Clik here to view.
Kleiner’s proof of Gromov’s theorem
This week there is a conference here at IPAM on expanders in pure and applied mathematics. I was an invited speaker, but I don’t actually work in expanders per se (though I am certainly interested in...
View ArticleClik here to view.
Approximate subgroups of linear groups
Emmanuel Breuillard, Ben Green, and I have just uploaded to the arXiv our paper “Approximate subgroups of linear groups“, submitted to GAFA. This paper contains (the first part) of the results...
View ArticleClik here to view.
Cayley graphs and the geometry of groups
In most undergraduate courses, groups are first introduced as a primarily algebraic concept – a set equipped with a number of algebraic operations (group multiplication, multiplicative inverse, and...
View ArticleClik here to view.
254B, Notes 2: Cayley graphs and Kazhdan’s property (T)
In the previous set of notes we introduced the notion of expansion in arbitrary -regular graphs. For the rest of the course, we will now focus attention primarily to a special type of -regular graph,...
View ArticleClik here to view.
254B, Notes 7: Sieving and expanders
In this final set of course notes, we discuss how (a generalisation of) the expansion results obtained in the preceding notes can be used for some nnumber-theoretic applications, and in particular to...
View ArticleClik here to view.
Cayley graphs and the algebra of groups
This is a sequel to my previous blog post “Cayley graphs and the geometry of groups“. In that post, the concept of a Cayley graph of a group was used to place some geometry on that group . In this...
View ArticleClik here to view.
Discretised wave equations
The wave equation is usually expressed in the form where is a function of both time and space , with being the Laplacian operator. One can generalise this equation in a number of ways, for instance by...
View Article
