Giacomo Ascione [pdf]
Titolo: Rollnik classes and Lieb-Thirring inequalities for pseudo-relativistic Schrodinger equations
Abstract: In this talk, we consider some extensions of the classical Rollnik class to the case of the pseudo-relativistic Schrodinger equation. The fractional Rollnik classes here introduced share a non-empty intersection with the Kato class and include Coulomb-type potentials with singularity up to the critical one of the Hardy potential. In particular, by means of the Birman-Swinger principle, we are able to show that pseudo-relativistic Schrodinger operators with fractional Rollnik potentials are still self-adjoint. In particular, during the talk, we will focus on a 0-exponent Lieb-Thirring inequality (i.e., a bound on the number of negative eigenvalues) and on the non-existence of negative or zero eigenvalues. This is a joint work with Atsuhide Ishida from Tokyo University of Science and Joszef Lorinczi from Renyi Institute of Mathematics.
Fausto Colantoni [pdf]
Titolo: Elastic Brownian motion with random jumps from the boundary
Abstract: We study an elastic Brownian motion on smooth domains, where the particle, instead of being killed at the boundary, restarts from a random position inside the domain. We characterize the process through its SDE and generator, and describe its invariant measure. Through time reversal, we explore connections with statistical mechanics and with Brownian motion under Poissonian resetting.
Simone Creo [pdf]
Titolo: On (fractional) inverse problems in irregular domains
Abstract: In this talk we consider parabolic inverse problems in irregular domains and in suitable smoother approximating structures. After proving well-posedness results, we prove that the solutions of the approximating problems converge in a suitable sense to the solution of the problem in the irregular
domain via Mosco convergence. We also present some applications. We then conclude by mentioning some recent results in the time-fractional case, i.e. we prove well-posedness results for inverse problems with Caputo-type fractional derivatives. These results are obtained in collaboration with M. R. Lancia, A. Mola, G. Mola and S. Romanelli.
Alessandra Meoli [pdf]
Titolo: Tempered stable time changes of bivariate Poisson counts with applications to shock models
Abstract:
Verdiana Mustaro [pdf]
Titolo: On some spatial transformations of multidimensional diffusion processes and related absorption problems
Abstract:
Luca Schiavone [pdf]
Titolo: Stochastic Hamiltonian Field Theories on globally hyperbolic spacetimes: a multisymplectic approach
Abstract: We develop a novel, fully geometric framework for first-order Hamiltonian field theories subject to stochastic influences.
Our construction combines the multisymplectic approach to classical field theories of F. Gay-Balmaz, J. C. Marrero, and N. Martínez [BMM2022], which employs a canonical affine bracket on a finite-dimensional phase space, with the formulation of stochastic Hamiltonian mechanics on manifolds due to J. A. Lazaro-Camì and J. P. Ortega [LCO2008]. By modeling the dynamics of a classical field as an evolution along stochastic worldlines on a globally hyperbolic spacetime, we derive a stochastic generalization of the de Donder-Weyl equations from a stochastic Heisenberg-like equation for currents. A stochastic version of Noether's Theorem for field theories is given, which provides a criterion to determine whether classical conservation laws are preserved in the presence of noise.
[BMM2022] F. Gay-Balmaz, J. C. Marrero, and N. Martínez. A new canonical affine bracket formulation of Hamiltonian Classical Field theories of first order. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 118: 1–60, 2024.
[LCO2008] J. A. Lazaro-Camì and J. P. Ortega. Stochastic Hamiltonian dynamical systems. Reports on Mathematical Physics, 61: 65–122, 2008.
Serena Spina [pdf]
Titolo: A generalized Ehrenfest model with catastrophes and the related Ornstein-Uhlenbeck process
Abstract:
to be apdated
Maria Chiara Bovier, Space-dependent Continuous Time Random Walk for Soil Moisture Modeling, [pdf]
Mirko D'Ovidio, On the non-local dynamic problems and non-Markov processes, [pdf]
Daniel Eduardo Cedeño Giron, Sampling Killed Anomalous Subdiffusions, [pdf]
Ruba Hussein Ismail Morsi, titolo, [pdf]
Francesco Virgili, On the infinitesimal behavior of semi-Markovian CTRWs, [pdf]
to be updated