Konstantinos Bessas, Università di Pavia, Generalized BMO-type seminorms and vector-valued Sobolev functions, Thursday, November 12, 2026, time 14:30, Aula seminari III piano
Abstract:Abstract:
We establish a pointwise limit theorem for a broad class of parameter-dependent BMO-type seminorms as the parameter tends to zero. By introducing novel BMO-type seminorms, we provide a unified framework that extends several existing results and yields derivative-free characterizations of Sobolev-type spaces, both in the scalar and in the vector-valued setting. More precisely, for any open set $\Omega\subset \mathbb{R}^n$ and any $p\in (1, \infty)$, we provide a characterization of the Sobolev space $W^{1,p}(\Omega; \mathbb{R}^m)$. In addition, we characterize the space $E^{1,p}(\Omega;\mathbb{R}^n)$ of $L^p$ maps with $p$-integrable distributional symmetric gradient. Finally, for all $p\in [1, \infty)$, we show that these seminorms converge to integral functionals with convex, $p$-homogeneous integrands associated with the distributional gradient and the symmetric gradient. The talk is based on joint work with Serena Guarino Lo Bianco (Università degli Studi di Modena e Reggio Emilia) and Roberta Schiattarella (Università degli Studi di Napoli Federico II).

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.