[Turkmath:8835] ISTB-8 (Istanbul Number Theory Meetings-8): March 16th, Saturday

[KAZIM Büyükboduk]

Dear Colleagues,

The 8th of the monthly Istanbul Number Theory Meetings will take place on
March 16th at Galatasaray University. The talks will start at 10:00; please
see below for the detailed schedule. We will once again have a day-long
talks by two speakers:

Ayhan Gunaydin (MSGSÜ) and Sonat Suer (Bilgi University).

We thank our speakers for agreeing to talk at our meeting and Galatasaray
University for hosting us.

Below you may find the information regarding the schedule, location of
the talks and their titles and abstracts. It would be a great pleasure to
meet many of the interested colleagues tomorrow!

Best Regards,

Kazim Buyukboduk


Istanbul Number Theory Meetings - 8
Location: Galatasaray University, Room P22
Date: March 16th, Saturday

Morning Talk (10:00-12:00):

Speaker: Sonat Suer
Title: A Fast Introduction to O-minimality
Abstract: An ordered first order structure M is called order minimal, or
o-minimal for short, if every definable subset of M can be defined using
the order alone. Any real closed field is o-minimal by a theorem of Tarski.
A more recent example is the real field together with restricted analytic
functions and the full exponential function. In any o-minimal structure M
one can decompose definable subsets of M^n into well behaved definable
subsets called cells, and using this, one can define notions of dimension
and Euler characteristics. In this respect, o-minimality is an axiomatic
approach to Grothendieck's hoped-for notion of tame topology.

In the first part of the talk, we will sketch the proof of the cell
decomposition theorem. The second part will be about uniformaization
theorems in o-minimal structures, setting the stage for the following talk
by Ayhan Günaydın.


Afternoon talk (13:30-15:30):

Speaker: Ayhan Günaydın
Title: Implementations of Pila-Wilkie counting theorem on number theoretic
problems
Abstract: Assuming the knowledge of the statement of Pila-Wilkie Theorem on
counting rational points of sets definable in o-minimal structures, we
present proofs of certain number theoretic problems of Diophantine nature.
The main example is a (re)-proof of the Manin-Mumford conjecture by Pila
and Zannier.  After presenting this proof, we shall focus on more general
problems of André-Oort type. (This isan expository talk, and none of the
results are due to the speaker.)
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