Analytic Functions on Non-Archimedian Fields (Matthias Hippold)
Using non-archimedian norms on the field of rational numbers Q and applying the same techniques that were used for constructing the field of complex numbers C, we can construct new complete, algebraically closed fields. The obvious notion of analytic functions on them gives no beautiful theory as there are too many of them. We will fix this issue by introducing the Berkovich affine line as the correct topological space for defining analytic functions on and see how this constitutes a theory that reflects most of the beautiful properties of holomorphic functions on C, such as Liouville’s theorem.

Forcing: becoming Prometheus (George Peterzil)
This talk will be a gentle and informal introduction to forcing, a mathematical technique developed by Paul Cohen in order to show that it is consistent with the axioms of set theory that the continuum hypothesis fails (and separately, that the axiom of choice fails, though we will not discuss this).
Among other things, we will explain what we mean by consistency, with ideas dating back to questions regarding Euclid’s fifth postulate, going through Gödel and reaching a peak with Forcing. We will discuss the differences and similarities between the previous three, and go over some of the basic ideas required in order to become Prometheus; that is, to introduce a model of set theory to reals from outside its universe in order to enlarge the size of the continuum.
A knowledge in the first logic course will be helpful for intuition, but is not required.