Every time I meet Peter Sarnak, he mentions his deep chagrin at being unable to blog, a sad state of affair which he attributes to his inability to type (straight quote). However, as he points out, he does the next best thing: he writes letters to various correspondents to explain a variety of topics, and then puts them on the web (together with some other papers, notes for lectures, and a few papers). And all this is well-worth looking at for inspiration and information. And since the address doesn’t seem to be as well-known as it could, here is the link.

Highlights of these are (to my mind at least):

* The Schur lectures on Arithmetic Quantum Chaos (1993); they have been published, but are not so easy to find. There has been a lot of recent progress (which I discussed briefly here; Sarnak also has a short letter on this topic, and is readying a more complete version as he prepares a lecture next week at IAS).

* The letter to Lagarias on integral Appolonian packings, a very beautiful topic where spectral theory of infinite covolume discrete subgroups meets number theory and geometry.

* The Notes on the Generalized Ramanujan conjectures, a great educational read for people who (like me) have been mostly comfortable with classical (*GL(2)*) modular forms, but want to see and learn what happens in higher rank.

* The letter to Morawetz on the supremum norms of eigenfunctions; again, it’s a topic where new phenomena occur when one moves beyond the classical case of hyperbolic surfaces (which still contains many mysteries, of course).

Great page indeed, thanks for mentioning it! If prof Sarnak reads this: it might be useful to add a number or date near each paper or letter on the webpage so that one may locate new additions easily (or are new ones always at the bottom of the page?).

The latest additions are always at the bottom, from what I can tell.