Thursday, July 14 2022

1-2pm: Evan Miller, University of British Columbia

Slides here or click HERE for part of the recorded presentation.

Title: On the regularity of the axisymmetric, swirl-free solutions of the Euler equation in four and higher dimensions

Abstract: In this talk, we will discuss the axisymmetric, swirl-free Euler equation in four and higher dimensions. We will show that in four and higher dimensions the axisymmetric, swirl-free Euler equation has properties which could allow finite-time singularity formation of a form that is excluded in three dimensions. We will also consider a model equation that is obtained by taking the infinite-dimensional limit of the vorticity equation in this setup. This model exhibits finite-time blowup of a Burgers shock type. The blowup result for the infinite dimensional model equation heavily suggests that smooth solutions of the Euler equation exhibit finite-time blowup in sufficiently high dimensions.
PDF HERE

2-3pm: Fletcher Gates, McMaster University

Slides here or click HERE for the recorded presentation.

Title: Weighted Haar and Alpert Wavelets: Dimension and Stability

Abstract: In this talk we discuss the properties of weighted Haar and Alpert wavelets. We will give a classification of the measures in which such wavelet bases are degenerate, and describe techniques for finding dimensions of the underlying spaces from which the wavelets are drawn. We will also present a stability result for weighted Haar wavelets in doubling measures, and some preliminary work regarding the question of stability in non-doubling measures.
PDF HERE

Zoom Coordinates as in Email Invitation. Email Scott Rodney at scott(dot)rodney(at)gmail(dot)com for technical support.