Regional Days on Model Theory and Applications
6th edition  Düsseldorf, 14th+15th of Feb 2024
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Main local organizers: Immi Halupczok, Nadja Hempel
Additional organizers: Florian Felix, Hamed Khalilian, Saba Aliyari
This RDMTA is funded by the DFG, via the
GRK 2240.
Schedule
Wednesday 14th:
9:4510.30  Welcome coffee 
10.3011.30  Silvain Rideau: Multi topological fields, approximations and NTP2 
 Abstract ▷
(Joint work with S. Montenegro)
The striking resemblance between the behaviour of pseudoalgebraically closed, pseudo real closed and pseudo $p$adically fields has lead to numerous attempts at describing their properties in a unified manner. In this talk I will present another of these attempts: the class of pseudo$T$closed fields, where $T$ is an enriched theory of fields. These fields verify a « localglobal » principle with respect to models of $T$ for the existence of points on varieties. Although it very much resembles previous such attempts, our approach is more model theoretic in flavour, both in its presentation and in the results we aim for.
The first result I would like to present is an approximation result, generalising a result of Kollar on PAC fields, respectively Johnson on henselian fields. This result can be rephrased as the fact that existential closeness in certain topological enrichments come for free from existential closeness as a field. The second result is a (model theoretic) classification result for bounded pseudo$T$closed fields, in the guise of the computation of their burden. One of the striking consequence of these two results is that a bounded perfect PAC field with $n$ independent valuations has burden $n$ and, in particular, is NTP2.

11.4012.40  Stefan Ludwig: Difference fields with an additive character on the fixed field 
 Abstract ▷
Motivated by work of Hrushovski on pseudofinite fields with an additive character we investigate the theory $\operatorname{ACFA}_+$ which is the model companion of the theory of difference fields with an additive character on the fixed field. Building on results by Hrushovski we can recover it as the characteristic 0asymptotic theory of the algebraic closure of finite fields with the Frobeniusautomorphism and the standard character on the fixed field. We characterise 3amalgamation in $\operatorname{ACFA}_+$ and obtain that $\operatorname{ACFA}_+$ is simple as well as a description of the connected component of the KimPillay group. If time permits we present some results on higher amalgamation.

12.4014.00  Lunch 
14.0015.00  Florian Felix: Universality of CluckersLoeser Motivic Integration 
 Abstract ▷
I will give an introduction to the topic of my PhD thesis. Raf Cluckers and Immanuel Halupczok showed that in the case of $p$adic integration an analogue of the Kontsevich and Zagier period conjecture is true: Equalities between semialgebraic sets come from a set of very easy transformation rules. While this does not provide an approach to the real case, it naturally leads to the question whether something similar holds in other nonarchimedean integration theories. I will give a general (and vague) introduction to motivic integration in the style of CluckersLoeser over $K((t))$ for a field $K$ of characeristic 0 using the $p$adics as a guiding principle to discuss similarities and differences between the $p$adic case and $K((t))$.

15.1016.10  Simone Ramello: Valued difference fields: beyond surjectivity 
 Abstract ▷
We tackle the problem of axiomatizing theories of valued difference fields in the case where the endomorphism is not surjective, building on previous work of Pal (in the inversive multiplicative case) and DorHalevi (in the noninversive contracting case). We establish the Relative Embedding Property for a natural elementary class of noninversive multiplicative valued difference fields, and deduce AK/Estyle transfer results.

16.1016.50  Coffee 
16.5017.50  Leon Chini: Model companions of ominimal theories with a rational vector space homomorphism 
 Abstract ▷
Let $T$ be a complete and modelcomplete firstorder theory, which defines a nontrivial rational vector space in every model. Define $T_\theta := T \cup \{\text{“$\theta$ is a homomorphism of said vector space”}\}$. We also consider certain extensions $T^C_\theta$ of $T_\theta$, which enforce that the kernels of some endomorphisms of the form $f[\theta] = \sum_{i=0}^d (f_i) \cdot \theta^i$ satisfy certain equations. I will present a criterion for when these expansions have a model companion. For three special expansions, I will explicitly state a characterization of existentially closed models and show how one uses this condition to make these characterizations first order. By previous work of Block Gorman, said condition holds in certain ominimal theories, which include $\operatorname{Th}(\mathbb{R}, 0, +, <)$ with the additive group as a vector space and $\operatorname{RCF}$ with the multiplicative group on the positive elements as a vector space. If time permits, I will present some results obtained for the respective model companions in these cases.

19.00  Conference dinner
at the Giosy,
which is here

 Menu ▷

Thursday 15th:
9.3010.30  Marco Amelio: Nonsplit sharply 2transitive groups in odd characteristic 
 Abstract ▷
(joint work with S. André and K. Tent)
Until recently, the existence of nonsplit sharply 2transitive groups (i.e., sharply 2transitive groups without a nontrivial normal abelian subgroup) was an open problem. The first examples were produced by Rips, Segev and Tent in 2017 and by Rips and Tent in 2019. It is possible to associate to every sharply 2transitive group a characteristic, that is either 0 or a positive prime number. The first of these examples have characteristic 2, while the other ones have characteristic 0, leaving the problem open for odd characteristics. In this talk, I will give some background on sharply 2transitive groups and a rough overview on how we adapted the construction used for characteristic to 0 to odd characteristic, using methods of geometric small cancellation.

10.3011.10  Coffee 
11.1012.10  Tingxiang Zou: Around the ElekesSzabó's Theorem

 Abstract ▷
The ElekesSzabó's Theorem roughly says the following: Let $R$ be
an algebraic ternary relation in $W_1\times W_2\times W_3$ defined in a field $K$ of
characteristic 0, such that any two coordinate is interalgebraic with the
third one, for example the collinear relation for three points in a curve.
Suppose there are arbitrarily large finite subsets $X_i$ of $W_i$ with each
$X_i$ of size $n$ and has bounded intersection with any subvariety of $W_i$,
such that the intersection of $R$ with $X_1\times X_2\times X_3$ has size approximately
$n^2$, then $R$ must be essentially the graph of addition of some commutative
algebraic group $G$. With Martin Bays and Jan Dobrowolski, we are trying to
remove the assumption of having bounded intersection with any
subvarieties. This assumption is called in general position. Along the
way, we develop a group action version of the ElekesSzabo's Theorem,
which seems necessary if one wants to remove the general position
assumption. In this talk, I will give an overview of the ElekesSzabó's
Theorem and the model theoretic approach towards it.

12.4014.00  Lunch 
Confirmed speakers
 Florian Felix (Düsseldorf)
 Leon Chini (Bonn)
 Marco Amelio (Münster)
 Silvain RideauKikuchi (Paris)
 Simone Ramello (Münster)
 Stefan Ludwig (Paris)
 Tingxiang Zou (Münster/Bonn)
Registration
If you want to participate, please
register here, preferably on the 05.02.2024 at latest.
For a limited number of young researchers, the hotel rooms can be funded.
The application deadline for this is 31.01.2024.
Travel and venue
Conference venue:
All talks will take place in lecture hall 5H, in the building 25.22. Coffee and cookies will be served
in room 25.22.00.53, which is very close to that lecture hall.
Map ▷
Hotel:
If you do not get the hotel room funded by us, please book a hotel on your own.
Speakers will be lodged at the HKhotel, which is in 25 min walking distance from the venue of the conference. Another nice hotel nearby is Haus Mooren.
Public transport tips:
 To find routes, you can use the website of the Deutsche Bahn or the
website of the Verkehrsverbund RheinRuhr. You can also download the
DB Navigator app.
 If you travel between Düsseldorf main station, the hotel and the university, you need a ticket Preisstufe A or Preisstufe A3. There are single tickets and tickets valid for several (e.g. 4) trips. If you arrive with a train ticket of the deutsche Bahn which, as destination, says "Düsseldorf+city", then that ticket is valid in the local transports.
 In case you buy a ticket from a ticket vending machine, you might (or might not) need to stamp your ticket using the stamp machines inside the trains/trams/subways.
Arrival by car:
If you arrive by car, we recommend parking on the
parking site P2 of the university.