Sandra Müller Determinacy Axioms
Abstract: Set theory can be understood as the search for the right axioms in mathematics, i.e., axioms that answer the questions left open by the standard axioms for set theory introduced by Zermelo and Fraenkel with the Axiom of Choice (ZFC). Canonical candidates for these axioms are large cardinals, determinacy axioms, and forcing axioms. We will focus on the second one, determinacy axioms, and say a bit about connections between large cardinals and determinacy.
Jonathan Schilhan Definability of combinatorial sets of reals
Abstract: The existence of many interesting sets of reals, familiar from other areas of mathematics, such as Hamel bases, Vitali sets or ultrafilters is guaranteed by the Axiom of Choice. But this doesn't give us any concrete description of these objects and it makes sense to ask how simple a definition of such sets can be. We will overview some of the classical and more recent results in this area and the methods used to obtain them.
Diego Mejia Coherent systems of finite support iterations
Abstract: We present some advances of the forcing technique of finite support iterations and its applications in combinatorics of the reals, more precisely, on constellations of classical cardinal characteristics of the continuum. We focus on techniques to construct "multidimensional" arrays of forcing generic extensions.
Monroe Eskew The tree property
Abstract: The tree property for a cardinal kappa asserts that for every tree of height kappa with levels of size <kappa, there is a cofinal branch. We will focus on this property for successor kappa and discuss the relationship with weak square, the approximation property, and saturated ideals.
Thilo Weinert Partition Relations - an Overview
Abstract: The ordinary symmetric and asymmetric partition relations are going to be defined, an overview over various results in the theory of partition relations proved during the last decades will be given and connections to other areas of set theory will be pointed out. Towards the end some open problems are going to be mentioned.