The space $S^3 \subset \mathbb{C}^2$, comes naturally equipped a contact structure: a geometry which gives strong connections between low-dimensional topology and symplectic geometry. We study Legendrian knots– knots which are compatible with the contact structure – and Lagrangian cobordisms between them in $\mathbb{C}^2$.
(Conference Room San Felipe)
10:30 - 11:00 Coffee Break (Conference Room San Felipe)
11:00 - 11:50 Anna Sakovich: Understanding angular momentum in General Relativity
Conserved quantities – mass, linear momentum, center of mass, and angular momentum – are important in various areas of physics as in many cases they provide an essential characterization of a physical system. The concepts of mass and linear momentum are by now well-established in General Relativity, and recently there has been a lot of progress in understanding the center of mass of isolated systems. However, we believe that the somewhat more mysterious notion of angular momentum deserves more attention. In this talk we will discuss the key geometric ideas behind this notion and outline the questions that our team plans to address.
(Conference Room San Felipe)
12:00 - 13:30 Group Work (Location to be assigned)
13:30 - 15:00 Lunch (Restaurant Hotel Hacienda Los Laureles)
15:00 - 16:00 Group Work (Location to be assigned)
16:00 - 16:30 Coffee Break (Conference Room San Felipe)
16:30 - 19:00 Group Work (Location to be assigned)
19:00 - 21:00 Dinner (Restaurant Hotel Hacienda Los Laureles)
Friday, June 28
07:30 - 09:00 Breakfast (Restaurant at your assigned hotel)
09:00 - 09:40 5-minute progress reports (Conference Room San Felipe)
09:40 - 10:30 Group Work (Location to be assigned)
10:30 - 11:00 Coffee Break (Conference Room San Felipe)
12:00 - 14:00 Lunch (Restaurant Hotel Hacienda Los Laureles)