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.
This presentation explores Mean Field Games (MFGs) through the lens of functional analysis, focusing on the role of monotonicity methods in understanding their properties. We begin by introducing MFGs as models of large populations of interacting rational agents and illustrate their derivation for deterministic problems. We then examine key questions regarding the existence and uniqueness of MFG solutions. Specifically, we present several new existence theorems obtained via $p$-Laplacian regularization. Finally, we discuss weak-strong uniqueness and establish conditions under which weak and strong solutions of MFGs coincide.
A well-known folklore theorem classifies 2-dimensional topological quantum field theories (TQFTs) in terms of Frobenius algebras, providing a unifying link between topology, algebra, and physics. In this talk, we explore what happens when the usual cobordism category is replaced by a category of nested cobordisms, in which 2-dimensional surfaces are equipped with embedded 1-dimensional submanifolds. We study symmetric monoidal functors out of this category and the resulting algebraic structures they encode. This talk is based on joint work with R. Hoekzema, L. Murray, N. Pacheco-Tallaj, C. Rovi, and S. Sridhar.
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.
