Lior Bary-Soroker:
Hardy-Littlewood tuple conjecture over large finite fields
Abstract:
The Hardy-Littlewood tuple conjecture predicts,
for a tuple of integers (a_1, ..., a_k),  
the number of integers n such that
n+a_1, ..., n+a_k are all prime.
In particular if a_1=0, a_2=2, 
this conjectures gives the number of twin primes. 

We shall discuss the analog of this conjecture
in the ring of polynomials F_q[x]
over a finite field F_q with q elements, 
and its solution in the limit q-->infinity, q odd.