Upcoming talks 2025/26
Filippo Cagnetti (Università di Parma)
February 26th, 2026
@ 14:30, Seminar room (2nd floor), Alan Turing Building
Title: Rigidity of the perimeter and Pólya-Szegö inequalities under circular rearrangement
Abstract: We discuss the circular symmetrization of sets and the corresponding rearrangement for Sobolev functions. As an application of our results, we show that in dimension 2 all the extremals of Morrey's inequality are foliated Schwarz symmetric.
Fanqin Zeng (Seoul National University)
February 26th, 2026
@ 15:30, Seminar room (2nd floor), Alan Turing Building
Title: Alignment Dynamics in Multi-Particle Systems with Switching Interaction Networks
Abstract: This talk concerns alignment phenomena in multi-particle systems with switching interaction networks, with a focus on the effects of randomness and time variability on collective behavior. Such systems arise naturally in consensus dynamics, collective motion, and distributed coordination, where interaction structures are often time-dependent and subject to random fluctuations.
For discrete consensus-type models, randomly switching network topologies may destroy classical connectivity assumptions and invariant quantities that are typically used to establish convergence. Nevertheless, asymptotic alignment can still be achieved under very weak conditions on the switching process and communication weights. These results demonstrate that consensus dynamics are remarkably robust with respect to strong randomness, nonuniform network activity, and the lack of uniform connectivity.
Going beyond asymptotic behavior, I will also discuss finite-time alignment in infinite-particle systems with switching interactions. In this setting, the infinite-dimensional nature of the system and the absence of conserved quantities render standard energy or Lyapunov methods ineffective. Instead, finite-time alignment is driven by nonlinear dissipation mechanisms, which can be revealed through diameter-type estimates on velocity differences and suitable differential inequalities. This approach allows us to capture finite-time convergence phenomena that lie beyond the reach of classical asymptotic analysis.
Alejandro Fernández-Jiménez (Amsterdam Center for Dynamics and Computation)
March 4th, 2026
@ 14:30, Seminar room (2nd floor), Alan Turing Building (TBC)
Title: A Li-Yau and Aronson-Bénilan approach for the Keller-Segel system
Abstract: In this talk we will focus on the Keller-Segel system, for d >= 2 and m = 2 - 2/d, i.e. the critical exponent. This system exhibits a rich behaviour and its dynamics depend on the initial mass. When the mass is below certain threshold (subcritical mass) there is global-in-time bounded solutions, if we are beyond this threshold (supercritical mass), one can construct solutions with finite time blow-up. Finally, if the mass is critical there exists global-in-time solutions but they are not bounded globally-in-time.
The main goal of the talk is to extend the classical Li-Yau and Aronson-Bénilan estimates in order to cover the Keller-Segel case. We are able to recover the estimate for subcritical and critical mass and, in particular, for a small (computable) mass we also obtain a regularising effect. We follow two strategies: for the small mass case we rely on concavity and harmonic analysis. For the general case of subcritical and critical mass our argument is based on a careful analysis of the subsolutions of the Liouville and the Lane--Emden equations combined with a contradiction argument.
The talk presents joint work with C. Elbar and F. Santambrogio.
Jan-Frederik Pietschmann (Universität Augsburg)
March 4th, 2026
@ 15:30, Seminar room (2nd floor), Alan Turing Building (TBC)
Title: Gradient flows on metric graphs with reservoirs: Microscopic derivation and multiscale limits
Abstract: We study evolution equations on metric graphs with reservoirs, that is graphs where a one-dimensional interval is associated to each edge and, in addition, the vertices are able to store and exchange mass with these intervals. Focusing on the case where the dynamics are driven by an entropy functional defined both on the metric edges and vertices, we provide a rigorous understanding of such systems of coupled ordinary and partial differential equations as (generalized) gradient flows in continuity equation format. Approximating the edges by a sequence of vertices, which yields a fully discrete system, we are able to establish existence of solutions in this formalism. Furthermore, we study several scaling limits using the recently developed framework of EDP convergence with embeddings to rigorously show convergence to gradient flows on reduced metric and combinatorial graphs. Finally, numerical studies confirm our theoretical findings and provide additional insights into the dynamics under rescaling.
Andrea Braides (Università degli Studi di Roma "Tor Vergata")
March 12th, 2026
@ 15:00, Seminar room (2nd floor), Alan Turing Building
Title: TBA
Abstract: TBA
Alessandro Goffi (Università di Firenze)
April 16th, 2026
@ 14:30, Seminar room (2nd floor), Alan Turing Building
Title: Quantitative vanishing viscosity approximation of fully nonlinear, non-convex, Hamilton-Jacobi equations with Hölder data.
Abstract: We discuss new quantitative estimates of the vanishing viscosity process for evolutionary Hamilton-Jacobi PDEs that are neither concave nor convex in the gradient and Hessian entries. I will describe a novel approach that exploits the regularizing properties of sup/inf-convolutions for viscosity solutions combined with the comparison principle. This method provides explicit sharp constants without assuming differentiability properties neither on solutions nor on the Hamiltonian. This is a joint work with Alekos Cecchin (Padova).