Matematica | Presentazione del Corso | Seminari e Convegni
Matematica Presentazione del Corso | Seminari e Convegni
Il giorno 15 Giugno 2023, presso l'AULA P1 del Dipartimento di Matematica, Università di Salerno, si terrà la Giornata INdAM 2023, organizzata dall'INdAM in collaborazione con il DipMat.
È possibile partecipare online usando il seguente link.
- 10:00-10:30 Apertura
- 10:30-11:30 Francois MURAT (Sorbonne Université, Paris) Unexpected results for a singular elliptic problem
- 11:30-12:00 Coffe Break
- 12:00-13:00 Paola ANTONIETTI (Politecnico di Milano) Mathematical and numerical modeling of neurodegenerative diseases
- 13:00-14:30 Pausa Pranzo a Buffet
- 14:30-15:30 Rita PARDINI (Università di Pisa) Exploring the boundary of the moduli space of stable surfaces: some explicit examples
- 15:30-16:00 Coffe Break
- 16:00-17:00 Ansgar JÜNGEL (Technische Universität, Wien) Multispecies diffusion systems towards neuromorphic computing
Francois Murat (Sorbonne Université, Paris) Unexpected results for a singular elliptic problem
Abstract: In this lecture, I will present recent results obtained in collaboration with Daniela Giachetti (Rome), Pedro J. Martinez Aparicio (Almeria), and Francesco Petitta (Rome), for the one-dimensional singular boundary value problem
- d/dx (a du/dx) = - dφ(u)/dx - dg/dx in (0, L), u(0) = u(L) = 0,
where the model for the singular function φ is φ(s) = 1/|s|^γ with γ > 0. This singular problem presents a number of unexpected phenomena: nonexistence of solutions under certain assumptions, existence of an infinite number of solutions under other assumptions, and non-continuity of the solution with respect to the data.
Paola Antonietti (Politecnico di Milano) Mathematical and numerical modeling of neurodegenerative diseases
Abstract: Neurodegenerative diseases (NDs) are complex disorders that primarily affect the neurons in the brain and nervous system, leading to progressive deterioration and loss of function over time. A common pathological hallmark among different NDs is the accumulation of disease– specific misfolded aggregated prionic proteins in different areas of the brain (Aβ and tau in Alzheimer’s disease, α–synuclein in Parkinson’s disease). In this talk, we discuss the numerical modeling of the misfolding process of α–synuclein in Parkinson’s disease. To characterize the progression of misfolded proteins across the brain, we consider a suitable mathematical model (based on Fisher–Kolmogorov equations). For its numerical discretization, we propose and analyze a high- order discontinuous Galerkin method on polyhedral grids (PolyDG) for space discretization coupled with a Crank-Nicolson scheme to advance in time. Numerical simulations in patient-specific brain geometries reconstructed from magnetic resonance images are presented. In the second part of the talk, we introduce and analyze a discontinuous Galerkin method for the semidiscrete numerical approximation of the equations of Multiple-Network Poroelastic Theory (MPET) in the dynamic formulation. The MPET model can comprehensively describe functional changes in the brain considering multiple scales of fluids and can be regarded as a preliminary attempt to model the perfusion in the brain. In this context, the cerebrospinal fluid transport plays an important role as a mechanism for waste removal (clearance) from the central nervous system, particularly important in Alzheimer’s disease. We present and analyze the numerical approach and we present simulations in three dimensional patient-specific geometries.
Rita Pardini (Università di Pisa) Exploring the boundary of the moduli space of stable surfaces: some explicit examples
Abstract: I will briefly recall the notion of stable surfaces and ofthe corresponding moduli space. Then I will outline a partial description of the boundary points in the case of surfaces with K^2=1, p_g=2 (joint work with Stephen Coughlan, Marco Franciosi, Julie Rana and Soenke Rollenske, in various combinations) and in the case of Campedelli and Burniat surfaces (joint workwith Valery Alexeev).
Ansgar Jüngel (Technische Universität, Wien) Multispecies diffusion systems towards neuromorphic computing
Abstract: Neuromorphic computing aims to develop biology-influenced algorithms and computer devices whose design is inspired by the neurons of the brain. In this talk, we present some diffusion models describing phenomena from cell biology, which may lead to the emergence of biological or artificial networks and help the understanding of neuromorphic applications. This includes the transport through ion channels, axon growth, and semiconductor memristors. A common feature of the models is that they describe multiple species with nonlinear (cross-) diffusion equations, whose mathematical analysis is challenging. We report some results on the existence of solutions, highlight the key ideas of the analysis, and present some numerical simulations.