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.
The subject of counting curves on 3-folds is extremely rich. Modern tools allow us to define several sophisticated invariants that we think of as "curve counts", such as Gromov-Witten, Donaldson-Thomas, Pandharipande-Thomas and Gopakumar-Vafa invariants. They are proven or expected to be equivalent to each other, in a precise sense. In this talk, I will give an idea of how these invariants are defined and what is known about them, focusing on these correspondences and rationality properties. Along the way, I'll explain a result of myself with Ivan Karpov concerning the rationality of PT generating series on Fano 3-folds; other than that, the talk will be mostly expository.
I will discuss a localized Big Bang formation result, for the Einstein-nonlinear scalar field equations, without symmetry assumptions and that does not require the initial data to be close to any fixed background solution. The key new ingredient for the proof is the introduction of a new gauge for Einstein's equations. This gauge has two advantages over the one used in previous localized Big Bang stability results. First, it is independent of the matter model, so it is possible that it can be used to prove Big Bang formation in the absence of a scalar field. And second, it is suitable to prove that the solutions induce geometric initial data on the singularity, thus providing a complete description of the asymptotics near the Big Bang.
