The reduced twisted C*-algebra A of an étale groupoid G has a canonical abelian subalgebra D: functions on G's unit space. When G has no non-trivial abelian subgroupoids (i.e., G is principal), then D is in fact maximal abelian. Remarkable work by Kumjian shows that the tuple (A,D) allows us to reconstruct the underlying groupoid G and its twist uniquely; this uses that D is not only masa but even what is called a C*-diagonal. In this talk, I show that twisted C*-algebras of non-principal groupoids can also have such C*-diagonal subalgebras, arising from non-trivial abelian subgroupoids, and I will discuss the reconstructed principal twisted groupoid of Kumjian for such pairs of algebras.

The classification program of C*-algebras aims to classify simple, separable, nuclear C*-algebras by their K-theory and traces, inspired by analogous results obtained for von Neumann algebras. A landmark result in this project was obtained in 2015, building upon the work of numerous researchers over the past 20 years. More recently, Carrión, Gabe, Schafhauser, Tikuisis, and White developed a new, more abstract approach to classification, which connects more explicitly to the von Neumann algebraic classification results. In their paper, they carry out this approach in the stably finite setting, while for the purely infinite case, they refer to the original result obtained by Kirchberg and Phillips. In this talk, I provide an overview of how the new approach can be adapted to classify purely infinite C*-algebras, recovering the Kirchberg-Phillips classification by K-theory and obtaining Kirchberg's absorption theorems as corollaries of classification rather than (pivotal) ingredients. This is joint work with Jamie Gabe.

The Camassa–Holm equation, which is nonlinear one-dimensional nonlinear PDE which is completely integrable and has  applications in several areas, has received considerable attention. We will discuss recent work regarding the Camassa—Holm equation with transport noise, more precisely, the equation $u_t+uu_x+P_x+\sigma u_x \circ dW=0$ and $P-P_{xx}=u^2+u_x^2/2$. În particular, we will show existence of a weak, global, dissipative solution of the Cauchy initial-value problem on the torus.  This is joint work with L. Galimberti (King’s College), K.H. Karlsen (Oslo), and P.H.C. Pang (NTNU/Oslo).

When studying interacting particle systems, two distinct categories emerge: indistinguishable systems, where particle identity does not influence system dynamics, and non-exchangeable systems, where particle identity plays a significant role. One way to conceptualize these second systems is to see them as particle systems on weighted graphs. In this talk, we focus on the latter category. Recent developments in graph theory have raised renewed interest in understanding largepopulation limits in these systems. Two main approaches have emerged: graph limits and mean-field limits. While mean-field limits were traditionally introduced for indistinguishable particles, they have been extended to the case of non-exchangeable particles recently. In this presentation, we introduce several models, mainly from the field of opinion dynamics, for which rigorous convergence results as N tends to infinity have been obtained. We also clarify the connection between the graph limit approach and the mean-field limit one. The works discussed draw from several papers, some co-authored with Nastassia Pouradier Duteil and David Poyato.