Pacific Northwest Geometry Seminar
Topic
Abstracts for the talks:
1. Toti Daskalapoulos
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Title: Ancient solutions of the Yamabe flow
Abstract: We construct new ancient compact solutions of the Yamabe flow. Our approach involves a parabolic analogue of the gluing method of solutions to the rescaled flow with constant scalar curvature.
2. Eric Bahuaud
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Title: The Yamabe flow of an incomplete edge metric
Abstract: In this talk I will describe recent work to understand the behaviour of the Yamabe flow in a singular setting modeled by an incomplete edge metric. I will discuss the background estimates obtained from the heat kernel, conditions for short-time existence and prospects for long-time existence. This is ongoing work with Boris Vertman.
3. Martin Li
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Title: Minimal Surfaces with Free Boundary and Geometric Applications
Abstract: Minimal surfaces have been a very useful tool in studying 3-manifold topology and geometry since the pioneering work of Schoen-Yau. When the 3-manifold M possess a boundary, it is natural to look at minimal surfaces with free boundary. In this talk, I will first describe a very general existence result for properly embedded minimal surfaces with free boundary. When the 3-manifold satisfies some curvature and boundary convexity assumptions, we show that the space of these minimal surfaces with a fixed topological type is compact in a very strong sense. As a geometric application, we prove a rigidity result for bounded convex domains in R^3 in terms of the area of a minimal surface which realize the "width" of the convex domain. If time permits, I will indicate some potential applications to mean curvature flow in R^3.
3. John Lott
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Title : Collapsing with a lower bound on the curvature operator
Abstract : Cheeger and Gromov characterized bounded curvature collapse in terms of F-structures. I'll describe how some of the Cheeger-Gromov results extend to collapse with just a lower bound on the curvature operator, in terms of fibered F-structures.
4. Jiaping Wang
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Title: Analysis on smooth metric measure spaces and applications
Abstract: We intend to explain some joint work with Ovidiu Munteanu concerning the analysis on smooth manifolds with densities.
Applications to the Ricci gradient solitons will also be discussed.
Speakers
Details
The Pacific Northwest Geometry Seminar (PNGS) is a regional meeting for geometers of all kinds. It is held every fall and spring, and every other winter, rotating among the following participating institutions:
Oregon State University
Portland State University
Stanford University
University of British Columbia
University of Oregon
University of Utah
University of Washington
Additional Information
Location: WMAX 110
For further information please visit the Pacific Northwest Geometry Seminar page at: http://www.math.washington.edu/~lee/PNGS/.
Location detials, Registration instructions, and additional info forthcoming.
Eric Bahuaud, Stanford University
Panagiota Daskalopoulos, Columbia University
Martin Li, University of British Columbia
John Lott, U.C. Berkeley
Jiaping Wang, University of Minnesota
The meetings are supported by the National Science Foundation (NSF), the Pacific Institute for the Mathematical Sciences (PIMS), and the host institutions.
