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Title and dates
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Organizers
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Abstract and participants
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January 30-31,
2009
Mini-workshop on Expansions of the real field by multiplicative
groups
January 30 start at 1:30 p.m.
Room 210
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Ayhan Gunaydin
Chris Miller |
Lou van den Dries, Philipp Hieronymi and Michael
Tychonievich
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March 5-6, 2009
start at 10:30 am
Mini-workshop on o-minimality for Certain Dulac Transition
Maps
Room 210
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Tobias Kaiser
Patrick Speissegger |
We present the main ideas for proving o-minimality
of the expansion of the real field generated by all Dulac transition
maps near a non-resonant hyperbolic singularity of a planar
analytic vector field. We also show how the existence of (non-explicit)
uniform bounds on the number of limit cycles of certain (very
special) families of analytic vector fields can be obtained
from our approach.
Jean-Philippe Rolin, Dmitry Novikov, Sergei Yakovenko
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March 15-21,
2009
Mini-workshop on the Infinitesimal Hilbert's 16th Problem
Room 210
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Dmitry Novikov
Sergei Yakovenko |
Edward Bierstone, Andrei Gabrielov, Boris Khesin,
Askold Khovanskii
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March 23-25,
2009
Mini-workshop on New Perspectives in Valuation Theory
Room 210
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Franz-Viktor Kuhlmann
Florian Pop
Bernard Teissier |
In recent years new perspectives in valuation
theory have begun to appear as well as unexpected applications.
The two historical flows of valuation theory, namely the Henselian
and the Zariskian, are merging like never before in the development
of Berkovich geometry and the new approaches to resolution of
singularities, which now extend to the singularities of vector
fields. One begins to really be able to do analysis on spaces
of of valuations, leading to important new results on complex
analytic dynamical sytems stemming from a radically new point
of view on the use of valuations of the ring of holomorphic
functions. There is a new understanding of the structure of
spaces of valuations with a given center, exemplified by the
valuative tree of Favre-Jonsson, and also of the more global
aspects for which tropical geometry gives useful hints. The
purpose of the workshop is to gather experts who are contributing
to this new perspective so that they can strengthen their common
views and share problems and results.
Charles Favre, Mattias Jonsson, Daniel Panazzolo, Florian Pop,
Mark Spivakovsky
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April
3-4, 2009
Miniworkshop on Differential Kaplansky
Theory
Room 210
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Salma Kuhlmann
Mickael Matusinski
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Let (K,<,d) be an ordered diffenrential field, and v the
natural valuation. We assume that d is compatible with
v, i.e. that v is a differential valuation in
the sense of M. Rosenlicht. Denote by k the residue
field and by (G,Ψ) the induced asymptotic couple; i.e.
G = v(K) is the value group endowed with the map Ψ(v(a))
:= v(a′: =a).
The purpose of this workshop is to study a differential Kaplansky
theory in this setting. We want to achieve progress on the
following problem: Find necessary and su±cient conditions
on (K; <, d) so that: (i) the data (G, Ψ) allows
to define a derivation d on the field of generalized
series k((G)); (ii) the induced asymptotic couple is precisely
(G,Ψ); (iii) there is an order preserving di®erential
embedding of (K,<,d) in (k((G)),<,d);
(iv) the embedding may be chosen to be truncation closed;
i.e. the image of the embedding is closed under the operation
of taking initial segments of series. Partial progress has
been achieved on this topic, for example regarding item (i),
we have described the construction of "well-defined"
derivations on k((G)). Regarding item (iii), J.M.Aroca
and J. Del Blanco have considered the case of archimedean
value group. Other approaches to this problem are described
in the works of M. Aschenbrenner - L. v. D. Dries on H - fields,
and the works of J. v. D. Hoeven on Transseries.
J. Del Blanco Marana, Franz-Viktor Kuhlmann, Lou van den Dries
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June 8-10,
2009
Mini-workshop on Finiteness theorems for certain quasi-regular
algebras and Hilbert's 16th problem
Room 210
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Abderaouf Mourtada |
Jean-Philippe Rolin, Patrick Speissegger
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Dates
TBA
Mini-workshop on decidability in analytic situations |
Gareth O. Jones |
The workshop aims to understand the work of Macintyre
and Wilkie on the real exponential field, and the more recent
work of Macintyre on Weierstrass functions. The relation with
the constructive results of Gabrielov and Vorobjov would also
be investigated. The hope is that after careful study of these
papers, we would be able to prove further constructive model
completeness results for theories related to those above. If
this goes to plan, we would then combine the constructive model
completeness with recent work around Schanuel?s conjecture,
with the aim of proving unconditional decidability results for
certain analytic expansions of the real field.
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