Sara Daneri
"At the roots of self-assembled patterns: intrinsic nonlocal curvatures"
Patterns, meant as periodically repeated geometric structures, emerge in several physical and biological systems both at small and very large scales. Such patterns are often rather simple and common to diverse physical systems: stripes/lamellae, checkerboards, periodically ordered spherical droplets, etc. It is universally believed that in many of such systems the emergence of patterns is due to the competition between short range attractive forces (which would prefer to form large droplets and aggregate the mass together) and long range repulsive forces (which would prefer to split the mass in smaller and smaller droplets). This mechanism is very important both from the theoretical and the applied point of view, because it allows microstructures to form without the aid of external forces (self-assembly).
In this talk we are going to present a recent approach which is able to give a rigorous explanation of such a phenomena, in some physical settings. The focus will be on the role played by newly found intrinsic nonlocal curvatures, which provide the link between the energy of admissible configurations and their spatial organization into patterns.
Giovanna Marcelli
"Adiabatic perturbation theory in quantum dynamics and its applications to the integer quantum Hall effect"
First, I will review the standard adiabatic theorem in quantum dynamics for gapped fermionic systems (GFS). Then, I will discuss the concepts of super-adiabaticity and higher-order response, from which the validity of the linear response for GFS can be deduced.
Finally, I will report recent results on the integer quantum Hall effect obtained in joint works, based on adiabatic perturbation theory.
Harini Desiraju
"Random curves and isomonodromy"
Schramm-Lowner Evolutions are a special class of random curves that are central to the study of 2D lattice models. In this talk, I will introduce the connection between the observables known as SLE martingales, and special transcendental functions from integrable systems known as isomonodromic tau-functions.
