May 26, 2018

Geometry and Model Theory Seminar 2007-08
at the Fields Institute

Past Seminars 2003-04 Past Seminars 2004-05 Past Seminars 2005-06 Past Seminars 2006-07
Organizer:Patrick Speissegger, McMaster


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, Stewart Library from 2- 4 p.m.
Please subscribe to the Fields mail list to be informed of upcoming semainrs.

Upcoming Seminars at the Fields Institute

Thursday, February 14, 2008, 2:00 - 3:00 p.m.

Mark Spivakovsky, Université Emile Picard, ToulouseThe Pierce-Birkhoff conjecture and connected sets in the real spectrum
A continuous real-valued function f from R^n to R is said to be piecewise polynomial if R^n can be expressed as a finite union of closed semi-algebraic sets, on each of which f is given by a polynomial in n variables. The Pierce-Birkhoff conjecture asserts that every piecewise polynomial function on R^n can be obtained from a finite family of polynomials by iterating the operations of maximum and minimum. The goal of this talk is to explain how to reduce the Pierce-Birkhoff conjecture to proving the connectedness of certain
explicitly described sets in the real spectrum of the polynomial ring.


Thursday, November 29, 2007, 2:00 - 3:00 p.m.

Guillaume Valette, University of Toronto
Vanishing homology
We define a new metric invariant for families of sets. The idea is to consider the cycles that are collapsing when we approach a given fiber of a family. We prove that the homology groups are finitely generated when the family is semi-algebraic, subanalytic or more generally definable in an o-minimal structure.

Thursday, November 1, 2007, 2:00 - 3:00 p.m.

Gareth Owen Jones, McMaster University
Model completeness results for polynomially bounded o-minimal structures
I will discuss Wilkie's strategy for proving model completeness results, and show how it can lead to some
new results generalizing Gabrielov's theorem of the complement.

Thursday, November 1, 2007, 3:30 - 4:30 p.m.,

Patrick Speissegger, McMaster University
Transition maps of non-resonant hyperbolic singularities are
It has been a long-standing hope, first spread by Van den Dries, that the concept of o-minimality might lead to new insights into Dulac's problem. The o-minimal structure mentioned in the title is a small step in this direction. I will give a quick review of Dulac's problem, and I will outline how we obtain o-minimality for the structure generated by all transition maps near non-resonant hyperbolic singularities. If time permits, I'll speculate a bit on why o-minimality might be useful for other problems related to Dulac's problem. (Joint work with Tobias Kaiser and Jean-Philippe Rolin.)

Thursday, October 11, 2007, 2:00 - 3:00 p.m.,

Rasul Shafikov, University of Western Ontario
Analytic Geometry questions in Complex Analysis
I will discuss some questions related to geometry of real and complex analytic sets that naturally appear in the theory of holomorphic and CR mappings.
Thursday, October 11, 2007, 3:30 - 4:30 p.m.,

Janusz Adamus, University of Western Ontario
Vertical components and local geometry of analytic mappings
Vertical components constitute a new and powerful tool in
the study of the local geometry of complex analytic mappings. We will explain how one can exploit them to establish a certain level of algebraic control over the geometric complexity of a morphism.


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