Live blog 2ND AMS-UMI INTERNATIONAL JOINT MEETING – Day 3

From July 23 to July 26, 2024, Università degli Studi di Palermo will host the 2nd International Joint Meeting co-organized by the Unione Matematica Italiana (UMI) and the American Mathematical Society (AMS). The 1st International AMS-UMI Joint Meeting was held from June 12 to June 16 2002 in Pisa.

On these pages every day we will provide live updates from the meeting: photos, short videos, events. This page will be automatically updates (if not it is enough to reload the page). Please, follow us to be updated and also on the UMI social media: Facebook, X (please, if you post some interesting content, use the hashtag #amsumi2024

To be oriented: the official website of the meeting

Complete Schedule

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At this link you can see what happened yesterday!

09:00 – 10:00 Invited Address Lecture, Sara Daneri (GSSI, L’Aquila, Italy)

Title: Continuous symmetry breaking: a rigorous approach

Abstract. At the base of spontaneous pattern formation is universally believed to be the competition between short range attractive and long range repulsive forces. Though such a phenomenon is observed in experiments and simulations, a rigorous understanding of the mechanisms at its base is still in most physical problems a challenging open problem. The main difficulties are due to the nonlocality of the interactions and, in more than one space dimensions, the symmetry breaking phenomenon (namely the fact that the interactions have a group of symmetries larger than the expected minimizers).

In this talk we will present a new rigorous approach which allows us to prove symmetry breaking for a class of functionals with isotropic interactions. In particular, we show that in a regime in which the competing interactions are of the same order, minimizers are one-dimensional (i.e. stripes/lamellae). This class of functionals includes physical energies related to pattern formation in thin magnetic films and colloidal systems.  This work has been obtained in collaboration with E. Runa.

Title: Birational geometry of varieties in positive and mixed characteristics

Abstract. After recent progress the classification of complex projective varieties, it is natural to ask if similar results hold in positive and mixed characteristics. Since the Kodaira vanishing theorem no longer holds in this context, many technical difficulties arise. In this talk, I will discuss some recent breakthroughs (in low dimensions) that are inspired by techniques coming from the theory of F-singularities and BCM-singularities.

B7, D’Aquino, Model Theory.

B7, D’Aquino, Model Theory.

B7, D’Aquino, Model Theory.