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.
Trisections give a diagrammatic description of smooth 4-manifolds, similar to Heegaard splittings in dimension three. In this talk, I will describe new 4-manifold invariants defined from trisection diagrams using categorical data. The input consists of three spherical fusion categories, a semisimple bimodule category with a bimodule trace, and a pivotal functor into the category of bimodule endofunctors.
The construction works by labelling the trisection diagrams with the categorical data and evaluating them using a diagrammatic calculus for bimodule categories. The details of this procedure ensures that the result is invariant under moves on trisections yielding the same 4-manifold. This construction generalises existing Hopf algebraic trisection invariants due to Chaidez-Cotler-Cui and recovers the Crane-Yetter and Bärenz-Barrett invariants as special cases. I will outline the main ideas of the construction and briefly discuss examples and connections to TQFTs.
Based on the work 2511.19384 with Catherine Meusburger (FAU) and Fiona Torzewska (Bristol).
In this talk I will discuss some results obtained in collaboration with Filipe C. Mena and former PhD student Vítor Bessa on the global dynamics of a minimally coupled scalar field interacting with a perfect-fluid through a friction-like term in spatially flat homogeneous and isotropic spacetimes. In particular, it is shown that the late time dynamics contain a rich variety of possible asymptotic states which in some cases are described by partially hyperbolic lines of equilibria, bands of periodic orbits or generalised Liénard systems.
On a background Minkowski spacetime, the Euler equations (both relativistic and not) are known to admit unstable homogeneous solutions with finite-time shock formation. Such shock formation can be suppressed on cosmological spacetimes whose spatial slices expand at an accelerated rate. However, situations with decelerated expansion, which are relevant in our early universe, are not as well understood. I will present some recent joint work in this direction, based on collaborations with David Fajman, Maciej Maliborski, Todd Oliynyk and Max Ofner.
