Week starting Monday 18 March 2019
We show some new rigidity result for the marked length spectrum of closed negatively curved manifolds (and more generally those with Anosov geodesic flows) in any dimension, answering partially a conjecture of Burns-Katok in ’85. The marked length spectrum is the length of closed geodesics, ordered by their free homotopy classes. This is joint work with T. Lefeuvre.
A brief introduction to stacks, bundle gerbes and their applications to T-dualities.
Many examples will be presented so the talk should be accessible to anyone to some background in differential geometry and algebraic topology.
After introducing several geometrical models that can be used to calculate multiplicities in Lie group theory, we describe associated polytopes whose volumes can be considered as approximations of those multiplicities.
For a balanced bistable reaction-diffusion equation, an axisymmetric traveling front has been well known. We prove that an axially asymmetric traveling front with any positive speed does exist in a balanced bistable reaction-diffusion equation. Our method is as follows. We use a pyramidal traveling front for an unbalanced reaction-diffusion equation whose cross section has a major axis and a minor axis. Preserving the ratio of the major axis and a minor axis to be a constant and taking the balanced limit, we obtain a traveling front in a balanced bistable reaction-diffusion equation. The cross section of this traveling front is a compact set with a major axis and a minor axis when the constant ratio is not $1$.
This is the first in a series of lectures on the foundations of quantum mechanics, addressed to mathematicians. Most of the lectures will be by John Hutchinson; later in the semester we will also have volunteer talks by participants on special topics.
Background Requirements: Some knowledge of finite dimensional complex inner product spaces. Primarily C^n(i.e. n-tuples of complex numbers), hermitian and unitary matrices/operators in this setting. Faculty, grad students or third year/honours mathematics students would be fine.
When & Where: First meeting 3.00 — 4.30 Friday 22 March, subsequent meetings begin April 5. Talks will be in the Hannah Neumann Seminar Room 1.37.