UCSD Differential Geometry Seminar (Math 258) 2002-03

Unless otherwise noted, all seminars are on Wednesdays 2:00 - 3:00 pm in Room 7218 APM

   

Winter 2003 Schedule

Janunary 08

Bing Cheng, Harvard and visiting UCSD

Title: Harnack inequality for differential forms
Abstract:

Jan 14

Xiaojun Huang, Rutgers, visiting UCSD( tentative, special time and place) at 6218, 10:00am -11:00am. (Postponed)

Title: TBA
Abstract:

Jan 22

Jim Isenberg, U Oregon, visiting UCSD

Title: The Nature of Singularities in Cosmological Solutions of Einstein's Equations
Abstract: The Hawking- Penrose singularity theorems tell us that cosmological solutions of Einstein's equations generically contain a singularity. But these theorems tell us little about what happens near such a singularity. Do the gravitational fields necessarily grow without bound? Can causality break down? What about the Cosmic Censor? Work done during the past ten years--both analytical and numerical--has gotten us a lot closer to answers to these questions. We survey this work, discussing both the mathematical ideas and the physical implications. We also discuss the likely direction of future studies.

Jan 23

Simon Garfunkel, Oakland U.

Title: Computational simulations on Ricci flow,
Abstract:

Jan 29

Salah Baouendi, UCSD

Title: (Postponed)
Abstract:

Feb 05

Peng Lu, U of Oregon, visiting UCSD

Title: Metric-transformation from collapsing and group action
Abstract:

Feb 12

Michael Chu, National Chung Cheng University, visiting UCSD

Title: The geometry of 3-dimensional Ricci soliton
Abstract:

Feb 18, 9:00--10:00 am

pengzi Miao, Stanford (Special date) at APM 7421

Title: Mass, quasi-mass and static extension in general relativity
Abstract:

Feb 18, 4:00--5:00 pm

Yu Ding, UC Irvine (Special date) at APM 6438

Title: Analysis on tangent cones
Abstract:

Feb 26

Lei Ni, UCSD

Title: Plurisubharmonic functions and a positive mass type theorem.
Abstract:

March 5

Jean Steiner, UCSD

Title: Analogs to the Mass and the Positive Mass Theorem on Spheres
Abstract: We describe two mass-like quantities arising from the Green's function for the Laplacian operator on surfaces. The Robin's mass is obtained by regularizing the logarithmic singularity of the Green's function. We show that the Robin's mass is connected to a spectral invariant. On spheres, we introduce a "geometrical mass", which is, a priori, a smooth function on the sphere. The goemetrical mass is shown to be independent of the point on the sphere, and it is also a spectral invariant. Moreover, a connection to a Sobolev-type inequality reveals that it is minimized at the standard round metric. The definition of the geometrical mass is inspired by the roles played by the Green's function for the conformal Laplacian and the Positive Mass Theorem in the solution to the Yamabe Problem.

March 12

Caitlin Wang, visiting UCSD

Title: Effect of geometry on solution of mean field theory
Abstract:

March 19

Xiaojun Huang, Rutgers, visiting UCSD

Title:On the d-bar equation of complex manifolds with non-smooth boundary
Abstract:

Spring 2002 Schedule

Fall 2002 Schedule

Questions: benchow@math.ucsd.edu or lni@math.ucsd.edu