March 21, 2023

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

Organizing Committee:
Patrick Speissegger (McMaster)
Chris Miller (Ohio State University)
Jean-Philippe Rolin (Université de Bourgogne)


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
9:20 - 9:30
Welcome and Introduction
Workshop Organizers
9:30 - 10:30
Tobias Kaiser (Universität Passau)
Spherical blowing up
10:30 - 11:00
Coffee Break
11:00 - 12:00
Gal Binyamini (Weizmann Institute, Israel)
Multiplicity and order of contact for regular and singular foliations
12:00 - 2:00
Lunch Break
2:00 - 3:00
Tamara Servi (CMAF Lisbon, Portugal)
Quantifier elimination for generalised quasi-analytic algebras of real functions
3:00 - 3:30
Coffee Break
3:30 - 4:30
Lou van den Dries (University of Illinois at Urbana-Champaign)
A progress report on the model theory of H-fields
Tuesday August 9
9:30 - 10:30
Philipp Hieronymi (University of Illinois at Urbana-Champaign, USA)
A dichotomy for expansions of the real field
10:30 - 11:00
Coffee Break
11:00 - 12:00
Sanjay Patel (McMaster)
o-minimal expansions by quasi-analytic functions of one variable
12:00 - 2:00
Lunch Break
2:00 - 3:00
Jana Mariková (McMaster University and Western Illinois University)
Definable sets in o-minimal fields with convex valuations
3:00 - 3:30
Coffee Break
3:30 - 4:30
Masahiro Shiota, Nagoya University
How to avoid method of integration of vector fields in singularity theory
5:00 - 6:00
Fields Atrium - cash bar
Wednesday August 10
9:30 - 10:30
Raf Cluckers (Université Lille 1, France and K.U. Leuven, Belgium)
10:30 - 11:00
Coffee Break
11:00 - 12:00
Olivier Le Gal (Universidad de Valladolid, Spain)
12:00 - 2:00
Coffee Break
2:00 - 3:00
Gareth Owen Jones (University of Manchester, UK)
Integer-valued definable functions
3:00 - 3:30
Coffee Break
3:30 - 4:30
Fernando Sanz (Universidad de Valladolid, Spain)
On restricted Analytic Gradients on Analytic Isolated Surface Singularities
Thursday August 11
9:30 - 10:30
Margaret Thomas (Universität Konstanz)
Counting Rational Points on Certain Pfaffian Sets
10:30 - 11:00
Coffee Break
11:00 - 12:00
Daniel Panazzolo (Université de Mulhouse, France)
Center manifolds for holomorphic three-dimensional vector fields
12:00 - 2:00
Lunch Break
2:00 - 3:00
Nicolai Vorobjov (University of Bath)
Approximation of definable sets by compact families, and upper bounds on homotopy and homology
3:00 - 3:30
Coffee Break
3:30 - 5:30
Open discussion meeting
*Fields Institute - 3rd Floor Stewart Library*
Friday August 12
9:30 - 10:30
Matthias Aschenbrenner (University of California, Los Angeles)
Vapnik-Chervonenkis density in model theory
10:30 - 11:00
Coffee Break
11:00 - 12:00
Michael Tychonievich (The Ohio State University, USA)
The set of restricted complex exponents for expansions of the reals
12:00 - 2:00
Lunch Break
2:00 - 3:00
Andrei Gabrielov, Purdue University
Semi-monotone sets and triangulation of tame monotone families



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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