## Archive for November, 2012

### Short MacArthur stats

November 18, 2012

The MacArthur Foundation rewards each year about 22 Fellows with a 5-year \$500,000 grant given in instalments. The only eligibility requirement is that the laureates must be either citizens or permanent residents of the US.   Let’s see the break-up of recent classes.

– This year there has been 23 recipients. Most are US citizens educated there, the 5 exceptions being Israeli mathematician Chudnovsky (the only mathematician), German photographer Barth, Mexican-American film-maker Almada, and two frenchmen: bow-maker Rolland and optical physicist Guyon.

– Last year, the 22 laureates had 4 non-US educated ones:  German physicist Greiner, Cuban percussionist Prieto, Italian silversmith Vitali, and Japanese developmental biologist Yamashita.

– In 2010 there has been 23 fellows, among which: Chinese fiction writer Li, Israeli optical physicist Lipson, French economist Saez, and Chinese computer security specialist Song.

So, the general recent trends seem to be:

– about a half of the fellows are scientists broadly speaking, the other half being connected to the arts

– about 18% are non-US educated, and 82% are US citizens educated there

– mathematicians are rare: before Chudnovsky there has been Mahadevan in 2009, Tao in 2006, and then it goes back to Yau in 2000. They were more numerous in the eighties it seems.

### The Monks-Peluse-Ye theorem on consecutive primes in arithmetic progressions

November 3, 2012

It has already been noted on this blog that REUs seem to be great opportunities for undergrads (and sometimes high schoolers) to produce interesting research.

The one that happened at Emory this last summer is a new impressive example: three instructors (among whom the famous Ken Ono) tutored nine talended undergrads, and within the six weeks of the program they produced six interesting papers!

The one that actually got me to that webpage is by three of the undergradutes: Monks, Peluse and Ye studied the interactions between the Green-Tao theorem on primes in arithmetic progressions and Shiu’s results on consecutive primes within a same congruence class. They obtained:

Theorem (Monks-Peluse-Ye) If the set of primes $\mathcal A$ is well-distributed (a technical definition) then there exist arbitrarily long strings of consecutive primes in $\mathcal A$ all of which lie in any given progression $\{a + qn\}$ with $\gcd(q, a) = 1$.

They actually have a quantitative version which bounds from below the length of the arithmetic progression by (a function of) the the size of $\mathcal A$.  And as a corollary they have:

Corollary (Monks-Perulse-Ye) For any irrational $\alpha > 0$ of fi nite type (i.e. most irrationals), there exist arbitrarily long strings of consecutive primes in ${\mathcal B}_{\alpha}=\{ { \lfloor \alpha \rfloor } , {\lfloor 2\alpha \rfloor } , {\lfloor 3\alpha \rfloor } , \cdots \}$ all of which lie in any progression $\{a+qn\}$ with $\gcd(q, a) = 1$.