ICTP Mathematics Seminar (Emanuel CARNEIRO) - Tuesday, 24 October, at 16:00

[ICTP Math Section]

M A T H E M A T I C S   S E M I N A R S   2017


Tuesday 24, October, at 16.00 hrs.


Emanuel Carneiro (IMPA, Brazil)


Title: Fourier optimization and prime gaps


Abstract:  Fourier optimization problems appear naturally within several 
different fields of mathematics, particularly in analysis and number 
theory. These are problems in which one imposes certain conditions on a 
function and its Fourier transform, and then wants to optimize a certain 
quantity. A recent example is given in the proof of the optimal sphere 
packing in dimensions 8 and 24. In this talk I want to show how certain 
optimization problems of this sort appear naturally in connection to the 
question of bounding the maximal gap between consecutive primes, under 
the Riemann hypothesis. In particular, we improve the best known bounds 
for this problem, that dates back to the works of Cramer in the 1920's.

This is a joint work with M. Milinovich (Univ. of Mississippi) and
K. Soundararajan (Stanford Univ.)



  VENUE:  Stasi Seminar Room (ICTP Leonardo da Vinci Building, first floor)