Seminários, para a disseminação informal de resultados de investigação, trabalho exploratório de equipas de investigação, actividades de difusão, etc., constituem a forma mais simples de encontros num centro de investigação de matemática.
O CAMGSD regista e publica o calendário dos seus seminários há bastante tempo, servindo páginas como esta não só como um método de anúncio dessas actividades mas também como um registo histórico.
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.
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).
