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.

Ewelina Zatorska, University of Warwick, Anelastic approximation for the degenerate compressible Navier-Stokes equations revisited , Wednesday, January 14, 2026, time 14:00, Aula seminari, terzo piano
Abstract:Abstract:
I will talk about our recent result in which we revisit the low Mach and low Froude numbers limit for the compressible Navier-Stokes equations with degenerate density-dependent viscosity. Using the relative entropy inequality based on the concept of k-entropy, we rigorously justified the convergence to the generalized anelastic approximation in the three-dimensional periodic domain for well-prepared initial data. For general ill-prepared initial data, we also obtained similar convergence result in the whole space, relying on dispersive estimates for acoustic waves. Compared with our earlier work [Fanelli and Zatorska, Commun. Math. Phys., 2023], the present analysis removes the need for the cold pressure component, so that the pressure law is purely isentropic without any additional regularizing term. This is joint work with Nilasis Chaudhuri, Francesco Fanelli, and Yang Li.

Lauren Conger, California Institute of Technology (Caltech), Monotonicity of Coupled Multispecies Wasserstein-2 Gradient Flows, Wednesday, November 26, 2025, time 11:15, Aula Seminari - III Piano
Abstract:Abstract:
We present a notion of $\lambda$-monotonicity for an $n$-species system of PDEs governed by flow dynamics, extending monotonicity in Banach spaces to the Wasserstein-2 metric space. We show that monotonicity implies the existence of and convergence to a unique steady state. In the special setting of Wasserstein-2 gradient descent of different energies for each species, we prove convergence to the unique Nash equilibrium of the associated energies and discuss the relationship between monotonicity and displacement convexity. This extends known zero-sum (min-max) results in infinite-dimensional game theory to the general-sum setting. We provide examples of monotone coupled gradient flow systems, including cross-diffusion, nonlocal interaction, and linear and nonlinear diffusion. Numerically, we demonstrate convergence of a four-player economic model for market competition, and an optimal transport problem. This is joint work with Ricardo Baptista, Franca Hoffmann, Eric Mazumdar, and Lillian Ratliff.

Elsa Maria Marchini, Politecnico di Milano, On some optimal control problems for moving sets, Thursday, November 20, 2025, time 15:15, Aula Seminari - III Piano
Abstract:Abstract:
The talk is concerned with a family of geometric evolution problems, modeling the spatial control of an invasive population within a plane region bounded by geographical barriers. The "contaminated region" is a set moving in the plane, which we would like to shrink as much as possible. To control the evolution of this set, we assign the velocity in the inward normal direction at every boundary point. Three main problems are studied: existence of an admissible strategy which eradicates the contamination in finite time, optimal strategies that achieve eradication in minimum time, strategies that minimize the average area of the contaminated set on a given time interval. For these optimization problems, that we like to see as “time dependent isoperimetric problems”, a sufficient condition for optimality is proved, together with several necessary conditions. Based on these conditions, optimal set-valued motions are explicitly constructed in a number of cases. Coauthors: Alberto Bressan and Vasile Staicu

Gioacchino Antonelli , University of Notre Dame, Connected sum of manifolds with spectral Ricci lower bounds, Monday, October 20, 2025, time 14:15, Aula Seminari - III Piano
Abstract:Abstract:
Let $n>2, \gamma>(n-1)/(n-2)$, and $\lambda$ a real number. Let $\mathrm{Ric}$ denote the lowest eigenvalue of the Ricci tensor. I will show that if $M$ and $N$ are two smooth n-dimensional manifolds that admit a complete Riemannian metric satisfying $-\gamma\Delta+\mathrm{Ric}>\lambda$, then their connected sum also admits a metric with the same property. The construction is geometrically similar to a Gromov-Lawson tunnel, and the range $\gamma>(n-1)/(n-2)$ is sharp for this result to hold. Join work with K. Xu.