# Past Functional Analysis Seminar

26 February 2013
17:00
to
18:16
Derek Kitson
Abstract
Laman's theorem characterises the minimally infinitesimally rigid frameworks in Euclidean space $\mathbb{R}^2$ in terms of $(2,3)$-tight graphs. An interesting problem is to determine whether analogous results hold for bar-joint frameworks in other normed linear spaces. In this talk we will show how this can be done for frameworks in the non-Euclidean spaces $(\mathbb{R}^2,\|\cdot\|_q)$ with $1\leq q\leq \infty$, $q\not=2$. This is joint work with Stephen Power.
• Functional Analysis Seminar
12 February 2013
17:00
to
18:16
Charles Batty
Abstract

A very efficient way to obtain rates of energy decay for damped wave equations is to use operator semigroups to pass from resolvent estimates to energy estimates.  This is known to give the optimal results in cases when the resolvent estimates have simple forms such as being exactly polynomial ($|s|^\alpha$).  After reviewing that theory this talk will discuss cases when the resolvent estimates are slightly different, for example $|s|^\alpha/ \log |s|$ or $|s|^\alpha \log |s|$.

• Functional Analysis Seminar
5 February 2013
17:00
to
18:27
Abstract
• Functional Analysis Seminar
29 January 2013
17:00
to
18:16
Andrew Morris
Abstract
We prove that strongly continuous groups generated by first-order systems $D$ on Riemannian manifolds have finite propagation speed. The new direct proof for self-adjoint systems also provides a new approach to the weak Huygens' principle for second-order hyperbolic equations. The techniques are also combined with the resolvent approach to sectorial operators to obtain $L^2$ off-diagonal estimates for functions of $D$, which are the starting point for obtaining $L^p$ estimates for Riesz transforms on manifolds where the heat semigroup does not satisfy pointwise Guassian bounds. The two approaches are then combined via a Calder\'{o}n reproducing formula that allows for the analysing function to interact with $D$ through the holomorphic functional calculus whilst the synthesising function interacts with $D$ through the Fourier transform. This is joint work with P.~Auscher and A.~McIntosh.
• Functional Analysis Seminar
22 January 2013
17:00
to
18:16
David Seifert
Abstract
• Functional Analysis Seminar
15 January 2013
17:00
to
18:12
Chris Heunen
Abstract
• Functional Analysis Seminar
27 November 2012
17:00
to
18:12
David Preiss
Abstract
• Functional Analysis Seminar
20 November 2012
17:00
to
18:10
Pablo Shmerkin
Abstract
• Functional Analysis Seminar
13 November 2012
17:00
to
18:15
Yuri Safarov
Abstract
• Functional Analysis Seminar