Jonathan Fraser - Talks and notes

I taught an online mini-course on Assouad dimension and fractal geometry in July 2023. The course was aimed at PhD students and was based on parts of my bookThe course was hosted by Jun-Jie Miao, East China Normal University, China. Here are the uncorrected notes from the lectures, including some exercises at the end of both parts.

part 1 - Assouad dimension, basic properties, tangents and projections

part 2 - Examples: self-similar sets, Mandelbrot percolation and self-affine carpets

Here are some videos from various talks:

Dimensions of parabolic Julia sets and Kleinian limit sets - Liverrpool Dynamics Seminar, 7 September 2022 (you might have to search a bit)

Dimensions of Kleinian orbital sets - St Andrews Analysis seminar, 28 September 2021

Fractals in science and nature - Scottish Mathematical Council conference 6 March 2021 (aimed at secondary school students)

A new perspective on the Sullivan dictionary via the Assouad dimension and the Assouad spectrum
- Seminaire Cristolien d'Analyse Multifractale, CNRS, France, 17 December 2020

An analyst's take on the integers - Undergraduate Maths and Stats Seminar, 18 November 2020

A nonlinear projection theorem for Assouad dimension and the distance set problem - St Andrews Analysis seminar, 22 September 2020

Fourier transforms of measures on the Brownian graph
- Fractal Geometry, Hyperbolic Dynamics and Thermodynamical Formalism, Brown University, 10 March 2016

I no longer maintain a list of talks here, but there is a fairly comprehensive list on my CV. I usually give board talks,
but here are some slides I've used in the past along with some partial information about when they were used.

Assouad dimension of distance sets - slides from talk at 2021 winter meeting of the Canadian Mathematical Society

Sullivan dictionary, Kleinian groups, Julia sets - joint work with Liam Stuart from 2020

Interpolating between dimensions - slides from opening keynote lecture at Fractal Geometry and Stochastics VI, Bad Herrenalb 2018

Fourier transforms and the Brownian graph - joint work with Tuomas Sahlsten, ICERM 2016

Fractals - introductory talk on fractals aimed at secondary school students

Fractals and dynamics - introductory talk given at YRM Oxford 2015

Assouad dimension - joint work with many people, Fractals and Related Fields III, Porquerolles Island, 2015

Slicing theorems for Fourier dimension and Kahane's problem - joint work with Tuomas Orponen and Tuomas Sahlsten, ETDS meeting, Jagiellonian University 2014

Distance problem and ergodic theory - joint work with Andy Ferguson, Tuomas Sahlsten, Mark Pollicott, one day ergodic theory meeting, 2014

The Kakeya problem - introductory talk

Assouad dimension of self-similar sets with overlaps - joint work with Alexander Henderson, Eric Olson, James Robinson, Workshop on Fractals, Jerusalem 2014

Scaling scenery of self-affine carpets - joint work with Andy Ferguson and Tuomas Sahlsten, Numbers in Ergodic Theory, Leiden, 2014

Analyticity of subadditive pressure - Kenneth Falconer's birthday conference, Paris 2014

Inhomogeneous IFSs - Fractal Geometry and Stochastics 5, Tabartz 2014

Lq dimensions of self-affine measures - used for various seminars, from around 2013

Assouad dimension of self-similar and self-affine sets - used for various seminars, from around 2013

Dimensions of box like self-affine sets - Advances in Fractals and Related Topics, Chinese University of Hong Kong, 2012

Generic dimensions of graphs and images - joint work with Richard Balka, Abel Farkas and James Hyde from around 2012

Generic dimensions of IFS attractors - EPSRC Workshop, Warwick 2012

Prevalent Hausdorff dimension of graphs - joint work with James Hyde, Related Fields II, Porquerolles Island 2011