
THE
FIELDS INSTITUTE FOR RESEARCH IN MATHEMATICAL SCIENCES
20th
ANNIVERSARY
YEAR 
Geometry
and Model Theory Seminar 201213
at the Fields Institute
Organizers: Ed Bierstone, Patrick Speissegger


Overview
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 199697,
geometers and model theorists have many common interests. The goal
of this seminar is to further explore interactions between the areas.
It served as the main seminar for the program on Ominimal
structures and real analytic geometry, which focussed on such
interactions arising around Hilbert's 16th problem.
The seminar meets once a month at the Fields Institute, Room 230,
on a Thursday announced below, for one talk 23pm and a second talk
3:304:30pm. Please subscribe to the Fields mail list to be informed
of upcoming seminars.
Past
Seminars 
Wed., Sept. 25, 2013
2:00 p.m.
Room 230

Jacob Tsimerman, Harvard University 
Thurs., May 16, 2013
11:00 a.m.
Room 210

Vincent Grandjean, Universidade Federal do Ceara (Fortaleza,
Brazil)
Lipschitz contact equivalence classes of analytic functions
do not have moduli
To make a long story short, the (smooth) contact equivalence
of two mappings was introduced (1960's) by J. Mather in
his tremendous work about the stability of smooth mappings.
For two germs of analytic functions it just means that the
ideals generated by each of the functions are the same.
Later, some notions appeared of topological (resp. biLipschitz)
contact equivalence refining (resp. coarsening) various
classifications of smooth mappings with singularities. Recently
BirbrairCostaFernandesRuas found a very simple equivalent
definition of biLipschitz contact equivalence between germs
of Lipschitz functions. The subsequent work by RuasValette
shows that a similar simple equivalent definition exists
for the biLipschitz contact equivalence for germs of Lipschitz
mappings. They also prove that germs of polynomial mappings
of given bounded degree admit only finitely many biLipschitz
contact equivalence classes.
The result I will present concerns only germs of plane
continuous subanalytic functions. We show that they can
be associated with a finite combinatorial object, called
a Hölder diagram, as a consequence of the BierstoneMilmanParusinski
rectilinearization theorem. The main result is that this
object completely classifies germs of plane Lipschitz subanalytic
functions under the subanalytic biLipschitz contact equivalence,
which implies that there are only countably many such classes.
I will try to present, in the slightly simpler case of germs
of real analytic functions, the main ideas to understand
the combinatorial object (Hölder Diagram) encoding
the germ.
This is joint work with L. Birbrair (UFC), A. Fernandes
(UFC) and A. Gabrielov (Purdue)

Wed., March 6, 2013
2:00 p.m.
Room 230 
Rahim Moosa, University of Waterloo
Algebraic reductions of hyperkaehler manifolds; model theory
In a 2010 paper, Campana, Oguiso, and Peternell make some
observations about the structure of the algebraic reduction
map on a nonalgebraic hyperkaehler compact complex manifold.
Anand Pillay and I have given a modeltheoretic treatment
of some of this material, leading both to an abstract modeltheoretic
generalisation as well as a slight improvement of the complexgoemetric
result. I will report on this work.

Wed., Feb. 13, 2013
2:00 p.m.
Room 210

Omar Leon Sanchez, University of Waterloo
The modelcompanion of partial differential fields with
an automorphism
We explain how one can characterize the existentially closed
models in terms of differentialalgebraic varieties, and
then show that this class is elementary using characteristic
sets of differential prime ideals.

Wed., Feb. 13, 2013
3:30 p.m.
Room 210 
Patrick Speissegger, McMaster University
Are all nonoscillatory trajectories of threedimensional
real analytic vector fields ominimal?
A few years ago, Rolin, Sanz and Schäfke constructed
a real analytic vector field in real 5space that has a
nonoscillatory trajectory that is not ominimal. In real
2space, no such trajectory exists, but the question remains
open in 3space and 4space. The construction used for the
example in 5space cannot work in 3 or 4space; together
with Le Gal and Sanz, we are trying to prove that no examples
exist in 3space. In this talk, I will outline what we have
learned so far.

Thurs., Nov. 29
2:00 p.m.
Room 230 
Hadi Seyedinejad (Western
University)
Fibre families of complex analytic mappings
Fibres of a morphism between complex spaces form a family
that encodes much information regarding the behaviour of
the morphism. In fact, the study of fibres leads us to efficient
testing methods for specific properties of the map, like
openness and flatness. I will survey some results from my
PhD project, that are mostly efforts to extend certain previous
criteria to the general setting of maps over the singular
targets. I will also discuss the long term goal of my approach,
which is to classify different
nonregular (e.g., nonopen) mappings in terms of singularities
in their family of fibres.

Thurs., Nov. 29
3:30 p.m.
Room 230

Gal Binyamini (University of Toronto)
Complexity of Noetherian functions
Noetherian functions are functions which satisfy certain
systems of differential equations. They are defined in a
manner analogous to the Pfaffian functions, but without
imposing a triangularity condition. The global finiteness
properties of the Pfaffian class do not carry over to the
Noetherian class. However, Khovanskii and Gabrielov have
conjectured that local analogs of these finiteness properties
remain. In the first part of the talk I will introduce the
Noetherian functions and some old results on their finiteness
properties. In the second part I will describe some recent
progress (joint with Dmitry Novikov) toward the general
conjecture mentioned above.

Oct. 11
4:30 p.m.
Room 210

David Marker (University of Illinois at Chicago)
Model Theory and Complex Exponentiation?
As the integers are definable in the complex exponential
field it's model theory has long been ignored. Still there
are interesting open questions about definability. Zilber
proposed a novel model theoretic attack. We will survey
Zilber's work and later developments.

Oct. 11
2:00 p.m.
Room 230 
Philipp Hieronymi (University
of Illinois at UrbanaChampagin)
Tame Geometry: A tale of two spirals
As part of Back2Fields
Colloquium Series 
Past
Seminars 
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