Seminars, for informal dissemination of research results, exploratory work by research teams, outreach activities, etc., constitute the simplest form of meetings at a Mathematics research centre.
CAMGSD has recorded the calendar of its seminars for a long time, this page serving both as a means of public announcement of forthcoming activities but also as a historic record.
The Hopfield model stands as a paradigm at the intersection of statistical physics, theoretical neuroscience, and machine learning. Originally introduced as a biologically inspired model of associative memory, it has since evolved into a foundational framework for understanding a wide range of complex systems.
On the one hand, its roots in neuroscience enable a fruitful cross-fertilization: biologically grounded mechanisms continue to inspire algorithmic refinements and performance improvements in modern associative memory models. On the other hand, its formal connection with Boltzmann machines provides a bridge to contemporary machine learning techniques, including strategies such as dropout, pre-training, and the optimization of activation functions.
From the perspective of statistical mechanics, the Hopfield model remains a cornerstone for the analytical study of high-dimensional systems with disorder and frustration. This viewpoint naturally extends to the investigation of structured datasets, where the model offers a tractable yet expressive starting point for developing analytical insights.
In this talk, after a gentle introduction to the model, we will highlight some of these current research directions, while keeping the presentation accessible to a non-technical audience.
The Vaidya spacetime is a spherically symmetric solution of the Einstein equations with a null dust source. This can be used to model the gravitational collapse of a thick shell of radiation: a flat interior region is matched at an inner boundary to the null dust filled region, which is then matched at an outer boundary to Schwarzschild spacetime. A central singularity inevitably forms, and depending on the profile of the energy density of the null dust, this singularity can be globally naked. Motivated by the cosmic censorship hypothesis, we consider perturbations of this configuration. We review previous work, and describe recent work where the perturbation of the inner boundary — the past null cone of the central singularity — is analysed using a framework for studying perturbations of general hypersurfaces. This sets boundary conditions for perturbations at the past null cone, and we then consider the 3+1 evolutionary problem, focussing on the question of the stability of the Cauchy horizon of the naked singularity.
We will concentrate on the problem of characterising the minimal speed of monotone fronts in monostable scalar reaction diffusion (and advection) equations. The emphasis will be on variational principles and the puzzling situation of explicitly solvable equations. If time permits, I will also cover voting models and the connection to renormalisation group theory.
We will concentrate on the problem of characterising the minimal speed of monotone fronts in monostable scalar reaction diffusion (and advection) equations. The emphasis will be on variational principles and the puzzling situation of explicitly solvable equations. If time permits, I will also cover voting models and the connection to renormalisation group theory.
We will concentrate on the problem of characterising the minimal speed of monotone fronts in monostable scalar reaction diffusion (and advection) equations. The emphasis will be on variational principles and the puzzling situation of explicitly solvable equations. If time permits, I will also cover voting models and the connection to renormalisation group theory.
