Geometry and Model Theory Seminar at the Fields Institute
The idea of the seminar is to bring together people from the group
in geometry and singularities at the University of Toronto (including
Ed Bierstone, Askold Khovanskii, Grisha Mihalkin and Pierre Milman)
and the model theory group at McMaster University (Bradd Hart, Deirdre
Haskell, Patrick Speissegger and Matt Valeriote).
As we discovered during the programs in Algebraic
Model Theory Program and the Singularity
Theory and Geometry Program at the Fields Institute in 1996-97,
geometers and model theorists have many common interests. The goal
of this seminar is to further explore interactions between the areas.
Seminars will take place in the Fields Institute, Room 230 from
2- 4 p.m.
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to be informed of upcoming semainrs.
| Jan. 18, 2007
Wieslaw Pawlucki, Uniwersytet Jagiellonski, Poland
Lipschitz cell decomposition in o-minimal structures
|Oct. 19, 2006
Tom Tucker, University of Rochester
Points of height zero on varieties over function fields
It follows from Northcott's theorem that if f:P^n lra
P^n is a map on projective space over a number field, then
the canonical height h_f associated to f has the property
that h_f(x) = 0 if and only if x is a preperiodic point of
f. This has not yet been proven for nonisotrivial f over function
fields, though M. Baker has proven it for n = 1. We will suggest
a proof that works more generally, using Hilbert schemes.
It appears that the missing ingredient in our proof may be
a bit of model theory, specifically the trichotomy theorem.
Gareth Owen Jones, McMaster University
The zero set property in certain o-minimal structures
I will show that in certain o-minimal expansions of the
reals, every definable closed set is the zero set of a smooth
(that is, infinitely differentiable) definable function. This
is joint work with Alex Wilkie.
|Sept. 21, 2006
Alexandre Rambaud, Université de Paris 7
Desingularization in certain quasi-analytic classes of
real functions via model-theory
Let E be a set of real functions; what are the model-theoretic
and geometric properties of the complete theory of the real
field in the language of E? What is the local structure of
the definable sets? I will prove (or give an idea of the proof
of) the quantifier elimination when E is a quasi-analytic
class of restricted real functions, closed under natural operations.
To obtain this result, I study the singularities of the definable
curves and generalize, using non-standard methods, certain
Guillaume Valette, University of Toronto
Hardt's Theorem: a bi-Lipschitz version
We will focus on real semi-algebraic sets and more generally
on o-minimal structures. A famous theorem, due to Hardt, states
that every semi-algebraic family may be trivialized generaically
in such a way that the obtained trivialization is a semi-algebraic
homeomorphism. We will explain that it is possible to get
a bi-Lipschitz semi-algberaic trivialization and give some
consequences about the metric properties of semi-algebraic
Past Seminars 2005-06
Past Seminars 2003-04
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