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August 8-12, 2011
o-minimal Structures and Real Analytic Geometry Retrospective
Workshop
hosted by the Fields Institute,
to be held at Bahen Centre Information Tech
40 St. George Street, Room 1220
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Organizing Committee:
Patrick Speissegger (McMaster)
Chris Miller (Ohio State University)
Jean-Philippe Rolin (Université de Bourgogne)
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OVERVIEW
Two years ago, we ran a thematic program on o-minimality and real
analytic geometry. Its main focus was on extending local resolution
of singularities techniques in order to establish the o-minimality
of certain expansions of the real field, such as those generated by
the functions studied by Ilyashenko and Ecalle in his proof of Dulac’s
problem. Many recent developments in the intersection of o-minimality
and real analytic geometry use resolution of singularities in crucial
ways, and they can in turn be viewed as extending the notion of resolution
of singularities in the sense of the preparation theorems mentioned
above. There is good reason to believe that extending resolution algorithms
to certain classes of functions involving exponential scales may help
shed new light on various interesting problems in real analytic geometry,
coming from Pfaffian geometry and dynamical systems. Examples of particular
interest to us are the classes of multisummable and of resurgent functions.
This workshop will survey progress made during and after our programme,
with a particular emphasis on work done by the (then) more junior
participants.
So far, the following have agreed to speak at the workshop:
Matthias Aschenbrenner, University of California, Los
Angeles
Gal Binyamini, Weizmann Institute, Israel
Raf Cluckers, Université Lille 1, France and K.U.
Leuven, Belgium
Andrei Gabrielov, Purdue University
Philipp Hieronymi, University of Illinois at Urbana-Champaign,
USA
Gareth Owen Jones, University of Manchester, UK
Olivier Le Gal, Universidad de Valladolid, Spain
Tobias Kaiser, Universität Passau
Jana Mariková, McMaster University and Western Illinois
University
Dan Miller, Emporia State University
Daniel Panazzolo, Université de Mulhouse, France
Sanjay Patel, McMaster
Fernando Sanz, Universidad de Valladolid, Spain
Tamara Servi, CMAF Lisbon, Portugal
Masahiro Shiota, Nagoya University
Michael Tychonievich, The Ohio State University, USA
Lou van den Dries, University of Illinois at Urbana-Champaign
Nicolai Vorobjov, University of Bath
Workshop Schedule
| Monday August 8 |
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9:20 - 9:30
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Welcome and Introduction
Workshop Organizers |
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9:30 - 10:30
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Tobias Kaiser (Universität Passau)
Spherical blowing up |
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10:30 - 11:00
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Coffee Break |
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11:00 - 12:00
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Gal Binyamini (Weizmann Institute, Israel)
Multiplicity and order of contact for regular and singular
foliations |
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12:00 - 2:00
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Lunch Break |
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2:00 - 3:00
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Tamara Servi (CMAF Lisbon, Portugal)
Quantifier elimination for generalised quasi-analytic
algebras of real functions |
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3:00 - 3:30
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Coffee Break |
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3:30 - 4:30
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Lou van den Dries (University of Illinois at Urbana-Champaign)
A progress report on the model theory of H-fields |
| Tuesday August 9 |
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9:30 - 10:30
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Philipp Hieronymi (University of Illinois at
Urbana-Champaign, USA)
A dichotomy for expansions of the real
field |
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10:30 - 11:00
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Coffee Break |
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11:00 - 12:00
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Sanjay Patel (McMaster)
o-minimal expansions by quasi-analytic functions of one
variable |
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12:00 - 2:00
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Lunch Break |
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2:00 - 3:00
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Jana Mariková (McMaster University and Western Illinois
University)
Definable sets in o-minimal fields with convex valuations
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3:00 - 3:30
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Coffee Break |
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3:30 - 4:30
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Masahiro Shiota, Nagoya University
How to avoid method of integration of vector fields in
singularity theory |
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5:00 - 6:00
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Reception
Fields Atrium - cash bar |
| Wednesday August 10 |
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9:30 - 10:30
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Raf Cluckers (Université Lille 1, France and K.U. Leuven,
Belgium) |
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10:30 - 11:00
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Coffee Break |
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11:00 - 12:00
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Olivier Le Gal (Universidad de Valladolid, Spain) |
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12:00 - 2:00
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Coffee Break |
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2:00 - 3:00
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Gareth Owen Jones (University of Manchester, UK)
Integer-valued definable functions |
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3:00 - 3:30
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Coffee Break |
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3:30 - 4:30
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Fernando Sanz (Universidad de Valladolid, Spain)
On restricted Analytic Gradients on Analytic Isolated
Surface Singularities |
| Thursday August 11 |
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9:30 - 10:30
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Margaret Thomas (Universität Konstanz)
Counting
Rational Points on Certain Pfaffian Sets |
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10:30 - 11:00
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Coffee Break |
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11:00 - 12:00
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Daniel Panazzolo (Université de Mulhouse, France)
Center manifolds for holomorphic
three-dimensional vector fields |
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12:00 - 2:00
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Lunch Break |
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2:00 - 3:00
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Nicolai Vorobjov (University of Bath)
Approximation of definable sets
by compact families, and upper bounds on homotopy and homology
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3:00 - 3:30
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Coffee Break |
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3:30 - 5:30
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Open discussion meeting
*Fields Institute - 3rd Floor Stewart Library* |
| Friday August 12 |
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9:30 - 10:30
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Matthias Aschenbrenner (University of California,
Los Angeles)
Vapnik-Chervonenkis density in model
theory |
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10:30 - 11:00
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Coffee Break |
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11:00 - 12:00
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Michael Tychonievich (The Ohio State University,
USA)
The set of restricted complex exponents for expansions
of the reals |
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12:00 - 2:00
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Lunch Break |
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2:00 - 3:00
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Andrei Gabrielov, Purdue University
Semi-monotone sets and triangulation
of tame monotone families |
CONFIRMED PARTICIPANTS
| Full Name |
University/Affiliation |
| Aschenbrenner, Matthias |
University of California, Los Angeles |
| Bierstone, Edward |
The Fields Institute |
| Binyamini, Gal |
Weizmann Institute of Science |
| Cluckers, Raf |
Université Lille 1 |
| Comte, Georges |
Université de Savoie |
| Dolich, Alfred |
East Stroudsburg Univesity |
| Freitag, James |
University of Illinois at Chicago |
| Glaze, Peter |
University of Illinois at Urbana-Champaign |
| Hart, Bradd |
McMaster University |
| Haskell, Deirdre |
McMaster University |
| Hieronymi, Philipp |
University of Illinois at Urbana-Champaign |
| Jones, Gareth |
University of Manchester |
| Kaiser, Tobias |
University of Passau |
| Kuhlmann, Salma |
University of Konstanz |
| Le Gal, Olivier |
Universidad de Valladolid |
| Maríková, Jana |
McMaster University |
| Miller, Christopher L. |
Ohio State University |
| Miller, Daniel |
Emporia State University |
| Panazzolo, Daniel |
Université de Haute-Alsace |
| Patel, Sanjay |
McMaster University |
| Pawlucki, Wieslaw |
Jagiellonian University |
| Rainer, Armin |
University of Vienna |
| Randriambololona, Serge |
University of Western Ontario |
| Rolin, Jean-Philippe |
Université de Bourgogne |
| Sanz, Fernando |
University of Valladolid |
| Servi, Tamara |
Universidade de Lisboa |
| Shiota, Masahiro |
Nagoya University |
| Speissegger, Patrick |
McMaster University |
| Thamrongthanyalak, Athipat |
University of California, Los Angeles |
| Thomas, Margaret |
Universität Konstanz |
| van den Dries, Lou |
University of Illinois at Urbana-Champaign |
| Vásquez Rifo, Elissa |
University of Talca |
| Vera Pacheco, Franklin |
University of Toronto |
| Vorobjov, Nicolai |
University of Bath |
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