REMINDER: Arithmetic and Analysis Day - Friday, 23 November, starting 9:30 - ICTP Stasi Seminar Room

[ICTP Math Section]

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Arithmetic and Analysis Day

November  23, 2018

Venue: Luigi Stasi seminar room (ICTP Leonardo da Vinci Building)

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9:30 - 10:30 Emanuel Carneiro (ICTP)

Title: Bounds for zeta and primes via Fourier analysis

Abstract: This will be a light talk (a survey-type talk with mention to 
several open problems) on some of the recent bounds for objects related 
to the Riemann zeta-function via the use of Fourier analysis machinery. 
Certain very interesting Fourier optimization problems come into play, 
naturally related to our number theoretical entities. Very little 
analysis/number theory background is expected in order to get the big 
picture of the talk.

10.30 - 11:00 Coffee break

11:00 - 12:00 Umberto Zannier (SNS, Pisa)

Title: Pell-Abel equation X^2-D(t)Y^2=1, to be solved in polynomials 
X(t),Y(t), and applications.

Abstract: We shall discuss the so-called Pell-Abel equation, i.e. 
X^2-D(t)Y^2=1. This is similar to the classical Pell equation (proposed 
in fact by Fermat), which appears in many issues of Number Theory.  The 
polynomial version seems less well-known, but is old as well, studied 
e.g. by Abel in 1826. We shall survey about this equation, illustrating 
different mathematical issue involving it. Then we shall also present 
some recent results about solvability of the equations, when D(t) runs 
through a pencil of polynomials.

12:00 Lunch

14:00 - 15:00 Danylo Radchenko (MPI)

Title: Universal optimality, Fourier interpolation, and modular forms

Abstract: I will talk about a joint work with Henry Cohn, Abhinav Kumar, 
Stephen D. Miller, and Maryna Viazovska.  We look at the problem of 
arranging points in Euclidean space in order to minimize their potential 
energy.  In some exceptional case it might turn out that a single 
configuration is optimal for all potentials that are completely 
monotone; in this case such a configuration is called universally 
optimal. We show that the E8 lattice and the Leech lattice are 
universally optimal in their respective dimensions.

15:00 - 15:30 Coffee break

15:30 - 16:30 Felipe Gonçalves (University of Bonn)

Title: Uncertainty principles connected with sphere packings.

Abstract: In this talk we discuss recently discovered uncertainty 
principles related to the problem of packing spheres in Euclidean 
space.  Time permitting, we will also discuss how these techniques can 
be used on other problems in number theory.

Everyone is welcome to attend

-- 
Koutou Mabilo
ICTP Mathematics Group
Leonardo Da Vinci Building
Strada Costiera no. 11
34151 Trieste, Italy
Tel. no.: +39-040-2240455

For to be free is not merely to cast off one's chains, but to live in a way
that respects and enhances the freedom of others. Nelson Mandela