Research Goals

 

SAGE provides a forum for experts in geometric analysis and related disciplines to explore open problems, further work-in-progress, and cultivate new and existing collaborations, especially across specialties. In contrast to a conference, where speakers give formal presentations of their completed results, the SAGE model invites participants to discuss ongoing, planned, and hoped-for research.

 

This year’s workshop will focus on emerging relationships between Optimal Transport and Riemannian Geometry, including topics of Bakry-Emery curvature, Synthetic Ricci curvature, Ma-Trudinger-Wang curvature, and Applications to Ricci Flow.

 

Schedule

 

Wednesday, September 1

        10:00-11:00       (RLM 8.136) Welcome and registration. Coffee, tea, and snacks provided.

        11:00-12:00       (RLM 9.166) Alessio Figalli: The geometry of the Ma-Trudinger-Wang condition

        12:00-12:30       Discussion.

        12:30-2:00         Lunch.

        2:00-3:00           (RLM 9.166) Guofang Wei: Spaces with Bakry-Emery Ricci Curvature Bounded from Below

        3:00-3:30           Discussion.

        4:00-5:00           (RLM 9.166) Artem Pulemotov: Parabolic equations and the Ricci flow on manifolds with boundary

        5:00-5:30           Discussion.

        6:30-8:30           Welcome dinner. El Chile Café

Thursday, September 2

        9:00-9:30           (RLM 8.136) Coffee, tea, and snacks.

9:30-10:30         (RLM 8.136) Nicola Gigli: Heat flow on Alexandrov spaces

        10:30-11:00       Discussion.

        11:00-12:00       (RLM 8.136) William Wylie: On the classification of warped product Einstein metrics

        12:00-12:30       Discussion.

        12:30-2:00         Lunch.

        2:00-3:00           (RLM 8.136): Anton Petrunin: Talk cancelled.

        4:00-5:00           (RLM 8.136) Emanuel Milman: A generalization of Caffarelli's Contraction Theorem via (reverse) heat-flow

        5:00-5:30           Discussion.

Friday, September 3

10:30-11:00       (RLM 8.136) Coffee, tea, and snacks.

        11:00-12:00       (RLM 9.166) Esther Cabezas-Rivas: Optimal transport as a source of intuition for the Ricci Flow

        12:00-12:30       Discussion.

        12:30-2:00         Lunch.

        2:00-3:00           (RLM 9.166): Young-Heon Kim: Regularity of optimal transportation maps on multiple products of spheres

        3:00-3:30           Discussion.

        4:00-5:00           (RLM 8.136) Jiakun Liu: Global regularity of the reflector problem

        5:00-5:30           Discussion.          

        7:00-9:00           Closing dinner. Botticelli’s South Congress

 

 

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