Pacific Northwest Geometry Seminar

  • Start Date: 05/05/2012
  • End Date: 05/06/2012
Speaker(s):

 

Eric Bahuaud, Stanford University

Panagiota Daskalopoulos, Columbia University

Martin Li, University of British Columbia

John Lott, U.C. Berkeley

Jiaping Wang, University of Minnesota

Location: 

University of British Columbia

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

-----------------------

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

---------------------------

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.

Description: 

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

Abstracts / Downloads / Reports: 
Final_Report.pdf
PNGS_Webarchive.zip
Schedule: 

Saturday May 5th

----------------

 

10:30-11:00 Reception, coffee, Breakfast snacks

 

11:00-12:00 Panagiota Daskalopolous, Columbia University (Ancient solutions of the Yamabe flow)

 

12:00-2:00 LUNCH

 

2:00-3:00 Eric Bahuaud, Stanford University

 

3:00-3:30 COFFEE BREAK

 

3:30-4:30 Martin Li, University of British Columbia

 

6:00 Conference Dinner

 

Sunday May 6th

----------------

9:00-9:30 Coffee, Breakfast snacks

 

9:30am -10:30am John Lott, U.C. Berkeley (Collapsing with a lower bound on the curvature operator)

 

10:30am-11:00am COFFEE BREAK

 

11:00am -12:00pm Jiaping Wang, University of Minnesota

Organizers:

Local Organizers:

Albert Chau, Jingyi Chen, Ailana Fraser

Other 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.

Sponsor: 

The meetings are supported by the National Science Foundation (NSF), the Pacific Institute for the Mathematical Sciences (PIMS), and the host institutions.