Title: Sealing Kurepa trees.
Abstract: In this talk, I'm going to describe Itamar Giron's master thesis. Most of the results in this talk are due to him. 
The main question of the thesis was whether there is a forcing notion that makes an arbitrary Kurepa tree into a non-distributive one, and how far can one go in this direction (can we get sealed Kurepa trees?).
We will start with the classical construction of a Kurepa tree in L (by Solovay). We will show that this tree is distributive in L. We will review the known constructions due to Poor and Shelah (generalized by Muller and me), of sealed Kurepa trees in L (can be generalized to canonical inner models).  
Then, we will also find a forcing extension in which for every Kurepa tree, one can add a branch without collapsing cardinals.  This means that even though it is easy to find non-distributive Kurepa trees, it is far less trivial to get from combinatorial assertions (such as diamond*), a sealed Kurepa tree. 
Finally, I will talk about the forcing notion that "specializes" a Kurepa tree over an arbitrary model of ZFC. This is Giron's main result, which requires the most sophisticated tools.