Home /  Introductory Workshop: Model Theory, Arithmetic Geometry and Number Theory

Workshop

Introductory Workshop: Model Theory, Arithmetic Geometry and Number Theory February 03, 2014 - February 07, 2014
To apply for Funding you must register by: November 15, 2013 almost 11 years ago
Parent Program:
Location: Mathematical Sciences Research Institute, Berkeley CA
Organizers Elisabeth Bouscaren (Centre National de la Recherche Scientifique (CNRS)), Antoine Chambert-Loir (Institut de Mathematiques de Jussieu), LEAD Rahim Moosa (University of Waterloo)
Speaker(s)

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Description
Model theory is a branch of mathematical logic whose structural techniques have proven to be remarkably useful in arithmetic geometry and number theory. We will introduce in this workshop some of the main themes of the program. In particular, we will be offering the following tutorials: 1. An Introduction to Stability-Theoretic Techniques, by Pierre Simon. 2. Model Theory and Diophantine Geometry, by Antoine Chambert-Loir, Ya'acov Peterzil, and  Anand Pillay. 3. Valued Fields and Berkovich Spaces, by Deirdre Haskell and Martin Hils. 4. Model theory and multiplicative combinatorics, by Lou van den Dries. In addition to the tutorials there will be several "state of the art" lectures on the program topics, indicating recent results as well as directions for future work. Speakers include Ekaterina Amerik, Ehud Hrushovski, Alice Medvedev, Terence Tao, and Margaret Thomas. The introductory workshop aims to familiarize graduate students, postdocs, and non-experts to major and new topics of the current program. Though the audience is expected to have a general mathematical background, knowledge of technical terminology and recent findings is not assumed. Bibliography (PDF)
Keywords and Mathematics Subject Classification (MSC)
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC
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To apply for funding, you must register by the funding application deadline displayed above.

Students, recent PhDs, women, and members of underrepresented minorities are particularly encouraged to apply. Funding awards are typically made 6 weeks before the workshop begins. Requests received after the funding deadline are considered only if additional funds become available.

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For information about recommended hotels for visits of under 30 days, visit Short-Term Housing. Questions? Contact coord@slmath.org.

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Schedule, Notes/Handouts & Videos
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Feb 03, 2014
Monday
09:15 AM - 09:30 AM
  Welcome
09:30 AM - 10:30 AM
  Specialities for non-specialists
Antoine Chambert-Loir (Institut de Mathematiques de Jussieu)
10:30 AM - 11:00 AM
  Tea
11:00 AM - 12:00 PM
  An Introduction to Stability-Theoretic Techniques
Pierre Simon (University of California, Berkeley)
12:00 PM - 02:00 PM
  Lunch
02:00 PM - 03:00 PM
  A model-theorist's view of algebraically closed valued fields
Deirdre Haskell (McMaster University)
03:00 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  MSRI/Evans Lecture: Around Approximate Subgroups (Evans Hall, UC Berkeley)
Ehud Hrushovski (The Hebrew University of Jerusalem)
Feb 04, 2014
Tuesday
09:30 AM - 10:30 AM
  Specialities for non-specialists
Antoine Chambert-Loir (Institut de Mathematiques de Jussieu)
10:30 AM - 11:00 AM
  Tea
11:00 AM - 12:00 PM
  An Introduction to Stability-Theoretic Techniques
Pierre Simon (University of California, Berkeley)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:30 PM
  Some applications of Hrushovski's theorem about the Frobenius map to algebraic dynamics
Ekaterina Amerik (Higher School of Economics)
02:30 PM - 03:30 PM
  A Model Theoretic Approach to Berkovich Spaces
Martin Hils (Westfälische Wilhelms-Universität Münster)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  Model theory and multiplicative combinatorics
Lou van den Dries (University of Illinois at Urbana-Champaign)
05:00 PM - 07:00 PM
  Reception
Feb 05, 2014
Wednesday
09:30 AM - 10:30 AM
  Specialities for non-specialists
Antoine Chambert-Loir (Institut de Mathematiques de Jussieu)
10:30 AM - 11:00 AM
  Tea
11:00 AM - 12:00 PM
  An Introduction to Stability-Theoretic Techniques
Pierre Simon (University of California, Berkeley)
12:00 PM - 01:00 PM
  The Pila-Wilkie Theorem and variations
Margaret Thomas (Purdue University)
Feb 06, 2014
Thursday
09:30 AM - 10:30 AM
  A Model Theoretic Approach to Berkovich Spaces
Martin Hils (Westfälische Wilhelms-Universität Münster)
10:30 AM - 11:00 AM
  Tea
11:00 AM - 12:00 PM
  Stability theory and Diophantine geometry
Anand Pillay (University of Notre Dame)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:30 PM
  O-Minimal Ingredients in Proofs of Arithmetical Conjectures Such as Manin-Mumford and Andre-Oort
Ya'acov Peterzil (University of Haifa)
02:30 PM - 03:30 PM
  Model theory and multiplicative combinatorics
Lou van den Dries (University of Illinois at Urbana-Champaign)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  A regularity lemma for definable sets over finite fields, and expanding polynomials
Terence Tao (University of California, Los Angeles)
Feb 07, 2014
Friday
09:30 AM - 10:30 AM
  A Model Theoretic Approach to Berkovich Spaces
Martin Hils (Westfälische Wilhelms-Universität Münster)
10:30 AM - 11:00 AM
  Tea
11:00 AM - 12:00 PM
  Stability theory and Diophantine geometry
Anand Pillay (University of Notre Dame)
12:00 PM - 01:30 PM
  Lunch
01:30 PM - 02:30 PM
  O-Minimal Ingredients in Proofs of Arithmetical Conjectures Such as Manin-Mumford and Andre-Oort
Ya'acov Peterzil (University of Haifa)
02:30 PM - 03:30 PM
  Algebraic Dynamics and the Model Theory of Difference Fields
Alice Medvedev (City College, CUNY)
03:30 PM - 04:00 PM
  Tea
04:00 PM - 05:00 PM
  Model theory and multiplicative combinatorics
Lou van den Dries (University of Illinois at Urbana-Champaign)