"An Introduction to Model Theory : The Compactness Theorem" by Jorge Carrasco and Daniel Ibaibarriaga. 

Abstract

After introducing the basic definitions of first order logic : languages, formulas, theories and structures, we will present a proof of the compactness theorem (Gödel,1931) via ultraproducts (Lós,1955). We will explain the origin of its name and give some surprising applications in different mathematical disciplines, making an strong emphasis on examples. 

"An Informal Introduction to Operads" by Roger Garrido.

Abstract 

The notion of an operad will be introduced via a series of examples. If there is time, some instances of A-infinity operads will be sketched. 

"An Introduction to Random Graphs" by Jofre Costa 

Abstract 

The talk will consist of an introduction to the concept of random graphs and their construction, as well as some examples and motivation behind them. It will also contain an introduction to the probabilistic method, showcasing its power, and some examples of the zero-one law of random graphs. 

"Introduction to Infinity-Categories" by Juan Martín 

Abstract

This talk will introduce the language of simplicial sets and provide motivation on how these objects provide a framework to talk of higher homotopies (and structures). Connections with classical algebraic topology will be stressed at all times. 

"Free Actions of Finite Groups on Spheres" by Pedro Mayorga

Abstract

In the talk we will discuss several restrictions to decide whether there exists a free action of a given group on a sphere.