Minicursos
Plenarista: Emanuel Carneiro, ICTP - Trieste
Titulo: Fourier optimization and number theory
Resumo: Some problems in number theory are naturally related to different types of oscillatory structures. In such situations, certain Fourier optimization problems emerge, carrying important information about the original number theoretical entity and also being of intrinsic interest in analysis.
The aim of this minicourse is to present a variety of number theory problems which are amenable to a Fourier optimization framework. These include: (i) bounding objects related to the Riemann zeta-function; (ii) estimating the size of prime gaps; (iii) bounding the pair correlation of zeros of the Riemann zeta-function; (iv) bounding the height of low-lying zeros over families of L-functions; (v) estimating the angular discrepancy of zeros of polynomials; (vi) bounding the least quadratic non-residue modulo a prime; (vii) bounding the least prime in an arithmetic progression.
No previous research background in number theory is required (at least to have an idea of what the minicourse is about); we will briefly review the main tools and definitions as we move along.
The aim of this minicourse is to present a variety of number theory problems which are amenable to a Fourier optimization framework. These include: (i) bounding objects related to the Riemann zeta-function; (ii) estimating the size of prime gaps; (iii) bounding the pair correlation of zeros of the Riemann zeta-function; (iv) bounding the height of low-lying zeros over families of L-functions; (v) estimating the angular discrepancy of zeros of polynomials; (vi) bounding the least quadratic non-residue modulo a prime; (vii) bounding the least prime in an arithmetic progression.
No previous research background in number theory is required (at least to have an idea of what the minicourse is about); we will briefly review the main tools and definitions as we move along.
Plenarista: Eduardo Teixeira, University of Central Florida
Titulo: Mini-course: an introduction to free boundary problems
Resumo: I will describe the mathematical theory of the obstacle problem.