Workshop on O-minimality and Diophantine Applications

June 19 - 23, 2017, The Fields Institute

Location: Fields Institute, Room 230

Description

The theory of o-minimality made a huge mark in arithmetic geometry with Pila's unconditional proof of the Andre-Oort conjecture for products of modular curves. Since then, there has been a lot of work on questions of unlikely intersections, centering around the Zilber-Pink conjecture, and very recently leading to a proof of the Andre-Oort conjecture for all Shimura varieties of abelian type. The aim of this workshop is to emphasize the recent applications to problems in unlikely intersections and functional transcendence.

Schedule

Monday, June 19th, 2017
09:30 to 10:30	Diophantine Approximation and o-minimality Philipp Habegger, University of Basel
10:30 to 11:00	Coffee break
11:00 to 12:00	Effective bounds for singular units Yuri Bilu, Université de Bordeaux
12:00 to 14:00	Lunch
14:00 to 15:00	Point counting and torsion points Harry Schmidt, University of Oxford
15:00 to 15:30	Coffee break
15:30 to 16:30	Intersections of class fields Lars Kühne, The Fields Institute
16:30 to 16:45	Break
16:45 to 17:10	The Stability of Jacobi Forms Jae-Hyun Yang, Inha University
17:15 to 17:40	Model Theory of Shimura Varieties Sebastian Eterovic, University of Oxford

Tuesday, June 20th, 2017
09:30 to 10:30	A valuation inequality for complex structure. Alex Wilkie, University of Oxford
10:30 to 11:00	Coffee break
11:00 to 12:00	zeroes and rational points of analytic functions Georges Comte, University Savoie-Mont Blanc
12:00 to 14:00	Lunch
14:00 to 15:00	The topological closure of algebraic and o-minimal flows on complex and real tori Starchenko Sergei, University of Notre Dame
15:00 to 15:30	Coffee break
15:30 to 16:30	Algebraic flows and o-minimality Andrei Yafaev, University College London
16:30 to 16:45	Break
16:45 to 17:10	Small sets in dense pairs Pantelis Eleftheriou, University of Konstanz
17:15 to 17:40	The critical height of a rational function Patrick Ingram, York University

Wednesday, June 21st, 2017
09:30 to 10:30	Variants of mild parameterizations, in definable families Raf Cluckers, Université de Lille
10:30 to 11:00	Coffee break
11:00 to 12:00	Differential equations and algebraic points on transcendental varieties Gal Benyamini, Weizmann Institute of Science

Thursday, June 22nd, 2017
09:30 to 10:30	Effective Pila--Wilkie bounds for restricted Pfaffian surfaces Margaret Thomas, The Fields Institute
10:30 to 11:00	Coffee break
11:00 to 12:00	Mild Parametrization in O-Minimal Structures Derya Ciray, University of Konstanz
12:00 to 14:00	Lunch
14:00 to 15:00	Unlikely Intersections in products of families of elliptic curves and the multiplicative group Laura Capuano, University of Oxford
15:00 to 15:30	Coffee break
15:30 to 16:30	Unlikely intersections in families of abelian varieties and some polynomial Diophantine equations Fabrizio Barroero, University of Basel
16:30 to 16:45	Break
16:45 to 17:10	A structure theorem for anomalous subvarieties of shimura varieties Jinbo REN, Institut des Hautes Études Scientifiques

Friday, June 23rd, 2017
09:30 to 10:30	Rational points on Fano varieties Marta Pieropan, Free University of Berlin
10:30 to 11:00	Coffee break
11:00 to 12:00	O-minimality and the Zilber-Pink conjecture for Shimura varieties Christopher Daw, University of Reading

Invited Speakers

Name	Affiliation
Fabrizio Barroero	University of Basel
Gal Benyamini	Weizmann Institute of Science
Yuri Bilu	Université de Bordeaux
Laura Capuano	University of Oxford
Derya Ciray	University of Konstanz
Raf Cluckers	Université de Lille
Georges Comte	University Savoie-Mont Blanc
Christopher Daw	University of Reading
Sebastian Eterovic	University of Oxford
Philipp Habegger	University of Basel
Lars Kühne	The Fields Institute
Marta Pieropan	Free University of Berlin
Harry Schmidt	University of Oxford
Starchenko Sergei	University of Notre Dame
Margaret Thomas	The Fields Institute
Alex Wilkie	University of Oxford
Andrei Yafaev	University College London

Registered Participants

Name	Affiliation
Mariam Abushammala	Zayed University
Ghorbat Ahmed	Government
Messab AIECH	Université Larbi Ben M'hidi
Shabnam Akhtari	University of Oregon
AMEGBEBOU AMEVI MAWUKO	universty of lome
Pablo Andujar Guerrero	Universität Konstanz
Fabrizio Barroero	University of Basel
Gal Benyamini	Weizmann Institute of Science
Yuri Bilu	Université de Bordeaux
Laura Capuano	University of Oxford
JIAMING CHEN	Université Paris Diderot
Derya Ciray	University of Konstanz
Raf Cluckers	Université de Lille
Georges Comte	University Savoie-Mont Blanc
Brian Cook	The Fields Institute
Greg Cousins	University of Notre Dame
Christopher Daw	University of Reading
Bryan Eelhart	The Fields Institute
Pantelis Eleftheriou	University of Konstanz
Sebastian Eterovic	University of Oxford
Bernadette Faye	University of Witwatersrand
James Freitag	University of Illinois at Chicago
John Friedlander	University of Toronto
Kyle Gannon	University of Notre Dame
Robert Grizzard	University of Wisconsin–Madison
Joseph Gunther	City University of New York
Philipp Habegger	University of Basel
Florian Herzig	University of Toronto
Khodabakhsh Hessami Pilehrood	The Fields Institute
Tatiana Hessami Pilehrood	University of Toronto
Su-ion Ih	University of Colorado Boulder
Patrick Ingram	York University
Gareth Jones	University of Manchester
Ernst Kani	Queen's University
Kian Kayler	Toronto Metropolitan University
Lars Kühne	The Fields Institute
Patrick Lank	University of New Mexico
Aubrey Laskowski	University of Illinois at Urbana-Champaign
Olivier Le Gal	Université de Savoie
Yu-Ru Liu	University of Waterloo
Florian Luca	Wits University
Alexander Mangerel	University of Toronto
Khadija Mbarki	Faculty of sciences of Monastir
Juan Manuel Menconi	Universidad de Buenos Aires (UBA)
Hamid Naderiyan	University of North Texas
Abhishek Oswal	University of Toronto
Marcelo Paredes	Universidad de Buenos Aires
Marta Pieropan	Free University of Berlin
Jonathan Pila	University of Oxford
Amalia Pizarro	Universidad de Valparaíso
Shi Qiu	University of Manchester
Jinbo REN	Institut des Hautes Études Scientifiques
Simon Rydin Myerson	University College London
Marcin Sabok	McGill University
Starchenko Sergei	University of Notre Dame
Margaret Thomas	The Fields Institute
Ling-Sang Tse	University of Toronto
Jacob Tsimerman	University of Toronto
Brian Tyrrell	Trinity College Dublin
Pierre Villemot	Université Savoie Mont Blanc
Erik Walsberg	University of Illinois at Urbana-Champaign
Zhiren Wang	The Pennsylvania State University
Michael Wan	University of California Berkeley
Roman Wencel	University of Wroclaw
Alex Wilkie	University of Oxford
Stanley Xiao	University of Oxford
Andrei Yafaev	University College London
Jae-Hyun Yang	Inha University
Jinhe Ye	University of Notre Dame
christian Yeke Okaso	Centre in Applied and Technological Research
Victor Zhang	California Institute of Technology
Ana Zumalacarregui	University of New South Wales