Mario Fuest, Leibniz Universität Hannover, Institut für Angewandte Mathematik, Chemotaxis systems with logistic source: boundedness vs. blow-up, Thursday, October 08, 2026, time 14:30, Aula seminari III piano
Abstract:Abstract:
This talk addresses the qualitative behaviour of solutions to Keller–Segel systems incorporating superlinear degradation terms, which describe the aggregation of organisms in response to chemical signals while accounting for population growth. We show (both for the fully parabolic system as well as for certain parabolic–elliptic simplifications) that solutions are always globally bounded if the logistic-type degradation is sufficiently strong while certain weaker but still superlinear dampening terms still allow for solutions blowing up in finite time.

Stefania Patrizi, The University of Texas at Austin, Multiple-interface dynamics in fractional Allen-Cahn equations, Tuesday, June 30, 2026, time 15:30, Aula seminari III piano
Abstract:Abstract:
In this talk, I will present several fractional Allen-Cahn problems involving multiple interfaces. The diffusion operator is given by the fractional Laplacian of order s, where s \in (0,1). In two dimensions, these equations model the dynamics of multiple dislocation loops in crystalline materials. We show that when s \geq 1/2, each interface evolves independently according to mean curvature flow. In contrast, when s < 1/2, the interfaces evolve by fractional mean curvature flow and are coupled through an interaction term generated by the presence of the other interfaces. This is a joint works with E. Hasani, T. Sangsawang, and M. Vaughan.

Joaquim Duran, Centre de Recerca Matemàtica, The \overline\partial-Robin Laplacian and its connection with graphene, Thursday, June 18, 2026, time 14:30, Aula seminari III piano
Abstract:Abstract:
This talk addresses the Robin-type problem $-\Delta u = f$ in $\Omega$, $2 \bar \nu \partial_{\bar z} u + au = 0$ on $\partial\Omega$, where $\Omega$ is a bounded C^2 domain in R^2, $f\in L^2(\Omega,\mathbb C)$ is prescribed, and a>0 is a parameter. The boundary condition involves an inherent complex structure, which prevents the use of typical results for real-valued problems (such as maximum principles, rearrangement techniques, or moving plane methods). As we shall see in the talk, this problem is connected with the behavior of electrons conducting electricity in graphene quantum dots. Exploring such a connection, we estimate the energies of these electrons.

Edoardo Mainini, Università di Genova, Gradient flows: from diffusion to Keller-Segel models, Tuesday, May 19, 2026, time 15:15, Aula seminari, terzo piano
Abstract:Abstract:
We discuss the gradient flow approach to aggregation-diffusion models of Keller-Segel type. We prove regularizing effect and sharp hypercontractivity estimates. As a consequence, we deduce several properties such as existence of solutions with measure data, energy dissipation identity, evolution variational inequalities and uniqueness, thus establishing a full parallel with the theory of gradient flows for diffusion models and geodesically convex functionals. 

Camilla Polvara, Sapienza Università di Roma, Critical Neumann problem in cones: bifurcation, stability, and symmetry breaking, Thursday, May 14, 2026, time 14:30, Aula seminari, terzo piano
Abstract:Abstract:
We consider the critical Neumann problem in cones. We prove that the standard bubbles, which are the only radial solutions, become unstable for a class of nonconvex cones, which is defined through the first Neumann eigenvalue of the Laplace Beltrami operator on the domain D on the unit sphere, which spans the cone. This immediately implies a symmetry breaking result for the minimizers of the Sobolev inequality. Actually, a bifurcation result from the standard bubbles can be proved. We also present a quantitative Sobolev inequality of Bianchi-Egnell type, which holds in any cone, even if the minimizers are not the standard bubbles. These results are contained in joint works with G. Ciraolo, F. Pacella, and L. Provenzano.

Alberto Maione, Politecnico di Milano, H-compactness for nonlocal linear operators in fractional divergence form, Thursday, May 07, 2026, time 14:30, Aula seminari, terzo piano
Abstract:Abstract:
In this talk, we present the mathematical theory of the homogenisation of composite materials, from its origins in the 1970s to some recent applications. In particular, we discuss a new H-compactness result for possibly non-symmetric and nonlocal linear operators in fractional divergence form. In the second part, we focus on symmetric operators and show that the H-convergence is equivalent to the Gamma-convergence of the associated nonlocal energies. This research is carried out in collaboration with Maicol Caponi (University of L'Aquila) and Alessandro Carbotti (University of Salento).