
August 812, 2011
ominimal 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)
JeanPhilippe Rolin (Université de Bourgogne)

OVERVIEW
Two years ago, we ran a thematic program on ominimality and real
analytic geometry. Its main focus was on extending local resolution
of singularities techniques in order to establish the ominimality
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 ominimality
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 UrbanaChampaign,
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 UrbanaChampaign
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 quasianalytic
algebras of real functions 
3:00  3:30

Coffee Break 
3:30  4:30

Lou van den Dries (University of Illinois at UrbanaChampaign)
A progress report on the model theory of Hfields 
Tuesday August 9 
9:30  10:30

Philipp Hieronymi (University of Illinois at
UrbanaChampaign, USA)
A dichotomy for expansions of the real
field 
10:30  11:00

Coffee Break 
11:00  12:00

Sanjay Patel (McMaster)
ominimal expansions by quasianalytic 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 ominimal 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

Reception
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)
Integervalued 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
threedimensional 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)
VapnikChervonenkis 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
Semimonotone 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 UrbanaChampaign 
Hart, Bradd 
McMaster University 
Haskell, Deirdre 
McMaster University 
Hieronymi, Philipp 
University of Illinois at UrbanaChampaign 
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 HauteAlsace 
Patel, Sanjay 
McMaster University 
Pawlucki, Wieslaw 
Jagiellonian University 
Rainer, Armin 
University of Vienna 
Randriambololona, Serge 
University of Western Ontario 
Rolin, JeanPhilippe 
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 UrbanaChampaign 
Vásquez Rifo, Elissa 
University of Talca 
Vera Pacheco, Franklin 
University of Toronto 
Vorobjov, Nicolai 
University of Bath 
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