Dear colleagues and friends,

we are glad to announce the forthcoming short courses and seminar in GSSI in June:

June 3-5 (short cours) & June 6 (seminar): Prof. Gian Michele Graf (ETH Zurich) June 10-12: Prof. Lenya Ryzhik (Stanford)

Please see at the end of the email for the detailed information.

Registration is free through the web form: https://indico.gssi.it/event/745/. Other courses hosted by the trimester can be found here: https://trimester2025.math.gssi.it/all_courses/.

We would be grateful if you could circulate the announcement among potentially interested students and researchers. For any information do not hesitate to contact us (patterns@gssi.itmailto:patterns@gssi.it).

———————————————— Venue: Main Lecture Hall, Gran Sasso Science Institute (Viale F. Crispi 7, L’Aquila) ———————————————— Matter and topology: an overview Gian Michele Graf (ETH Zurich)

3/6 (Tue) 14:15-15:45 5/6 (Thu) 14:15-15:45 6/6 (Fri) 09:00-10:45

Topological insulators are materials that are conducting at their edge, though not in the bulk. Their essential physical properties are encoded by an index. After reviewing the historical origins, and the Quantum Hall effect in particular, the appropriate indices will be discussed (Chern numbers, index of a pair of projections), as well as bulk-edge correspondence. Thereafter symmetry protected topological insulators will be addressed. The focus will be on symmetries like time-reversal and particle-hole conjugation and, correspondingly, on the Quantum Spin Hall effect and Majorana zero modes in superconductors, in physical dimensions d=2 and 1, respectively. More broadly, the Kitaev table describes the kind of indices that occur in relation to many more symmetries, in any dimension d, and its derivation will be treated. Special topics beyond the above framework, such as time-dependent systems (Floquet or quantum pumps) or classical systems (hydrodynamics) may occur too, as time permits. ———————————————— SMAQ Seminar: Adiabatic charge pumps and Galilei covariance Gian Michele Graf (ETH Zurich)

6/6 (Fri) 14:00-15:30

The Thouless theory of quantum pumps establishes quantized transport per cycle and determines the necessary conditions. When the description is shifted to a moving reference frame, as suggested by recent experiments on ultracold gases, transported and residing charges mix. That transformation is encoded in Galilean space and time, but underlying it is one of vector bundles that may be described in a number of ways, that may or may not rely on Bloch theory. In one of them, the transformation mixes strong and weak indices of a bundle on a 2-torus; in another one, a 3-torus is at center stage; in yet another one, and somewhat informal way, the transformation is related to a paradox that astonished seafarers of centuries past. Joint work with T. Esslinger and F. Santi. ———————————————— Branching Brownian motion and knowledge diffusion: from Fisher-KPP to MFG Lenya Ryzhik (Stanford​)

10/6 (Tue) 16:15-17:45 11/6 (Wed) 10:45-12:15 & 16:15-17:45 12/6 (Thu) 16:15-17:45

We will first discuss the general connection, via the voting models, between the branching Brownian motion (BBM) and the Fisher-KPP and other semilinear parabolic equations. This connection, together with the long time asymptotics of the solutions, allows, in particular, to deduce some fine properties of BBM, such as the law of large numbers and fluctuations of the limiting process near the maximum of BBM. In the second half of the lectures, we will discuss some knowledge diffusion models that arise in macroeconomics and lead to mean-field game type of problems that are also related to non-local Fisher-KPP equations. ————————————————

With our best wishes,

Lu Xu Assistant Professor (RTDb) Gran Sasso Science Institute