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 current activity related to asymptotics and singularity formation in geometric evolution equations.

Schedule

All talks are in RLM 11.176.

Please note that there is time set aside for open discussion after each research talk.

Monday, May 5

Monday’s schedule is integrated with outreach components of SAGE. See our outreach page for more information.

10:00..10:30 – Registration. Coffee and snacks provided.

10:30..11:30 – Presentation introducing invited undergraduates to workshop research topics.

12:00..2:00 – Pizza lunch for undergraduate participants. Introductions to faculty research areas.

2:00..3:00 – John King: Extinction behavior of the equation of fast nonlinear diffusion.

3:30..4:00 – Break. Coffee and cookies provided.

Tuesday, May 6

10:00..10:30 – Gathering time. Coffee and snacks provided.

10:30..11:30 – Sophie Chen: Conformally compact Einstein manifolds.

12:00..2:00 – Lunch (click here for some choices)

2:00..3:00 – David Garfinkle: Numerical simulations of singularities in general relativity and Ricci flow.

3:30..4:00 – Break. Coffee and cookies provided.

4:00..5:00 – Thalia Jeffres: Vertical blow-ups and applications to capillarity.

Wednesday, May 7

10:00..10:30 – Gathering time. Coffee and snacks provided.

10:30..11:30 – Brett Kotschwar: Some geometric consequences of an entropy formula for a nonlinear parabolic equation.

12:00..2:00 – Lunch (click here for some choices)

2:00..3:00 – Mariel Saez: Self-similar expanding solutions for the planar network flow.

3:30..4:00 – Break. Coffee and cookies provided.

4:00..5:00 – I. M. Sigal: On collapse dynamics in Yang-Mills and wave map equations.

6:00..???? – Outing: The Oasis on Lake Travis.

Thursday, May 8

10:00..10:30 – Gathering time. Coffee and snacks provided.

10:30..11:30 – Forum: presentation and discussion of open problems.

12:00..2:00 - Lunch (click here for some choices)

2:00..4:00 – Opportunity for individual discussion and collaboration.

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