Our meetings take place at noon, unless otherwise noted.
Stephen, JCMB 6206, 25 February 2011
NotesThis talk will be an introduction into Ap classes, their key properties and the main theorem which says that they are exactly the weights that give rise to measures with which the maximal function is bounded on Lp(mu). If there is time I shall also discuss some applications of these results.
Tim, JCMB 6206, 18 February 2011
NotesA discussion of some of the content of Tao's notes on "Recent progress on the restriction conjecture"; in particular, the section on the wave packet decomposition.
George, JCMB 5326, Monday 7 February 2011 at 11am
NotesOn Friday, Tao will be talking about "Recent progress on Fourier Restriction by Bourgain and Guth". I will give an introduction to the restriction problem, and hopefully help to set the scene for Tao's talk.
Tim, JCMB 5325, Monday 24 January 2011 at 11am
NotesSome background information to prepare for Shuji Machihara's talk in the Analysis Seminar.
George, JCMB 4312, 3 December 2010
This will be a (hopefully accessible) overview of the topic I have been working on for the past few months. We will look at an inequality which is closely related to those considered by Wolff in 2000 in connection with local smoothing for the wave equation. This inequality was studied by Garrigos and Seeger in their 2010 paper; after looking at their result, we will apply some ideas of Bourgain to obtain further partial results. This will be quite number-theoretic in nature, but I will gloss over the gory details.
Eric, JCMB 4312, 19 November 2010
NotesTo begin our investigation, we consider the continuity of the sample paths of a 1 dimension Brownian motion. Many of these properties will follow from Levy's construction, given in the last talk. After discussing continuity, we will explore ways in which Brownian motion is less well behaved. We will prove the Theorem of Paley, Wiener and Zygmund that says almost surely Brownian Motion is nowhere differentiable.
Eric, JCMB 4312, 5 November 2010
NotesNext we define a 1 dimensional Brownian motion and give a constructive proof of its existence, after Paul Levy. Then we investigate some of Brownian motion's simple invariance properties with a view toward discussing continuity and differentiability at a later date.
Eric, JCMB 4312, 29 October 2010
NotesOur goal is to introduce Brownian motion, an important object in probability theory. We begin with a reminder of certain key ideas in probability theory and a discussion of Gaussian variables (to make the topic intelligible for those who haven't seen any probability for a while).
Josef, JCMB 4312, 22 October 2010
NotesIn this talk we look at the Dirichlet problem. We first revise the basic properties of harmonic functions; using these properties we will introduce the elliptic measure. Once this is done, we motivate what is meant by the Dirichlet problem with boundary data in Lp, called (D)p, and give a characterisation of when (D)p holds.
Marina, JCMB 4312, 15 October 2010
NotesWe will talk about a version of Littlewood-Paley theory and demonstrate its importance through the study of multipliers.
Tim, JCMB 4312, Monday 11 October 2010
Notes TrickiWe will look at a common (and useful) technique used in analysis proofs - perhaps some day in your thesis?!
