Excerpts from the Grothendieck-Serre Correspondence

Like many fellow mathematicians, I was very sad to hear the news that Alexander Grothendieckpassed away yesterday.  The word “genius” is overused; or rather, does not possess sufficiently fine gradations.  I know quite a few mathematical geniuses, but Grothendieck was a singularity.  His ideas were so original, so profound, and so revolutionary – and he had so many of them! – that I will not even attempt to summarize his contributions to mathematics here.  Rather, I thought that I would share some of my favorite passages from the fascinating Grothendieck-Serre Correspondence, published in a bilingual edition by the AMS and SMF.   They illuminate in brief flashes what made Grothendieck so extraordinary — but also human.  They also illustrate how influential Serre was on Grothendieck’s mathematical development.  Before I begin, here is a quote from another wonderful book, Alexander Grothendieck: A Mathematical Portrait, edited by Leila Schneps:

…the…

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254A announcement: Analytic prime number theory

In the winter quarter (starting January 5) I will be teaching a graduate topics course entitled “An introduction to analytic prime number theory“. As the name suggests, this is a course covering many of the analytic number theory techniques used to study the distribution of the prime numbers \$latex {{mathcal P} = {2,3,5,7,11,dots}}&fg=000000\$. I will list the topics I intend to cover in this course below the fold. As with my previous courses, I will place lecture notes online on my blog in advance of the physical lectures.

The type of results about primes that one aspires to prove here is well captured by Landau’s classical list of problems:

1. Even Goldbach conjecture: every even number \$latex {N}&fg=000000\$ greater than two is expressible as the sum of two primes.
2. Twin prime conjecture: there are infinitely many pairs \$latex {n,n+2}&fg=000000\$ which are simultaneously prime.
3. Legendre’s conjecture:…

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