Fourier optimization, prime gaps, and zeta zeros

17
Jan

P25 (Room G02/03), Science South Bldg 26

11.00am to 12.00pm

There are many situations where one imposes conditions on a function and its Fourier transform and then wants to optimize a certain quantity. I will describe how these types of Fourier optimization problems can lead to the strongest known estimates for the maximum gap between consecutive primes assuming the Riemann hypothesis.

We can also use Fourier optimization to prove the strongest known conditional estimates for the number of zeta zeros in an interval on the critical line. If there is time, I will include a discussion of effective versions of these results. This is based on joint works with E. Carneiro, V. Chandee, and K. Soundararajan.

About the Speaker

Micah Baruch Milinovich grew up in rural Wisconsin before attending University of Rochester in upstate New York. He became a math major after realizing at age 19 that he would never become an astronaut. After a brief stint as a school teacher in inner city Queens, he returned to the University of Rochester to pursue a PhD in Mathematics under the direction of Professor Steven M. Gonek. Since 2008, he has been on the faculty at the University of Mississippi, colloquially known as Ole Miss, in Oxford, Mississippi where he lives with his wife Qin (pronounced "Chin"), his son Max, and his border collie Logan. View his University of Mississipi profile here.

 

Morning tea will be served immediately outside P25 at 10:30am. 

For more information about this seminar, contact Dr Tim Trudgian

 

Image credit: TANAKA Juuyoh on flickr (CC0 1.0)