Stanford University
Department of Mathematics

 

Geometry Seminar Winter 2012

Organizers: Jacob Bernstein (jbern@math.*), Brian Clarke (bfclarke@*) and Yanir Rubinstein (yanir@math.*)

Time: Wednesdays at 4 PM

Location: 383N

 

(*=stanford.edu)


Next Seminar

 
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.


Fall Quarter

 
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:

Abstract:

TBA

14 March

Speaker: TBA

Title:

Abstract:

TBA


Past Quarters

 
For the Fall 2011 Schedule go here
For the Spring 2011 Schedule go here
For the Winter 2011 Schedule go here
For the Fall 2010 Schedule go here
For the Spring 2010 Schedule go here
For the Winter 2010 Schedule go here
For the Fall 2009 Schedule go here