14:00 Yibei Li (Imperial): A brief introduction to model theory
Model theory is a branch of mathematical logic where it applies logic to the studies of structures in pure mathematics such as groups, graphs, rings etc. With the help of model theory, we can obtain simpler proofs of some theorems, a notable one of which is the weak Nullstellensatz. In this talk, I will first go through some basic definitions in model theory and then show how it can be applied in different areas of mathematics.
15:00 Giovanni Placini (LMU München): Sasakian geometry and topology
Sasakian geometry is the odd dimensional analogue of Kähler geometry, namely a manifold is Sasakian if its Riemannian cone is Kähler. Certain features of Kähler geometry, such as the Hodge decomposition, survive mutatis mutandis in the Sasakian setting. Due to this closeness, many of the natural questions in Kähler geometry have interesting counterparts in the Sasakian world. On the other hand, the relation between the two geometries is not completely straight- forward, and there is an abundance of open questions in the field.
As in the Kähler case, Sasakian manifolds can be viewed as a coming together of several geometric structures; in this talk, I will give examples that highlight the difference between those structures, and explain certain fundamental con- structions of Sasakian manifolds. I will mention some Sasakian invariants and topological obstructions to the existence of Sasakian structures, and touch upon the relation between Sasaki and K ̈ahler groups.