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.
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.
Given any open, bounded set $\Omega$, we consider suitable combinations, via a reference function $\Phi$, of the first $p$-eigenvalue of the Dirichlet Laplacian of partitions of $\Omega$. We give two different formulations of the problem, one geometrical and one functional. We prove relations among the two formulations, existence and regularity of optimal partitions, convergence, and stability with respect to $p$ and to $\Phi$. Based on a joint work with G. Stefani (Padova).
Existing machine learning frameworks operate over the field of real numbers ($\mathbb{R}$) and learn representations in real (Euclidean or Hilbert) vector spaces (e.g., $\mathbb{R}^d$). Their underlying geometric properties align well with intuitive concepts such as linear separability, minimum enclosing balls, and subspace projection; and basic calculus provides a toolbox for learning through gradient-based optimization.
But is this the only possible choice? In this seminar, we study the suitability of a radically different field as an alternative to $\mathbb{R}$ — the ultrametric and non-archimedean space of $p$-adic numbers, $\mathbb{Q}_p$. The hierarchical structure of the $p$-adics and their interpretation as infinite strings make them an appealing tool for code theory and hierarchical representation learning. Our exploratory theoretical work establishes the building blocks for classification, regression, and representation learning with the $p$-adics, providing learning models and algorithms. We illustrate how simple Quillian semantic networks can be represented as a compact $p$-adic linear network, a construction which is not possible with the field of reals. We finish by discussing open problems and opportunities for future research enabled by this new framework.
Recent results on black hole interiors suggest a failure of strong cosmic censorship for charged black holes in the presence of a positive cosmological constant. In this talk we show that, in the context of the Einstein-Maxwell-real scalar field system, such violations are non-generic in a larger moduli space of non-smooth (spherically symmetric) initial data.
