Morning talks will be in the conference room Wean Hall 6120.
10:30 -- 11:30 John Baldwin, UIC. ``An outline of Zilber's programs''
I will discuss the analysis of the infinitary theory of complex numbers with exponentiation; role of Hrushovski construction and various theorems or conjectures in algebraic number theory including two conjectures of Zilber and of Schanuel. I will spend some time talking about the `analytic models' of Hrushovski construction.11:30 -- 12:30 John Baldwin, UIC. ``Using infinitary logic to understand Hrushovski's construction''
Brief introduction followed by an open-ended discussion.12:30 -- 1:30 LUNCH
Afternoon talks are in PPB 300.
1:30 -- 2:30 Alexei Kolesnikov, CMU. ``Morley's theorem for excellent classes''
The proof of Morley's theorem for excellent classes is remarkably close to a first order proof of this result. I will sketch an outline of the appropriate first order proof, and then build it up to the proof in excellent classes. This should make the parallels between some notions in the first order logic and in excellent classes more transparent. I will point out how the excellency is used in the proof. This will be discussed in more detail in the next talk.2:30 -- 3:30 Andres Villaveces, CMU. ``On key properties of excellent classes''
Some of the key results necessary to develop the theory of excellent classes are the theorems that allow to ``transfer up'' the positive properties (like existence or uniqueness). I will sketch a proof of such a theorem. This will complement the proof in the previous talk.3:30 -- 4:00 Discussion.