MenuEvents for 02/10/2017 from all calendars
Mathematical Physics and Harmonic Analysis Seminar
Time: 1:50PM - 2:50PM
Location: BLOC 628
Speaker: M. Zyskin, Univ. Nottingham, UK
Title: Transformation groups and discrete structures in continuum description of defective crystals
Abstract: Davini description of elasticity and plasticity of defective crystal involves a frame of continuum 'lattice vector' fields, and dislocation density matrix, capturing the structure constants of the Lie bracket of those vector fields. Those fields together describe kinematics of a defective crystal, allowing for elastic and certain plastic deformations. A truncation assumption for the energy functional leads to considering finite dimensional Lie algebras of 'lattice vector' fields and corresponding transformation groups. In low spatial dimensions, such groups may be classified. Discrete crystal structures emerge in such context as discrete subgroups of the corresponding Lie groups. This approach includes the usual crystal lattices as a particular case. In my talk I will focus on cases of non-constant dislocation density, corresponding to 2 dimensional crystals with 3 dimensional algebras of lattice vector fields. (This work is a joint project with Gareth Parry).
Linear Analysis Seminar
Time: 3:00PM - 4:00PM
Location: BLOC 220
Speaker: Koichi Shimada, Kyoto University
Title: Maximal amenability of generator subalgebras in q-Gaussians
Abstract: In this talk, we present an explicit example of maximal amenable subalgebras of q-Gaussians; if the absolute value of q is small, any subalgebra generated by a q-Gaussian random variable is maximal amenable in the q-Gaussian. We show this based on Popa's theory on the asymptotic orthogonality property. To achieve this, we construct a Riesz basis in the same way as Radulescu did for radial masas of the free group factors. This is a joint work with Sandeepan Parekh and Chenxu Wen.
Algebra and Combinatorics Seminar
Time: 3:00PM - 3:50PM
Location: BLOC 628
Speaker: Xiaoxian Tang, Texas A&M University
Title: Computing bounds for equiangular lines in Euclidean spaces
Abstract: Determining the maximum number of equiangular lines in a r-dimensional Euclidean vector space is an open problem in combinatorics, frame theory, graph theory, linear algebra and many related areas. So far the exact maximum number is only known for a few small dimensions. In this talk, we compute the upper bound of number of equiangular lines by combing the classical pillar decomposition and the semi-definite programming (SDP) method. Our computational results show an explicit bound, which is strictly less than the well-known Gerzon's bound for the dimensions between 44 and 400. Particularly, when the angles is arccos(1/5) or arccos(1/7), we dramatically improve the known SDP bounds.
Colloquium - Grigori Avramidi
Time: 4:00PM - 5:00PM
Location: BLOC 220
Speaker: Grigori Avramidi
Description:
Title: Topology of ends of finite volume, nonpositively curved manifolds
Abstract:
The structure of ends of a nonpositively curved, locally symmetric manifold M is very well understood. By Borel-Serre, the thin part of the universal cover of such a manifold is homotopy equivalent to a rational Tits building. This is a simplicial complex built out of the algebra of the locally symmetric space which turns out to have dimension less than dim M/2. In this talk, I will give examples illustrating this, and then I will explain aspects of the locally symmetric situation that are true for more general nonpositively curved manifolds. The main result is that the homology of the thin part of the universal cover vanishes in dimension greater or equal to dim M/2. One application is that any complex homotopy eqiuvalent to M has dimension greater or equal to dim M/2.
