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Viorel Barbu (Octav Meyer Institute of Mathematics of the Romanian Academy)26/10/2026, 09:00
For the initial data in the Wasserstein space $W_{2}$ and with finite Gibbs--Boltzmann entropy, the solution to the nonlinear Fokker-Planck equation is time absolutely continuous in the Wasserstein metric. Moreover, for initial data with exponential decay, the solution is convergent in $L^{1}(\mathbb R^{d})$ for $t$ convergent to $+\infty$ to a stationary solution of this equation.
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Giorgio Metafune (Università del Salento)26/10/2026, 09:45
We describe the spectrum of degenerate hypoelliptic Ornstein-Uhlenbeck operators in $L^p(\mathbb R^N)$ with respect to the Lebesgue measure. It turns out that the spectrum is the sum of the spectra of the diffusion term and of the drift term. Our result gives a complete picture of the spectral properties of Ornstein--Uhlenbeck operators in $L^p$ spaces.
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Gabriela Marinoschi (Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy)26/10/2026, 11:00
We present an inverse problem related to the dynamics of an age-structured population in which the evolution of individuals is also influenced by some random events. The model consists in a stochastic equation describing the time and age evolution of a population, governed by vital factors and influenced by a linear multiplicative noise perturbation, possibly related to emigration,...
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Mimmo Iannelli (Università di Trento)26/10/2026, 11:45
In 1926 Vito Volterra proposed his prey-predator model within his "Teoria Matematica della Lotta per la Vita" and gave an explanation to some biological oscillations observed in several natural contexts. Since then, several extensions of Volterra model have been considered, in the context of O.D.E. modeling, to explain the rich behavior of ecological prey-predator system. These *models have...
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Piermarco Cannarsa (Università degli Studi di Roma Tor Vergata)26/10/2026, 14:00
Degenerate evolution equations arise when the diffusion or propagation mechanism vanishes on part of the spatial domain. A natural inverse problem is then to determine the location and the strength of the degeneracy from suitable observations of the solution. In this talk I will discuss a class of inverse problems for strongly degenerate evolution equations, starting from one-dimensional...
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Catalin-George Lefter ("Al. I. Cuza" University and Octav Mayer Institute of Mathematics of the Romanian Academy)26/10/2026, 14:45
We consider systems of reaction-diffusion equations coupled in zero order terms, with general homogeneous boundary conditions, in domains with a particular geometry (annular type domains). We establish specific Carleman estimates with boundary observations relying on the possibility of choosing special auxiliary functions, due to the geometry of the domain. These observability estimates are...
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Iulian Cimpean (University of Bucharest and Romanian Academy)26/10/2026, 16:00
The superposition principle turns a solution of a (possibly nonlinear) Fokker–Planck equation into a probability measure on path space that solves the associated martingale problem. It does not, in general, produce a Markov process, and the strong Markov property for such path laws has remained open in general even in the linear case. In the first part of the talk we show how potential theory...
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Stefano Bonaccorsi (Università di Trento)26/10/2026, 16:45
This talk is based on an ongoing project with Z. Brzezniak, where we study a stochastic diffusion-transport problem on a finite star graph with a nonlinear dynamic condition at the junction and a reflecting obstacle acting on the junction variable. A natural physical interpretation is the evolution of a concentration in a network of thin channels connected to a small central reservoir. Along...
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Massimiliano Gubinelli (University of Oxford)27/10/2026, 09:00
[TBA]
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Enrico Priola (Università di Pavia)27/10/2026, 09:45
We study stochastic Burgers equation driven by a rough noise $(-\Delta)^{\gamma} \: \mathrm d W_t$, where $\Delta$ is the Laplacian in one dimension with Dirichlet boundary conditions, and $\gamma \in [0,1/4)$. We prove exponential estimates for the solution $X_t^x$, starting from $x \in L^2(0,1)$, by showing that there exists some constant $\lambda >0$ for...
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Benjamin Gess (Technische Universität Berlin and Max Planck Institute for Mathematics in the Sciences)27/10/2026, 11:00
We consider stochastic McKean–Vlasov equations whose deterministic dynamics can exhibit phase transitions and nonuniform equilibria. We establish that under suitable assumptions, sufficiently strong divergence-free transport noise makes the Dirac mass at the homogeneous density the unique invariant probability measure. The proof combines enhanced dissipation, local Eulerian stability through a...
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Davide Augusto Bignamini (Università degli Studi dell'Insubria)27/10/2026, 11:45
We study a stochastic reaction–diffusion equation on the whole real line, driven by space–time white noise, with a possibly nonlocal diffusion operator and a superquadratic potential. Unlike the case of bounded intervals, on the whole line the invariant measures cannot be described by an explicit density with respect to a Gaussian measure. We formulate the equation in suitable weighted spaces...
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Marco Fuhrman (Università degli Studi di Milano)27/10/2026, 14:00
We study optimal control problems for a class of dynamical systems of McKean–Vlasov type exhibiting mean-field effects, namely where the coefficients also depend on the joint distribution of the state and control. The controlled system is subject to regime switching driven by a hidden Markov chain, so that the problems under consideration are partially observed. The main contribution of this...
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Federica Masiero (Università degli Studi di Milano-Bicocca)27/10/2026, 14:45
We study a class of McKean-Vlasov SDEs in a Hilbert space $H$ and prove that the associated transition semigroup (which is defined on a Wasserstein space $\mathcal{P}_p(H)$ for some $p\ge 1$) possesses a smoothing property, i.e., it transforms continuous functions admitting the linear functional derivative $\frac{\delta}{\delta m}$ into functions admitting the measure derivative $D_m$. This...
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Fulvia Confortola (Politecnico di Milano)27/10/2026, 16:00
We deal with stochastic optimal control problems for integral stochastic Volterra equations in a finite-dimensional setting. The noise term is driven by a pure jump Lévy process and the control acts on the intensity of the jumps. We use the machinery of Laplace transform to lift the original control problem in a suitable infinite dimensional space large enough to contain all the information...
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Carlo Orrieri (Università di Pavia)27/10/2026, 16:45
In the talk we address pathwise uniqueness for stochastic PDEs with drift in differential form. The result is firstly presented in the general framework of stochastic evolution equations on separable Hilbert spaces and subsequently applied to several classes of examples. The talk is based on a joint work with D. Addona, D. Bignamini and L. Scarpa.
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Arnaud Debussche (École Normale Supérieure de Rennes)28/10/2026, 09:45
We study randomly advected incompressible Navier-Stokes equations, where the advecting field is a mean-zero, divergence-free, space-time stationary velocity field with smooth order-one correlations. We introduce a two-parameter family of models in which the advection is accelerated on a fast temporal scale $\epsilon^2$ and has spatial correlation length $\delta$; the critical regime...
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Margherita Zanella (Politecnico di Milano)28/10/2026, 11:00
We investigate the long time behavior of a stochastic Allen-Cahn-Navier-Stokes system modeling the dynamics of binary mixtures of immiscible fluids. The model features the thermodynamically relevant Flory-Huggins logarithmic potential and incorporates two stochastic forcing terms: one driving the velocity field in the Navier-Stokes equation and the other acting on the phase variable in the...
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Luca Scarpa (Politecnico di Milano)28/10/2026, 11:45
We establish strong Feller property and irreducibility for the transition semigroup associated to a class of nonlinear stochastic partial differential equations with multiplicative degenerate noise. As a byproduct, we prove uniqueness of the invariant measure under very mild assumptions. The drift of the equation diverges exactly where the noise coefficient vanishes, resulting in a competition...
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