Tuesday 15 October 2019, 1.30PM to 5:30pm

**Speaker(s):** Various

The next Northern Number Theory Seminar (NuTS) will be held at York on Tuesday 15 October 2019. Below and attached are the details. Everybody is welcome to attend!

The Northern NuTS is a joint research seminar in number theory. It links the number theory research groups of Durham, Manchester, Nottingham, Sheffield and York.

The seminar is funded by the LMS Grant Scheme 3. The website for Northern NuTS is https://www.maths.nottingham.ac.uk/plp/pmzcw/northernnuts.html

**All talks are in the Topos**

1.30pm – 2.20pm Emma Bailey (University of Bristol)

2.45pm – 3.45pm Pablo Shmerkin (T. Di Tella University and CONICET)

4.30pm -- 5.30pm Patrice Philippon (Institute de Mathématiques de Jussieu)

**Emma Bailey (University of Bristol)**

Title: Moments of moments

Abstract: I will motivate and present results concerning moments of moments of the Riemann zeta function alongside those of characteristic polynomials of random unitary matrices. The study of moments of moments has been furthered through connections with probability, combinatorics, and representation theory. This is joint work with Jon Keating.

**Pablo Shmerkin (T. Di Tella University and CONICET) **

Title: Multiplying by 2 and by 3: old conjectures and new results

Abstract: In the 1960s, H. Furstenberg proposed a series of conjectures which, in different ways, aim to capture the heuristic principle that "expansions in different bases have no common structure". I will discuss a sample of these conjectures, some which remain open and some which have been established in recent years. These problems lie at the intersection of Ergodic Theory and Fractal Geometry, but no previous background on either area will be assumed.

**Patrice Philippon (Institute de Mathématiques de Jussieu) **

Title: Around two problems of Hardy

Abstract: Let $\alpha>1$ and $\lambda$ be real numbers. About a century ago, Hardy asked: ``In what circumstances can it be true that the distance of $\lambda \alpha^n$ to the nearest integer tends to $0$ as $n$ goes to $\infty$?”. This question is still open. We will present some advances in this topic and around a related problem of Mahler, in the case $\alpha$ is algebraic. This is joint work with Purusottam Rath.

We plan to go to dinner after the last talk. If you are interested in coming please contact Sanju Velani (sanju.velani@york.ac.uk)

**Location:** Department of Mathematics, University of York