| 11 January |
Speaker:Frederick Tsz-Ho Fong (Stanford)
Title:
Abstract:
TBA
|
| 18 January |
Speaker: Gerhard Huisken (AEI Potsdam)
Title: Interior estimates for mean curvature flow
Abstract:
The lecture discusses joint work with
Carlo Sinestrari on geometric estimates for
mean curvature flow that are interior in space
and time.
|
| 25 January |
Speaker: Richard Melrose (MIT)
Title: Smooth gluing and extremal Kaehler metrics
Abstract:
Abstract: As part of the general question raised by Calabi of the existence of extremal metrics in a given Kaehler class, several authors have considered the possibility of `lifting' a constant scalar curvature Khler (or more generally an extremal) metric under the blow-up of a finite collection of points (in particular see Arezzo and Pacard, Arezzo, Pacard and Singer and Szkelyhidi). I will discuss joint work with Michael Singer in which we show how to carry out these `gluing constructions' systematically in terms of smooth analysis at the boundary of a manifold with corners and as a consequence obtain more detailed information on the degeneration of these families of metrics.
|
| 1 February |
Speaker: TBA
Title:
Abstract:
TBA
|
| 8 February |
Speaker: Yi Wang (Stanford)
Title: The Aleksandrov-Fenchel inequalities for quermassintegrals on
k+1-convex domains
Abstract:
Abstract: In this talk, I will discuss some joint work with
Sun-Yung Alice Chang on the Aleksandrov-Fenchel inequalities for
quermassintegrals on a class of non-convex domains.
|
| 15 February |
Speaker: Joel Hass (UC Davis)
Title: Topological and Physical Knot Theory
Abstract:
The theory of knots and links studies one-dimensional submanifolds of 3-dimensional space. These are often described as loops of string, or rope, with their ends glued together. Real ropes and strings however are not one-dimensional, but have a positive thickness and a finite length. For many applications the thickness of the knot plays an essential role in determining the possible configurations. I will discuss joint work with Alexander Coward that gives the expected, but until now unproven, result that the theory of physical knots and links differs from the topological theory.
|
| 22 February |
Speaker: John Lott (UC Berkeley)
Title: Mean curvature flow in a Ricci flow background
Abstract:
Mean curvature flow (MCF) was orginally defined for hypersurfaces in
Euclidean space. It was then extended to hypersurfaces in an arbitrary
Riemannian manifold. We will show that MCF has nicer properties when the
background geometry evolves by the Ricci flow. We will discuss a link
between Perelman's monotonic quantities for Ricci flow and Hamilton's
differential Harnack expression for MCF, following work of Ecker for MCF
in Euclidean space.
|
| 29 February |
Speaker: Hao Fang (Iowa)
Title: On the inverse sigma_k flow on Kahler manifolds
Abstract:
We study the convergence behavior of the general inverse $\sigma_k$ flow on K\"{a}hler manifolds with initial metrics satisfying the Calabi Ansatz. The limiting metrics can be either smooth or singular. In the latter case, interesting conic singularities along negative self-intersected sub-varieties are formed as a result of partial `blow downs'. This is a joint work with Mijia Lai.
|
| 7 March |
Speaker: Rick Schoen (Stanford)
Title: A new mean curvature proof of the spacetime positive mass theorem
Abstract:
We describe recent joint work with Michael Eichmair, Lan-Hsuan Huang, and Dan Lee. The original Schoen/Yau mean curvature proof of the general positive mass theorem only gave directly the positivity of energy. We give a direct proof of the timelike character of the total energy momentum vector using the MOTS equation. We also improve the density theorems for initial sets satisfying the dominant energy condition.
|
14 March
(Joint with Analysis and PDE Seminar) |
Speaker: Andras Vasy (Stanford)
Title: Scattering on hyperbolic and Lorentzian spaces
Abstract:
In this talk I describe a new approach to analysis on (Riemannian) asymptotically hyperbolic spaces. This approach connects them via an extension across the boundary to asymptotically de Sitter (Lorentzian) spaces, as well as to a family of operators arising from an asymptotically Minkowski-type space.
Although the problems to be analyzed are no longer elliptic, we now have microlocal tools to handle such problems in a Fredholm framework, stable under perturbations.
This talk will emphasize the geometric aspects of the connections between these spaces, briefly touching on the underlying analysis.
Similar tools also apply for analysis on black hole backgrounds.
|
21 March
3:00 pm |
Speaker: Simon Brendle (Stanford)
Title: Rotational symmetry of self-similar solutions to the Ricci flow
Abstract:
Let (M,g) be a three-dimensional steady gradient Ricci soliton which is non-flat and noncollapsed. We show that (M,g) is isometric to the Bryant soliton, giving an affirmative answer to a problem mentioned in Perelman's first paper.
|
21 March
4:00 pm |
Speaker: S. T. Yau (Harvard)
Title: Geometry and spectral theory for graphs
Abstract:
TBA
|