Lectures in 2021 Fall

We discuss the motion of a general compressible, viscous, and heat conducting fluid confined to a bounded cavity that is both mechanically and thermally open.

This talk aims at providing an introduction to some concepts from singularity theory, and in particular singularities of complex surfaces, and their relation to lowdimensional topology.

The aim of this lecture is to give an overview of the smooth four-dimensional Poincar´e conjecture.

In the first part of the talk we will provide a fairly complete proofs of the 2-squares Theorem (Fermat), the 4-squares theorem (Lagrange) and of the 3-squares theorem (Gauss/Legendre). In the second part, we will describe the shape of the set of such representations.

We survey some basic results in geometric graph theory and highlight some open problems whose solution may be within reach.

Recent developments in graph limits