Two more Clay-Mahler lectures

I am posting the last two talks in my Clay-Mahler lecture series here:

• “Structure and randomness in the prime numbers“.  This public lecture is slightly updated from a previous talk of the same name given last year, but is largely the same material.
• “Perelman’s proof of the Poincaré conjecture“.  Here I try (perhaps ambitiously) to give an overview of Perelman’s proof of the Poincaré conjecture into an hour-length talk for a general mathematical audience.  It is a little unpolished, as I have not given any version of this talk before, but I hope to update it a bit in the future.

[Update, Sep 14: Poincaré conjecture slides revised.]

[Update, Sep 18: Prime slides revised also.]

The cosmic distance ladder

I am uploading another of my Clay-Mahler lectures here, namely my public talk on the cosmic distance ladder (4.3MB, PDF).  These slides are based on my previous talks of the same name, but I have updated and reorganised the graphics significantly as I was not fully satisfied with the previous arrangement.

[Update, Sep 4: slides updated.  The Powerpoint version of the slides (8MB) are available here.]

[Update, Oct 26: slides updated again.]

More Mahler lectures

I am posting here four more of my Mahler lectures, each of which is based on earlier talks of mine:

• Compressed sensing.  This is an updated and reformatted version of my ANZIAM talk on this topic.
• Discrete random matrices.  This talk is a survey on recent developments on the universality phenomenon in random matrices, including work of myself and Van Vu.  It covers similar material to my Netanyahu lecture, which has not previously appeared in electronic form.
• Recent progress in additive prime number theory.  This is an updated and reformatted version of my AMS lecture on this topic.
• Recent progress on the Kakeya conjecture.  This is an updated and reformatted version of my Fefferman conference lecture.

As always, comments, corrections, and other feedback are welcome.

Mathematical research and the internet

I’ll be in Australia for the next month or so, giving my share of the Clay-Mahler lectures at various institutions in the country.  My first lecture is next Monday at Melbourne University, entitled “Mathematical research and the internet“.  This public lecture discusses how various internet technologies (such as blogging) are beginning to transform the way mathematicians do research.

In the spirit of that article, I have decided to upload an advance copy of the talk here, and would welcome any comments or feedback (I still have a little bit of time to revise the article).   [NB: the PDF file is about 5MB in size; the original Powerpoint presentation was 10MB!]

[Update, August 31: the talk has been updated in view of feedback from this blog and elsewhere.  For comparison, the older version of the talk can be found here.]

[Update, Sep 4: Video of the talk and other information is available here.]