Giacomo Sodini, TU Wien, Sobolev functions on spaces of measures and applications, Thursday, March 05, 2026, time 14:30, Aula seminari, III piano
Abstract:Abstract:
After a brief introduction to the Wasserstein and Hellinger-Kantorovich distances on the space of (probability) measures, we discuss two approaches to the definition of differentiable functions on spaces of measures. Provided a suitable (and in a way canonical) reference measure is chosen, we show that the two approaches coincide. Finally, we discuss some possible applications such as the study of HJB equations and stochastic processes on spaces of measures.

Fabio E. G. Cipriani, Politecnico di Milano, Existence, degeneracy, discreteness and stability of ground states by logarithmic Sobolev inequalities on Clifford algebras, Thursday, Febraury 26, 2026, time 14:30, Aula seminari III piano
Abstract:Abstract:
We prove existence, finite degeneracy, discreteness and stability of ground states of energy forms satisfying logarithmic Sobolev inequalities with respect to not necessarily tracial states on von Neumann algebras. The results are then applied to discuss existence and properties of ground states of Hamiltonians considered by L. Gross in QFT, describing, on a suitable Clifford algebra, spin 1/2 Dirac particles, subject to interactions with an unbounded external scalar field.

Alberto Farina, Université de Picardie Jules Verne, One-dimensional symmetry results for semilinear equations and inequalities on half-spaces, Tuesday, Febraury 24, 2026, time 14:30, Aula seminari, terzo piano
Abstract:Abstract:
We consider non-negative solutions, possibly unbounded, to the semilinear equation $-\Delta u=f(u)$ in the upper half-space $R^N_+$ and we prove new one-dimensional symmetry results. Some Liouville-type theorems are also proven in the case of differential inequalities in $R^N_+$, even without imposing any boundary condition. Although subject to dimensional restrictions, our results apply to a broad family of functions $f$. In particular, they apply to all non-negative function $f$ that behaves at least linearly at infinity.

Emanuele Salato, Politecnico di Torino, An isoperimetric inequality for twisted eigenvalues with one orthogonality constraint, Thursday, Febraury 19, 2026, time 14:30, Aula Seminari, terzo piano
Abstract:Abstract:
We introduce a new type of eigenvalues whose corresponding eigenfunctions satisfy an orthogonality constraint with respect to a given function. Then we study a shape optimization problem arising in this setting. Based on a joint work with D. Zucco.

Daniele Castorina, Università di Napoli Federico II, MEAN-FIELD SPARSE OPTIMAL CONTROL OF SYSTEMS WITH ADDITIVE WHITE NOISE, Thursday, Febraury 05, 2026, time 14:30, Aula seminari III piano
Abstract:Abstract:
We analyze the problem of controlling a multiagent system with additive white noise through parsimonious interventions on a selected subset of the agents (leaders). For such a controlled system with an SDE constraint, we introduce a rigorous limit process toward an infinite dimensional optimal control problem constrained by the coupling of a system of ODEs for the leaders with a McKean--Vlasov type of SDE, governing the dynamics of the prototypical follower. The latter is, under some assumptions on the distribution of the initial data, equivalent with a (nonlinear parabolic) PDE-ODE system. The derivation of the limit mean-field optimal control problem is achieved by linking the mean-field limit of the governing equations together with the Gamma-limit of the cost functionals for the finite-dimensional problems. This is a joint research project with Francesca Anceschi (Ancona), Giacomo Ascione (SSM Napoli) and Francesco Solombrino (Lecce).

Carlo Mantegazza, Università di Napoli Federico II, Quasiconvexity in the Riemannian setting, Thursday, Febraury 05, 2026, time 15:30, Aula seminari III piano
Abstract:Abstract:
We introduce a notion of quasiconvexity for integrands defined on the tangent bundle of a Riemannian manifold. We prove that this condition characterizes the sequential lower semicontinuity of the associated integral functionals with respect to the weak^* topology of W^{1,\infty}, generalizing the classical Euclidean results by Morrey and Acerbi--Fusco. Moreover, we also extend the notions of polyconvexity and rank--one convexity to this context and establish the hierarchy between polyconvexity, quasiconvexity, and rank--one convexity, as in the Euclidean setting. Joint work with Aurora Corbisiero e Chiara Leone.