主讲人 / Speaker

Georgios Daskalopoulos

Brown University

时间 / Time

Thursday 13:30-15:05, Oct. 17, 2024

Friday 9:50-11:25 am, Oct. 18, 2024

Monday 15:20-16:55, Oct. 21, 2024

Thursday 13:30-15:05, Oct. 24, 2024

地点 / Venue

B725

Shuangqing Complex Building A

线上 / Online（to be confirmed)

Zoom meeting ID: 405 416 0815

pw: 111111

课程介绍 / Description

In a 1998 preprint, Bill Thurston outlined a Teichmueller theory based on maps between hyperbolic surfaces which minimize the Lipschitz constant in their homotopy class (minimum stretch or best Lipschitz maps). In these lectures I'll present joint work with Karen Uhlenbeck where we initiated the analytic study of several of the key concepts appearing in Thurston's work. In particular, I will introduce a special class of best Lipschitz maps called infinity harmonic and their dual geodesic laminations. I will explain how these techniques can be used to explain Thurston's prediction about the duality between best Lipschitz maps and geodesic laminations (max flow min cut principle, convexity and L^0 <--> L^infinity duality).

I will start by explaining the major ideas in the simpler case of maps into the circle. In the process I will pose several open problems and conjectures that need to be addressed in the future research. I will try to be as elementary as possible assuming only the minimum knowledge of calculus of variations and topology.

主讲人简介 / About the Speaker

My interest is in nonlinear geometric analysis and applications to topology, geometry, and mathematical physics. In the last years, I have been working on harmonic maps between singular spaces and applications to Teichmueller theory and three-dimensional topology.

In addition, I have been working on some nonlinear parabolic equations related to the Yang-Mills flow on Kaehler manifolds.