Begun in October, 2011, the Istanbul Model Theory Seminar usually meets weekly, in the mathematics department of Istanbul Bilgi University or Mimar Sinan Fine Arts University, or elsewhere, as indicated below.

There is a Google Group for this seminar: all interested are encouraged to join this group, for announcements and (rarely) discussion.

The present page has sections for the following semesters:

- Models and Groups, Istanbul Center for Mathematical Sciences, October 16–18, 2014
- Caucasian
Mathematics Conference, Tbilisi, Georgia, September 5 and 6, 2014:
thematic session
Algebra and Model Theory

chaired by Tuna Altınel and Ayşe Berkman - Algebraic differential equations for analytic covering maps, colloquium by Thomas Scanlon, Wednesday, May 28, 2014, 14:00, Bogazici University mathematics department
- Summer School Around Valuation Theory, May 22–26, 2014, Şirince
- Supergeneric subsets of a group, colloquium by Bruno Poizat, Wednesday, April 2, 2014, 14:00, Bogazici University mathematics department
- Models and Groups, Istanbul Center for Mathematical Sciences, March 27–29, 2014
- Zariski topology of an abstract group, talk by Dikran Dikranjan at Mimar Sinan, Thursday, January 23, 2014, 16:00
- Between Model Theory and Additive Combinatorics, colloquium by Ehud Hrushovski at Boğaziçi University Department of Mathematics, Wednesday, November 20, 2013, 14:00
- Models and Groups, Istanbul Center for Mathematical Sciences, September 13–14, 2013
- Model Theory 2013, 10th–15th June 2013, Ravello, Italy

Who | What | When | where |
---|---|---|---|

Piotr Kowalski | on joint work with Serge Randriambololona on Zilber's (more precisely, Peterzil's) conjecture in the valued field context | June 27, 16:00 | Galatasaray |

Tuesdays, 16:30–18:30, Istanbul Bilgi University (Dolapdere Campus), room 514 (5th floor)

Who | What | When | where |
---|---|---|---|

Gönenç Onay // Piotr Kowalski | model-theoretic types and Berkovich points // summary | June 23, 15:00 | Mimar Sinan, Fındıklı campus |

Thomas Scanlon | intuitions around the main theorem of the paper by Hrushovski–Loeser | May 27, 16:30 | IMBM, Boğaziçi |

Piotr Kowalski | I will describe the analytic structure on Berkovich affine n-space (with special attention for the n=1 case). Then I will define Berkovich spaces in general and (Berkovich) analytifications of algebraic varieties. Time permitting, I will state the results and conjectures concerning the topological structure of Berkovich spaces including the main theorem of the paper by Hrushovski and Loeser. | May 6, 16:30 | Bilgi |

David Pierce | Spherical completeness (edited notes [pdf format]) | April 29, 16:30 | Mimar Sinan |

Piotr Kowalski | I will discuss a bit more branching points on Witch's Broom, describe the analytic structure on Berkovich affine line and proceed towards the definition of Berkovich space. | April 22, 16:30 | Bilgi |

Piotr Kowalski | I will briefly recall the construction of the Berkovich affine line and then focus on visualizing this space for the trivial case and the (non-trivial) non-Archimedean case. I will discuss Berkovich's classification theorem which splits points on the Berkovich affine line into 4 types. | April 15, 16:30 | Bilgi |

Piotr Kowalski | I will talk about the origins of the notion of Berkovich space.
The talk will be based on the introduction to Berkovich's book | April 8, 16:30 | Bilgi |

A minicourse by Piotr Kowalski:

I plan to introduce some notions of geometric model theory (Morley rank, stability) in the concrete cases of fields (with a possible extra structure). I would like to emphasize connections between algebraic geometry and model theory, both on a basic level: Ax's theorem and completeness of ACF

_{0}, Chevalley's Theorem on Constructible Sets and elimination of quantifiers, existence of the field of definition and elimination of imaginaries; and (time permitting) on a more advanced level: Zilber's trichotomy and diophantine geometry, rationality of Poincare power series and elimination of quantifiers for p-adics.

Who | What | When | where |
---|---|---|---|

Piotr Kowalski | Model Theory of Fields: I plan to talk about omega-stable/stable theories and give a rough geography of different theories of fields. | March 13, 10:30 | Mimar Sinan |

Piotr Kowalski | Model Theory of Fields: definition/examples of Morley rank and quantifier elimination for ACF with some applications | March 6, 10:30 | Mimar Sinan |

Piotr Kowalski | Model Theory of Fields: basic (affine) algebraic geometry notions, Morley rank, quantifier elimination for ACF and possibly fields of definition/elimination of imaginaries in ACF | February 27, 10:00 | Mimar Sinan |

Piotr Kowalski | Model Theory of Fields: brief introduction to languages, structures, theories, models; Compactness thm (no proof), Skolem-Lowenheim, model completeness of ACF and Hilbert Nullstellensatz | February 20, 10:00 | Mimar Sinan |

Our basic reference this semester is Chatzidakis and Hrushovski, Model
theory of difference fields (*Trans. Amer. Math. Soc.* 351
(1999), no. 8, 2997–3071; review).
Ancillary references are:

- Alice Medvedev, Minimal Sets in ACFA (PhD thesis: pdf file)
- Notes from the workshop The geometry of the Frobenius automorphism (CIRM, 25–29 March 2013)
- Zoé Chatzidakis, Model theory of difference fields (lecture notes, Notre Dame, 2000: pdf file)

Who | What | When | where |
---|---|---|---|

Burak Kaya | Countable Borel equivalence relations and their applications | January 15, 15:00 | Mimar Sinan |

Piotr Kowalski | Elimination of Imaginaries in ACFA | December 23, 15:30 | Mimar Sinan |

Serge Randriambololona | December 9, 15:30 | Mimar Sinan | |

Ayhan Günaydın | December 2, 15:30 | Mimar Sinan | |

David Pierce | November 25, 15:30 | Mimar Sinan | |

David Pierce | November 18, 15:30 | Mimar Sinan | |

Serge Randriambololona | November 11, 15:30 | Mimar Sinan | |

Serge Randriambololona | November 4, 15:30 | Mimar Sinan | |

Özlem Beyarslan | (Difference algebra) | October 28, 16:00 | Mimar Sinan |

David Pierce | (Axiomatization of ACFA) | October 7, 16:00 | Mimar Sinan |

In the spring of 2013, we meet Thursdays, 16:00–18:00, unless otherwise noted.

Who | What | When | where |
---|---|---|---|

Gregory Cherlin | Homogeneous ordered graphs (Mimar Sinan general mathematics seminar) | May 17, 16:00–17:00 | Mimar Sinan |

David Pierce | Descartes as model theorist | May 16 | Mimar Sinan |

Oleg Belegradek | Covering definable open sets by open cells | May 9 | Mimar Sinan |

Gönenç Onay | C-minimal modules | May 2 | Mimar Sinan |

Ayşe Berkman | Generically sharply transitive actions in the finite Morley rank context | April 25 | Mimar Sinan |

Piotr Kowalski | Report on the CIRM workshop, The geometry of the Frobenius automorphism | April 18 | Mimar Sinan |

Alexandre Borovik | Finite, locally finite, and pseudofinite groups | April 11 | Mimar Sinan |

Ludomir Newelski | Topological dynamics and model theory | April 4 (16:00–18:00) | Mimar Sinan |

April 2 (Tuesday), 15:00–17:00 | Galatasaray (P 19) | ||

Piotr Kowalski | I will give a preparatory talk before Newelski's lecture. My plan is to recall the following notions: complete types and their Stone topology, Cantor-Bendixson rank, (local) Morley rank, forking in stable theories, stable groups and their generic types. | March 21 | Mimar Sinan |

Cédric Milliet | Two remarks on shattering types and an application to groups which are hyperdefinable in a theory without the independence property | March 14 | Galatasaray (FEF 8) |

Piotr Kowalski | Chains of theories and group (scheme) actions | March 7 | Bilgi |

David Pierce | Chains of theories | February 28 | Mimar Sinan |

Piotr Kowalski | Canonical Base Property (Zariski geometries vs jet spaces) | February 21 | Istanbul Matematiksel Bilimler Merkezi (Boğaziçi Üniversitesi) |

In the fall of 2012, we meet Thursdays, 15:30–17:30. We plan to read:

M. Aschenbrenner, A. Dolich, D. Haskell, D. Macpherson, S. Starchenko,

**Vapnik-Chervonenkis
density in some theories without the independence property, I**

arXiv:1109.5438v1 [math.LO]

Who | What | When | where |
---|---|---|---|

Doğan Bilge | Rigid moieties of relational homogeneous structures | December 27 | Mimar Sinan |

David Pierce | Chains of theories | November 29 | Mimar Sinan |

Ayhan Günaydın | (on the paper above) | November 8 | Mimar Sinan |

Adrien Deloro | Representations of finite Morley rank | November 1 | Mimar Sinan |

Tuna Altınel | A Jordan decomposition for minimal simple groups of finite Morley rank | November 1 | Mimar Sinan |

Sonat Suer | (on the paper above) | October 18 | Mimar Sinan |

David Pierce | (on Compactness and the paper above) | October 11 | Mimar Sinan |

Ayhan Günaydın | (on the paper above) | October 4 | Mimar Sinan |

Oleg Belegradek | Homogeneity in relatively free groups | October 4 | Mimar Sinan |

all interested | organizational | September 27 | Mimar Sinan |

In the spring of 2012, we meet Thursdays, 15:00–17:00.

Some of our attention is taken by lectures by Bruno Poizat:

- slides (34 pp.)
- ‘Centralisateurs génériques’ (20 pp.)

Slides (12 pp.) from Cédric Milliet's talk are also linked to below.

Otherwise our main interest is in:

MR2833482

Hrushovski, Ehud (IL-HEBR-IM)

**Stable group theory and approximate subgroups.**

*J. Amer. Math. Soc.* 25 (2012), no. 1, 189–243.

03C45 (11P70)

Ancillary material includes:

- Lou van den Dries's notes
- Terence Tao's blog
- Some notes (by David
Pierce) on:
- Morley's categoricity theorem (possibly useful for reviewing some of the model-theoretic ideas at play);
- Keisler measures, &c. (linked to also below).

Who | What | When | where |
---|---|---|---|

Piotr Kowalski | I will give a proof of Theorem 2.11 from van den Dries' notes (and following these notes) using the Stabilizer Theorem. | April 19, 15:20 | Bilgi |

Jakub Gismatullin (University of Leeds and Uniwersytet Wrocławski) | On model-theoretic connected components | April 19, 14:10 | Bilgi |

Piotr Kowalski | Stable group theory and approximate subgroups (Keisler measures, S1-ideals and the stabilizer theorem proceeding to a combinatorial application (following Hrushovski´s paper and van den Dries´s notes) | April 12 | Bilgi |

David Pierce | Stable group theory and approximate subgroups | April 5 | Mimar Sinan |

David Pierce | Stable group theory and approximate subgroups | March 29 | Bilgi |

Bruno Poizat | Some dubious properties of groups of finite Morley rank | March 22 | Mimar Sinan |

Cédric Milliet | Definable soluble and nilpotent envelopes “around” subgroups in simple theory | March 22 | Mimar Sinan |

Bruno Poizat | Some dubious properties of groups of finite Morley rank | March 15 | Mimar Sinan |

Bruno Poizat | Some dubious properties of groups of finite Morley rank | March 8 | Mimar Sinan |

Gönenç Onay | Stable group theory and approximate subgroups | March 1 | Bilgi |

Gönenç Onay | Stable group theory and approximate subgroups | February 23 | Mimar Sinan |

Piotr Kowalski | Stable group theory and approximate subgroups | February 16 | Bilgi |

The main topic of interest in the fall of 2011 is free groups. We read Champetier and Guirardel, Limit groups as limits of free groups: compactifying the set of free groups.

Notes (by David Pierce) based on the seminars.

Who | What | When | where |
---|---|---|---|

Ayşe Berkman | Limit groups | December 30 | Bilgi |

Ayşe Berkman | Limit groups | December 23 | Mimar Sinan |

Özlem Beyarslan | Algebraic closure in pseudo-finite fields | December 23 | Mimar Sinan |

David Pierce | Limit groups | December 16 | Bilgi |

Özlem Beyarslan | Algebraic closure in pseudo-finite fields | December 16 | Bilgi |

David Pierce | Limit groups | December 9 | Mimar Sinan |

David Pierce | Limit groups | December 2 | Bilgi |

Salih Durhan | Hahn fields | December 2 | Bilgi |

David Pierce | Limit groups | November 18 | Mimar Sinan |

Oleg Belegradek | Coset-minimal groups | November 18 | Mimar Sinan |

Piotr Kowalski | Limit groups | November 4 | Bilgi |

Cédric Milliet | Definable envelopes around abelian, nilpotent or soluble subgroups in a group with simple theory | November 4 | Bilgi |

Piotr Kowalski | Limit groups | October 28 | Mimar Sinan |

Cédric Milliet | Definable envelopes around abelian, nilpotent or soluble subgroups in a group with simple theory | October 28 | Mimar Sinan |

Piotr Kowalski | Limit groups | October 21 | Bilgi |

Oleg Belegradek | Burnside problem | October 21 | Bilgi |

Ali Nesin | Free groups; trees | October 14 | Mimar Sinan |

Ali Nesin | Free groups | October 7 | Bilgi |

This webpage is maintained by David Pierce.

*Last change: Wednesday, 20 August 2014, 14:41:54 EEST*