
SCIENTIFIC PROGRAMS AND ACTIVTIES 

September 20, 2014  
Geometry and Model Theory Seminar 201011
Organizers: Ed Bierstone, Patrick Speissegger

SEMINARS 201011 

June 30, 2011  Chris Miller Oscillatory trajectories, Minkowski dimension and definability. In recent joint work with A. Fornasiero and P. Hieronymi,
we showed that an expansion of the real field (in the sense
of model 
May 19, 2011 
Patrick Speissegger, McMaster Nonoscillatory vs. interlaced trajectories

Gal Binyamini, Weizmann Institute Multiplicity and order of contact for regular and singular
foliations 

Vincent Grandjean, Fields Institute In this joint work with Daniel Grieser (Oldenburg, Germany), we want to address a naive and elementary question: Given an isolated surface singularity X in (M,g), can a neighbourhood of the singular point be foliated by geodesics reaching the singular point ? Then could we define an exponentiallike mapping at a such point, or if you like get some polarlike coordinates where the halflines would be replaced by a geodesic ray? And what would be the regularity of such an exponential mapping? Conical singularities of any dimension (Melrose & Wunsch) satisify this property and it can even be done analytically if the setting is real analytic (Lebeau). With D. Grieser, we have exhibited simple classes of examples of nonconical real analytic surfaces with an isolated singularity, and cuspidallike, in the Euclidean 3space, such that the geodesics reaching the singular point behave differently according to the considered class. We obsviously have in mind singular real algebraic sets, or germs or subanalytic sets, as model of the singularities we are interested in dealing with. If times allow I will make some connections with Hardt conjecture about the subanaliticity (or definability in a some larger ominimal structure) of the inner distance on semialgebraic sets, and try to explain how the current work could allow to provide counterexamples. 

PAST SEMINARS 

March 24, 2011 
Dmitry Novikov (Weizmann Institute of Science) The limit cycles appearing in perturbations of Darboux integrable planar polynomial vector fields are closely connected to the zeros of socalled pseudoabelian integrals, a generalization of abelian integrals. Therefore, one is interested in upper bounds for the number of zeros of such integrals. Even for an individual system this question is far less trivial than its analogue for abelian integrals. The natural conjecture, generalizing the VarchenkoKhovanskii theorem, claims existence of an upper bound depending on the degrees only. I'll describe the progress toward solving this conjecture. 
Nov. 18, 2010 
Gareth O. Jones (University of Manchester) Janusz Adamus (University of Western Ontario) 
Oct. 21, 2010 
Jana Mariková (McMaster University) We let R be an ominimal field, V a convex subring, and k_ind
the corresponding residue field with structure induced from
R.
I present an approach to Zilber's conjecture (that the complex
exponential field is quasiminimal) based on an analytic continuation
conjecture for complex functions definable in ominimal structures.
As an application of the ideas involved here, I prove that
the smallest ring R of analytic germs (at 0, say, in the complex
plane) containing the polynomials and closed under taking
logarithms and raising to real powers has the following property:
every f in R has an analytic continuation along all but finitely
many rays emanating from 0. (If we replace "finitely
many" by "countably many" the result is obvious.)
This is, of course, a purely mathematical result, but I do
not know how to prove it without going via definability in
certain 0minimal structures. 
Sept. 23, 2010 
Vincent Grandjean (Fields Institute) Tobias Kaiser (Universität Regensburg) 