This talk explores neuromorphic computing, an emerging field at the intersection of computational neuroscience and hardware design, focusing on the potential of using stochastic relaxation in recurrent spiking neural networks to efficiently solve combinatorial optimization problems on state-of-the-art neuromorphic chips. We explore the connection between spiking neural networks and the Ising Model, detailing how optimization problems can be mapped to the energy landscape's ground states and how annealing can be used for stochastic relaxation. Integrating these components introduces challenges, particularly the misalignment of neuronal dynamics and ineffective noise generation. We propose to address them by resorting to chaotic networks and a more bio-plausible neural sampling approach.

To a forward-backward stochastic differential equation is naturally associated a quasilinear partial differential equation. In the spirit of the work of Gaeta, we develop a theory of symmetries for FBSDE's. These symmetries turn out to be related to the symmetries (in Olver's sense) of the corresponding quasilinear PDE. An analogous theory is developed for BSDE's.

This is joint work with Dr. Anas Ouknine (Rouen).

We use the framework of Quantitative Hydrodynamics to derive a CLT around its hydrodynamic limit for an interacting particle system inspired by integrate-and-fire neuron models. The hydrodynamic limit of this model was originally derived by Chariker, De Masi, Lebowitz and Presutti, and as an important intermediate step we show that this convergence holds at optimal $L^2$-speed. Joint with Milton Jara and Yangrui Xiang.

This talk investigates the mathematical structure of path measures, both from a measure-theoretical perspective and through stochastic differential equations. The realization of path measures as Langevin systems hinges on the pivotal role of second-order Hamilton-Jacobi-Bellman equations, which form the foundation of stochastic geometric mechanics and applications in stochastic thermodynamics. We explore the emergence of the Onsager-Machlup functional in large deviation theory, the rates of entropy production in irreversible thermodynamic processes, and entropy minimization problems encoded in stochastic geometric mechanics.

In this talk, we present a generalised second-order Boltzmann-Gibbs principle for conservative interacting particle systems on a lattice whose stationary measures are not of product type and not invariant under particle jumps. The result, which requires neither a spectral gap bound nor an equivalence of ensembles, extends the classical framework to settings with correlated invariant measures and is based on quantitative bounds for the correlation decay. As an application, we show that the equilibrium density fluctuations of the Katz-Lebowitz-Spohn model, for a suitable choice of parameters, converge under diffusive scaling to the stationary energy solution of the stochastic Burgers equation. Based on joint work with P. Gonçalves and G. M. Schütz.