Colloquio di Matematica del Dini

Bogoliubov theory for dilute quantum systems

Venerdì 31 marzo alle ore 14:30 in aula 202, tenuto dal Prof. Benjamin Schlein (Universität Zürich)

Abstract: In this talk, I am going to present a recently developed, mathematically rigorous version of Bogoliubov theory and I am going to explain how it can be used to describe correlations in many-body quantum systems and to determine the low-energy spectrum of dilute gases.



On the topology of hyper-Kähler manifolds

Venerdì 28 ottobre, aula 202 del DiMaI, ore 14:30, tenuta dalla Prof.ssa Claire
Voisin (Institut de Mathématiques de Jussieu)

Abstract: Hyper-Kähler manifolds are symplectic holomorphic compact
Kähler manifolds, a particular class of complex manifolds with trivial
canonical bundle. They form a very restricted class, both from the
Riemannian and complex geometry viewpoints. They also satisfy strong
topological restrictions that I will describe, and that follow from
the study of their deformations. I will also explain further
restrictions in dimension $4$, and a classification result obtained in
collaboration with Debarre, Huybrechts and Macrì.



Physics-based and data-driven mathematical models for the simulation
of the heart function

Giovedì 31 marzo, aula 203 del DiMaI, ore 14:30, tenuto dal Prof. Alfio Quarteroni (Polimi - EPFL)

Abstract: This seminar focuses on machine learning (the computers’
ability to learn based on training from large data sets) and
computational science (the use of mathematical models originated from
fundamental principles of physics) in solving mathematical problems of
interest in real life. Similarities and differences, potentials, and
limitations are discussed, as well as the enormous possibilities
offered by their synergistic use. The driving application will be the
simulation of the cardiac function, in both physiological and
pathological regimes


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