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.
In this talk, I will discuss our recent result. Either there is a counterexample to black hole uniqueness, or the following statement holds. Axisymmetric, complete, simply connected, maximal initial data sets for the Einstein equations of nonnegative energy density with ends that are either asymptotically flat or asymptotically cylindrical, admit an ADM mass lower bound given by the square root of total angular momentum. Moreover, equality is achieved only for a constant time slice of an extreme Kerr spacetime. The proof is based on a novel flow of singular harmonic maps with hyperbolic plane target, under which the renormalized harmonic energy is monotonically nonincreasing. Relevant properties of the flow are achieved through a refined asymptotic analysis of solutions to the linearized harmonic map equations.
The Malmquist-Takenaka (MT) system is a complete orthonormal system in $H^2(T)$ generated by an arbitrary sequence of points in the unit disk that do not approach the boundary very fast. The nth point of the sequence is responsible for multiplying the nth and subsequent terms of the system by a Möbius transform taking the point to 0. One can recover the classical trigonometric system, its perturbations or conformal transformations, as particular examples of the MT system. However, for many interesting choices of the generating sequence, the MT system is less understood. We prove almost everywhere convergence of the MT series for three different classes of generating sequences.
By Alexander's theorem, every link in the 3-sphere can be represented as the closure of a braid. Lorenz links and twisted torus links are two families that have been extensively studied and are well-described in terms of braids. In this talk, we will present a natural generalization of Lorenz links and twisted torus links that produces all links in the 3-sphere. This provides a simpler braid description for all links in the 3-sphere.
