Abstracts:

 

Godel's incompleteness using number extensions (David Zisselman)

In this talk I'll present "number extensions'' , a new technique of proof. I will explore a new proof of both Godel's incompleteness theorems using this technique. This talk will not assume much prior knowledge in logic or set theory and I'll try to give illustrations about the proof. As a side note I shall remark that the technique is also useful for dealing with other questions in computability. But I won't be able to talk about such applications in this talk.

 

Roman Gonin
Perverse sheaves provide an important tool in representation theory. Due to the Riemann-Hilbert correspondence, their category is isomorphic to the category of D-modules; in many examples, their sections have natural actions of interesting algebras. Lusztig introduced perverse character sheaves which match with representations of G(F_q). The category of perverse sheaves is determined by the perverse t-structure. The exactness of a functor with respect to the t-structure plays an important role in this area. There is a conjecture of R. Bezrukavnikov and A. Yom Din regarding such exactness of a transform of basic importance in this field: the composition of the Harish-Chandra transform and the Radon transform. This conjecture is already established for character sheaves;  I am working on the generalization of this for all sheaves.