THEMATIC PROGRAMS

Thematic Program on o-minimal Structures and Real Analytic Geometry January-June 2009 January 12 - 16, 2009 Winter School in o-minimal Geometry Organized by: Matthias Aschenbrenner	Supported by

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OVERVIEW

The structure of this workshop, modeled on the very successful annual Arizona Winter School in Number Theory (http://swc.math.arizona.edu/), is the following: between three and five leading researchers give intensive tutorials (roughly five lectures per speaker) on the focus areas discussed during the semester, including posing problems. In small groups, graduate students work on these problems during the workshop. The meeting culminates with presentations by the students on their solutions. In order to give students the possibility to prepare adequately, the lecturers are asked to provide, a few weeks ahead of the workshop, a preliminary version of their lecture notes, or at least a list of suitable references and statements of the problems to be discussed. The final version of the lectures notes will be published later as part of the proceedings of the program.

This format provides an intensive introduction to the topics and open problems related to the proposed program, and is designed to ensure significant interaction among all participants, especially between the students and the senior lecturers. The topics to be covered were selected to prepare the participants for the semester- long graduate courses, to commence after the introductory workshop. Our current plan is to have lectures in the following areas:

1. Model Theory (Deirdre Haskell)
2. o-minimality (Sergei Starchenko)
3. Real Analytic Geometry (K. Kurdyka) Manuscripta Mathematica
4. Planar Real Analytic Vector Fields (S. Yakovenko) - lectures are the relevant sections from the book Ilyashenko & Yakovenko, Lectures on analytic differential equations, AMS, 2007, Grad. Studies in Math vol. 86.

Winter School schedule:

Monday, January 12
8:45- 9:00	Welcome & Introduction -- Juris Steprans and Matthias Aschenbrenner
9:00-10:00	Introduction to Model Theory -- Deirdre Haskell
10:00-11:00	Introduction to Real Analytic Geometry -- K. Kurdyka
11:00-11:30	Coffee
11:30-12:30	Introduction to Model Theory -- Deirdre Haskell
12:30-2:00	Lunch
2:00-3:00	Analytic Vector Fields: Singularities and Limit Cycles-- S. Yakovenko
3:00-3:30	Tea break
3:30-4:30	Introduction to o-minimality-- Sergei Starchenko
4:30-5:30	Reception
Tuesday, January 13
9:00-10:00	Introduction to Model Theory -- Deirdre Haskell
10:00-11:00	Introduction to o-minimality-- Sergei Starchenko
11:00-11:30	Coffee
11:30-12:30	Introduction to Real Analytic Geometry -- K. Kurdyka
12:30-2:00	Lunch
2:00-3:00	Analytic Vector Fields: Singularities and Limit Cycles-- S. Yakovenko
3:00-3:30	Tea break
3:30-4:30	Introduction to o-minimality-- Sergei Starchenko
4:30-5:30	Analytic Vector Fields: Singularities and Limit Cycles-- S. Yakovenko
Wednesday, January 14
9:00-10:00	Real Analytic Geometry -- K. Kurdyka
10:00-11:00	Introduction to o-minimality-- Sergei Starchenko
11:00-11:30	Coffee
11:30-12:30	Introduction to Model Theory -- Deirdre Haskell
12:30-2:00	: Lunch
2:00-3:00	Analytic Vector Fields: Singularities and Limit Cycles -- S. Yakovenko
3:00-3:30	Tea break
3:30-4:30	Real Analytic Geometry -- K. Kurdyka
Thursday, January 15
9:00-10:00	Real Analytic Geometry -- K. Kurdyka
10:00-11:00	Introduction to o-minimality-- Sergei Starchenko
11:00-11:30	Coffee
11:30-12:30	Introduction to Model Theory -- Deirdre Haskell
	Afternoon: free time for students to work on projects
Friday, January 16:
9:00-10:00	Analytic Vector Fields: Singularities and Limit Cycles -- S. Yakovenko
10:00-11:00	Haskell students
11:00-11:30	Coffee
11:30-12:30	Starchenko students
12:30-2:00	Lunch
2:00-3:00	Yakovenko students
3:00-3:30	Tea break
3:30-4:30	Kurdyka students

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