May 30, 2024

Thematic Program on o-minimal Structures and Real Analytic Geometry --January-June 2009

June 22 - 26, 2009
Workshop on
Finiteness Problems in Dynamical Systems

Organized by Fernando Sanz and Patrick Speissegger

Supported by

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This workshop is the final activity of the Program and so it is intended as a kind of conclusion of the whole Semester. It will consist on one-hour invited lectures focused on different aspects related to finiteness properties, tame geometry and quasianaliticity of objects coming naturally from differential equations or dynamical systems. Topics may include pfaffian sets, non-oscillating trajectories and associated Hardy fields, limit cycles, Dulac transition maps, abelian integrals, diffeomorphisms, normalizations and formal solutions.

Guest Speakers: (speaker abstracts)

Andreas Fischer (Fields Institute)
Andrei Gabrielov (Purdue University)
Tobias Kaiser (University of Passau)
Krzysztof Kurdyka (Université de Savoie)
Olivier Le Gal (University of Toronto)
Jean-Marie Lion (Université de Rennes 1)
David Marín Pérez (Universitat Autònoma de Barcelona)
Chris Miller (Ohio State University)
Dmitry Novikov (Weizmann Institute of Science)

Daniel Panazzolo (Universidade de São Paulo)
Adam Parusinski (Université d'Angers)
Cristiane Rousseau (Université de Montréal)
Tere Seara (Universitat Politècnica de Catalunya)
Masahiro Shiota (Nagoya University)
Lou van den Dries (University of Illinois at Urbana-Champaign)
Joris van der Hoeven (Université Paris-Sud)
Alex Wilkie (University of Manchester)
Yosef Yomdin (The Weizmann Institute of Science)

Workshop Schedule

Monday June 22
8:45 - 9:00 Welcome and Introduction
Matthias Neufang & Workshop Organizers
9:00 - 10:00 Adam Parusinski (Université d'Angers)
Limits of gradient directions at a singular point
10:00 - 10:30 Break
10:30 - 11:30 Andreas Fischer (Fields Institute)
Definable versions of theorems by Kirszbraum and Helly
11:30 - 2:00 Lunch Break
2:00 - 3:00 Lou van den Dries (University of Illinois at Urbana-Champaign)
Asymptotic real differential algebra
3:00 - 3:30 Break
3:30 - 4:30 Dmitry Novikov (Weizmann Institute of Science)
Infinitesimal Hilbert 16th problem: recent progress
4:30 - 6:00 Reception
Fields Institute
Tuesday June 23
9:00 - 10:00 Chris Miller (Ohio State University)
Expansions of o-minimal structures by trajectories of definable planar vector fields
10:00 - 10:30 Break
10:30 - 11:30 Tere Seara (Universitat Politècnica de Catalunya)
Resurgence of inner solutions for analytical perturbations of the McMillan map
11:30 - 2:00 Lunch Break
2:00 - 3:00 Tobias Kaiser (University of Passau)
On the resolution of singularities for power series with perturbation by logarithmic terms
3:00 - 3:30 Break
3:30 - 4:30 Christiane Rousseau (Université de Montréal)
Orbital analytic classification of germs of families unfolding a codimension 1 resonant saddle or saddle-node
Wednesday June 24
9:00 - 10:00 Andrei Gabrielov (Purdue University)
Triangulation of monotone o-minimal families
10:00 - 10:30 Break
10:30 - 11:30 Jean-Marie Lion (Université de Rennes 1)
Pfaffian sets
11:30 - 2:00 Lunch Break
2:00 - 3:00 Joris van der Hoeven (Université Paris-Sud)
Machine computations with transseries
3:00 - 3:30 Break
3:30 - 4:30 David Marin (Universitat Autonoma de Barcelona)
Unfolding of resonant saddles and the Dulac time
Thursday June 25
9:00 - 10:00 Daniel Panazzolo (Universidade de São Paulo)
The group of power and translations and its relation to generalized Witt algebras
10:00 - 10:30 Break
10:30 - 11:30 Masahiro Shiota (Nagoya University)
O-minimal Hauptvermutung
  Free Afternoon
Friday June 26
9:00 - 10:00 Yosef Yomdin (The Weizmann Institute of Science)
Poincare Inversion, Moment inversion, Compositions, and Signal Processing
10:00 - 10:30 Break
10:30 - 11:30 Olivier Le Gal (University of Toronto)
O-minimality for solutions of analytic 2-dimensional linear ODEs
11:30 - 2:00 Lunch Break
2:00 - 3:00 Krzysztof Kurdyka (Université de Savoie)
On the structure of gradient extremal set of generic function
3:00 - 3:30 Break
3:30 - 4:30 Alex Wilkie (University of Manchester)
Some Model Theory for Complex Analytic Functions
Confirmed participants as of June 26, 2009
Fullname University/Affiliation
Andrews, Rob (no affiliation)
Aschenbrenner, Matthias University of California, Los Angeles
Bierstone, Edward University of Toronto
Bilski, Marcin Jagiellonian University
Brower, Donald University of Notre Dame
Caycedo, Juan Diego University of Oxford
Comte, Georges Université de Nice - Sophia Antipolis
Cotter, Sarah University of Notre Dame
Dinh, Si Tiep Fields Institute
Edmundo, Mário Jorge Universidade de Lisboa
Eleftheriou, Pantelis Universidade de Lisboa
Fischer, Andreas Fields Institute
Foster, Tom University of Oxford
Gabrielov, Andrei Purdue University
Gunaydin, Ayhan University of Oxford
Hart, Bradd McMaster University
Haskell, Deirdre McMaster University
Hieronymi, Philipp University of Oxford
Ingram, Patrick University of Waterloo
Jelonek, Zbigniew Instytut Matematyczny
Jones, Gareth University of Manchester
Kaiser, Tobias University of Passau
Kuhlmann, Salma University of Saskatchewan
Kurdyka, Krzysztof Université de Savoie
Le Gal, Olivier University of Toronto
Lion, Jean-Marie Université de Rennes 1
Malliaris, Maryanthe University of California, Berkeley
Marikova, Jana McMaster University
Marín, David Universitat Autònoma de Barcelona
Matusinski, Mickaël University of Saskatchewan
Miller, Christopher L. Ohio State University
Mourtada, Abderaouf Université de Bourgogne
Novikov, Dmitry Weizmann Institute of Science
Panazzolo, Daniel Universidade de São Paulo
Parusinski, Adam Université d'Angers
Patel, Sanjay McMaster University
Piekosz, Artur Politechnika Krakowska
Rainer, Armin University of Pisa
Ramakrishnan, Janak Université Claude Bernard Lyon I
Randriambololona, Serge Universite Lyon 1
Rennet, Alexander University of California, Berkeley
Rolin, Jean-Philippe Université de Bourgogne
Rousseau, Christiane Université de Montréal
Sanz, Fernando University of Valladolid
Seara, Tere M. Universitat Politècnica de Catalunya
Servi, Tamara Centro de Matemática e Aplicações Fundamentais
Shiota, Masahiro Nagoya University
Speissegger, Patrick McMaster University
Teymuri Garakani, Mahdi Institute for Research in Fundamental Sciences
Thomas, Margaret University of Oxford
Trotman, David University of Provence
Valette, Anna Uniwersytet Jagiellonski
Valette, Guillaume PAN
van den Dries, Lou University of Illinois at Urbana-Champaign
van der Hoeven, Joris Université Paris-Sud
Vasquez Rifo, Elisa University of Minnesota
Villaverde, Rafael Martín University of Bourgogne, France
Wilkie, Alex University of Manchester
Yomdin, Yosef The Weizmann Institute of Science


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