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 a classical game two players, Alice and Bob, take turns to play $n$ moves each. Alice starts. For each move each player has two options, 1 and 2. The outcome is determined by the exact sequences of moves played by each player. Prior to the game, a winner is assigned to each of the $2^{2n}$ possible outcomes in an i.i.d. fashion, where $p$ is the probability that Bob is the winner for a given outcome. Then it is known that there exists a value $p_c\in (0,1)$ such that the probability that Bob has a winning strategy for large $n$ tends to one if $p>p_c$ and to zero if $p< p_c$. We study a modification of this game for which the outcome is determined by the exact sequence of moves played by Alice as before, but in the case of Bob all that matters is how often he has played move 1. We show that also in this case, there exists a sharp threshold $p'_c$ that determines which player has with large probability a winning strategy in the limit as $n$ tends to infinity. Joint work with Anja Sturm (Göttingen) and Natalia Cardona-Tobón (Bogotá).
I will first introduce the bigraded cohomology for real algebraic varieties developed by Johannes Huisman and Dewi Gleuher. This is a cohomology theory that refines the equivariant cohomology "à la Kahn-Krasnov" of the complex points of a real variety, the latter often being preferred (by the algebraic geometers) in the cohomological study of real algebraic varieties. Since the construction of this bigraded cohomology and its associated characteristic classes relies on the sheaf exponential morphism, I will explain how to produce an arithmetic (or algebraic) variant of these cohomology groups, whose main advantage is toeliminate topological or transcendental conditions. I will conclude by comparing these two versions of bigraded cohomology.
