Time: 16:30-18:00

Location: Mondi 3

Speaker 1: Anna Zanoli (first year student)

Title: A walk through number fields: counting dihedral extensions

Abstract: Malle’s conjecture predicts the asymptotic behavior of the number of field extensions with a fixed Galois group. In recent years, Gundlach put forward a multi-invariants version of this conjecture, which we verify for the specific case of Galois D4-extensions of Q. Even if you’re not a Galois-groups-groupie (yet), hopefully this talk will give you some insights on how to tackle a number theoretical problem with a blend of algebraic and analytic tools.

Speaker 2:  Davide Desio (first year student)

Title: The Bosonization of Interacting Fermionic Systems

Abstract: The derivation of effective field theories to describe electron gases as a model for conducting materials is a fundamental problem in the modern mathematical physics. In the last century, avant-garde mathematics has been created to describe the behaviour of systems with many electrons. In the 1930s, the Hartree-Fock method was introduced to describe the electronic structure of large atomic nuclei and later applied to conducting materials. Although the Hartree-Fock theory has been proved to be successful in the description of large electronic structures, it fails in the description of the conductivity properties of materials. It is therefore necessary to go beyond the Hartree-Fock approximation and develop a deep understanding of the nontrivial quantum correlations. In 1953, David Bohm and David Pines proposed the random phase approximation (RPA) as an effective field theory to study the properties of high-density electron gases. The RPA can be interpreted as collective bosonic oscillations, whose energy minimum represents the leading order  correction to the correlation energy of the system. In this colloquium, we are going to explore the most recent mathematical results on the approximate bosonization of many electron systems as a rigorous approach to the random phase approximation.