April 1, 2023 at Yale University

GATSBY is a conference organized by the geometry/topology groups at Brown and Yale. 

All are welcome! If you're planning to attend, please register. 

Speakers

Schedule (talks in Dunham Lab 220)

10-10:30 Coffee/breakfast

10:30-11:15 Wolf background talk 

11:15-11:45 Break

11:45-12:30 Wright background talk 

12:30-2 Lunch (catered)

2-2:45 Wolf research talk 

2:45-3:15 Break

3:15-4 Wright research talk

Abstracts

• Alex Wright

Background talk: The Bounded Geodesic Image Theorem

We will introduce the curve graph, together with some of the foundational results on its study due to Masur and Minsky, with special focus on the Bounded Geodesic Image Theorem. We will try to convey some of the intuition coming from different points of view. 

Research talk: Spheres in the curve complex and linear connectivity of the Gromov boundary

For a vertex c and an integer radius r, the sphere S_r(c) is the induced graph on the set of vertices of distance r from c. We will show that spheres in the curve graph are typically connected, and discuss connectivity properties of the "sphere at infinity". We will also explain the motivation and context for this work, touching on Cannon's conjecture and convex cocompactness. 

• Michael Wolf

Background talk: We begin in the morning with a background talk on the geometry of harmonic maps of surfaces via some elementary examples; we aim to also perhaps illustrate some basic technique, assuming no prior exposure to harmonic maps.

Research talk: Ray structures in Lower Teichmuller Spaces

We study 'rays' in the Hitchin/Teichmuller component of representations of surface groups in PSL(2,ℝ) and SL(3,ℝ).  These families reflect rays of holomorphic differentials associated to the harmonic maps which are equivariant with respect to the representations.  In Teichmuller space, these rays interpolate between Teichmuller geodesics and Thurston geodesics in a way we will explain. By restricting to Thurston geodesics which have an energy minimization feature, we find something like an exponential map in the Thurston metric for Teichmuller space with the Thurston boundary as visibility boundary. In the SL(3,ℝ) Hitchin component, holonomies along the rays have asymptotics predicted by periods (i.e integrals using the local geometry) of the defining holomorphic differentials, and an endpoint given by an associated real building.

Organizers: Franco Vargas Pallete and Subhadip Dey and Bena Tshishiku

Previous iterations: Fall 2022, Spring 2019, Fall 2015, Spring  2015, Fall 2014, Spring 2014, Fall 2013,  Spring 2013, Spring 2012