SCIENTIFIC PROGRAMS AND ACTIVITIES

October 25, 2014

Tuesday, December 11, 2007
FIELDS MINISYMPOSIUM ON THE CALCULUS OF VARIATIONS

Calculus of variations is a foundational tool in physics, geometry and economics.
Our aim is to bring together experienced and young researchers who use this tool to share their work and inspire each other in these disparate fields.
This mini-symposium follows the CMS Winter meeting in nearby London, Ontario.

Conference Home page

Registration on site

9h30 Registration and coffee (6th floor lounge, Bahen Center at 40 St. George)
10h30
BA 6183
David Jerison (MIT)
Gradient bounds for a free boundary
In the early 1980s, Alt and Caffarelli proved regularity theorems for a Bernoulli-type free boundary problem in analogy with the regularity theory of minimal surfaces. By now the analogy is highly developed. Each problem has variational formulation and its Euler-Lagrange equation and can be considered as the singular limit of a semilinear elliptic equation. In this talk, we will discuss joint work with Daniela de Silva in which we prove the analogue for this free boundary problem of the classical theorem of Bombieri, de Giorgi, and Miranda that minimal graphs are Lipschitz graphs. The method also gives a new proof of the classical theorem, which, while harder than many (all?) existing proofs, provides extra insight.
11h30
BA 6183
Niky Kamran (McGill University)
A Rigorous Treatment of Energy Extraction from a Rotating Black Hole
We prove that by choosing a suitable wave packet as initial data for the scalar wave equation in Kerr geometry, one can extract energy from the black hole, thereby putting supperradiance, the wave analogue of the Penrose process, into a rigorous mathematical framework. We quantify the maximal energy gain, and we also estimate the infinitesimal change of mass and angular momentum of the black hole, in agreement with Christodoulou's result for the Penrose process.
This is joint work with Felix Finster, Joel Smoller and Shing-Tung Yau.
14h10
BA 6183
William Minicozzi (Johns Hopkins University)
The rate of change of width under flows
I will discuss a geometric invariant, that we call the width, of a manifold and first show how it can be realized as the sum of areas of minimal 2-spheres. When M is a homotopy 3-sphere, the width is loosely speaking the area of the smallest 2-sphere needed to ``pull over'' M.
Second, we will estimate the rate of change of width under various geometric flows to prove sharp estimates for extinction times.
This is joint work with Toby Colding.
  Refreshments to follow in the mathematics lounge.
N.B. The CMS session ends on Monday by lunchtime. So we recommend returning to Toronto Monday night.
To arrive Tuesday morning, the best option is the train arriving at 10:21; the math dept. is a quick cab ride away at at St. George and College, one block east of Spadina. Click here for directions and more.
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