This is the webpage of the UCLan Model Theory Seminar; a regular research seminar run by the Model Theory research group, based in the Jeremiah Horrocks Institute at the University of Central Lancashire.

Everyone is welcome to attend. The seminar is organised by Sylvy Anscombe. Please  contact her  for more details.

### Autumn 2019

• A general Mathematics seminar will resume in the Autumn. Watch this space!

### Autumn 2018 and Spring 2019

• The seminar is on hiatus this academic year, replaced by an informal reading group. Please  contact me  for more details.

### Summer 2018

This summer, instead of the model theory seminar, we are running Sandwiches and Light Theorems'. The seminar will run on Fridays between 1pm and 2pm, unless otherwise stated, and it will be held in Leighton 305. All are welcome!

• Monday 20th August

• Sandwiches and Light Theorems
Tom Kirk, UCLan
time: 1pm-2pm
location: LE305 (Leighton), Sylvy and Matt's office

• Friday 10th August

• Sandwiches and Light Theorems
Sylvy Anscombe, UCLan
title: Approximation in Algebra: from the Chinese Remainder Theorem to the present day
time: 1pm-2pm
location: LE305 (Leighton), Sylvy and Matt's office

• Thursday 2nd August

• Sandwiches and Light Theorems
Sylvy Anscombe, UCLan
title: Sums of squares
abstract: We introduce the study of sums of squares, be they integers, rationals, or reals.
time: 1pm-2pm
location: LE305 (Leighton), Sylvy and Matt's office

• Friday 6th July

• Sandwiches and Light Theorems
Tom Kirk, UCLan
title: The $p$-adic numbers
abstract: A light and non-specialist discussion of the $p$-adic numbers.
time: 1pm-2pm
location: LE303 (Leighton)

### Spring 2018

The seminar will run on Thursdays between 3pm and 5pm, unless otherwise stated. Usually we have coffee before the seminar. All are welcome!

• Week 13, Thursday 11th January

• Sylvy Anscombe, UCLan
title: Introduction to Pseudofinite Fields I
abstract:
time: 3pm-5pm
location: LE305 (Leighton)

• Reading Week, Thursday 18th January

• Sylvy Anscombe, UCLan
title: Introduction to Pseudofinite Fields II
abstract:
time: 3pm-5pm
location: LE305 (Leighton)

• Week 14, Thursday 25th January

• Sylvy Anscombe, UCLan
title: Introduction to Pseudofinite Fields III
abstract:
time: 2pm-4pm
location: LE305 (Leighton)

• Week 15, Thursday 1st February

• Sylvy Anscombe, UCLan
title: Introduction to Pseudofinite Fields IV
abstract:
time: 3pm-5pm
location: LE305 (Leighton)

• Week 16, Thursday 8th February

• TBA
title: TBA
abstract:
time: 3pm-5pm
location: LE305 (Leighton)

• Week 17, Thursday 15th February

• Sylvy Anscombe, UCLan
title: Introduction to Pseudofinite Fields V
abstract:
time: 3pm-5pm
location: LE305 (Leighton)

### Spring 2017

The seminar will run on Mondays between 2pm and 4pm, unless otherwise stated. The location will vary from week to week, so please see each listing below for details. Usually we have lunch before the seminar, and drinks and dinner afterwards. All are welcome!

• Week 15, Monday 23rd January

• Isabel Müller, Universität Münster
title: Building-like geometries of finite Morley rank
abstract:
time: 2pm-4pm
location: LE303 (Leighton)

• Week 16, Monday 30th January

• Charlotte Kestner, UCLan
title: Pierre Simon's "Type decomposition in NIP Theories"
abstract:
time: 3pm-5pm
location: HB206 (Harris)

• Week 17, Monday 6th February

• Sylvy Anscombe, UCLan
title: Pseudofinite and PAC fields
abstract: We continue to study Ax's famous paper
time: 3pm-5pm
location: HB206 (Harris)

• Week 18, Monday 13th February

• Davide Penazzi, UCLan
title: TBA
abstract: TBA
time: 3pm-5pm
location: HB206 (Harris)

• Week 19, Monday 20th February

• Tom Kirk, UCLan
title: TBA
abstract: TBA
time: 3pm-5pm
location: HB206 (Harris)

• Week 20, Monday 27th February

• Sylvy Anscombe, UCLan
title: TBA
abstract: TBA
time: 2pm-4pm
location: LE303 (Leighton)

• Week 21, Monday 6th March

• Alex Morrow, UCLan
title: TBA
abstract: TBA
time: 2pm-4pm
location: LE111 (Leighton)

• Week 22, Monday 13th March

• Darío García, University of Leeds
title: Higher amalgamation in measurable structures
abstract: The concept of MS-measurable structures appeared as a generalization of a result of Chatzidakis-van den Dries-Macintyre about the asymptotic size of definable sets in the class of finite fields, and have been extensively studied in recent years by several researchers (Macpherson, Steinhorn, Elwes, Ryten, Wolf, Anscombe, among others). MS-measurable structures are known to be supersimple of finite U-rank, and some examples are provided by taking infinite ultraproducts of the following classes of finite structures: the class of finite fields, the class of cyclic groups, the Paley graphs (whose infinite ultraproducts are elementarily equivalent to the random graph), the class of finite groups of fixed Lie type, etc.

In this talk I will present a survey on unpublished work of David Evans about MS-measurable structures, in which he uses Towsner's proof of Szemeredi's theorem to show that a "higher amalgamation property" holds for MS-measurable structures, but not generally in structures which are supersimple of finite U-rank. In addition, Evans shows that some of Hrushovski's non locally modular supersimple omega-categorical structures are not MS-measurable, answering negatively a question of Elwes and Macpherson about the MS-measurability for supersimple finite U-rank unimodular structures.

time: 2pm-4pm
location: LE303 (Leighton)

• Week 23, Monday 20th March

• Mark Kambites, University of Manchester
title: Random walks on semigroups
abstract: TBA
time: 2pm-4pm
location: LE303 (Leighton)

• Week 24, Monday 27th March

• no seminar

• Week 25, Monday 3rd April

• Omar Leon Sanchez, University of Manchester
title: Definability of ranks (in families) in differential fields
abstract: As the theory $DCF_{0,m}$ of differentially closed fields of characteristic zero with several commuting derivations is omega-stable, we have at our disposal Morley and Lascar rank. A natural question to ask is whether these ranks are definable in families of definable sets. The answer is "no" (for instance, one can see this using results on the 2nd Painlevé equation). Nonetheless, we have another notion of rank in this context: the Kolchin polynomial. In this talk I will explain why this rank is in fact definable. This is joint work with G. Binyamini, J. Freitag and W. Li.
time: 2pm-4pm
location: LE303 (Leighton)

### Autumn 2016

The seminar will run on Mondays between 2pm and 4pm, unless otherwise stated. The location will vary from week to week, so please see each listing below for details. Usually we have lunch before the seminar, and drinks and dinner afterwards. All are welcome!

• Week 1, Monday 26th September

• TBA,
title: group discussion
time: 2pm-4pm
location: KM015 (Kirkham)

• Week 2, Monday 3rd October

• Charlotte Kestner, UCLan
time: 2pm-4pm
location: HB159 (Harris)

• Week 3, Monday 10th October

• Sylvy Anscombe, UCLan
time: 2pm-4pm
location: HB159 (Harris)

• Week 4, Monday 17th October

• Tom Kirk, UCLan
time: 2pm-4pm
location: HB159 (Harris)

• Week 5, Monday 24th October

• no seminar

• Week 6, Monday 31st October

• Davide Penazzi, UCLan
time: 2pm-4pm
location: HB159 (Harris)

• Week 7, Monday 7th November

• Charlotte Kestner, UCLan
time: 2pm-4pm
location: HB159 (Harris)

• Week 8, Monday 14th November

• Sylvy Anscombe, UCLan
time: 2pm-4pm
location: LH325 (Livesey)

• Week 9, Monday 21st November

• Tom Kirk, UCLan
time: 2pm-4pm
location: HB159 (Harris)

• Week 10, Monday 28th November

• Davide Penazzi, UCLan
time: 2pm-4pm
location: HB159 (Harris)

• Week 11, Monday 5th December

• Charlotte Kestner, UCLan
time: 2pm-4pm
location: HB159 (Harris)

• Week 12, Monday 12th December

• Tom Kirk, UCLan
time: 2pm-4pm
location: HB159 (Harris)

### July 2016

In July 2016, Gareth Boxall is visiting us from Stellenbosch University under the Distinguished Visitors Programme. He will be giving two talks. The first is part of the JHI seminar series, and the second is a Model Theory Seminar.

• Week 33, Thursday 14th July

• Gareth Boxall, Stellenbosch University
(JHI Seminar)
title: Complex Exponentiation
abstract: I shall discuss the structure $\mathbb{C}_{\exp}$ which consists of the set $\mathbb{C}$ of complex numbers together with the operations of addition and multiplication and the exponential function $\exp(z) = e^z$. A polynomial is anything that can be formed from variables and complex numbers using the operations of addition and multiplication. An exponential polynomial is anything that can be formed from variables and complex numbers using addition, multiplication and the function $\exp$. The study of $\mathbb{C}_{\exp}$ inevitably involves the study of exponential polynomials. I shall discuss these with reference to what is known about polynomials.
time: 2pm-3pm
location: LE002 (Leighton)

Gareth Boxall, Stellenbosch University
title: A special case of quasi-minimality
abstract: Zilber conjectured that every subset of the complex field $\mathbb{C}$ which is first-order definable in the complex exponential ring $\mathbb{C}$ is either countable or cocountable. We prove this in the special case of a set arising as the projection to $\mathbb{C}$ of the solution set of a single exponential polynomial equation. By an exponential polynomial we mean anything formed from variables and complex numbers using the operations of addition, multiplication and $\exp$ (so we allow $\exp$ of $\exp$).
time: 3pm-5pm
location: LE002 (Leighton)

### Summer 2016

The seminar will run on Thursdays between 2pm and 4pm, unless otherwise stated. The location will vary from week to week, so please see each listing below for details. Usually we have lunch before the seminar, and drinks and dinner afterwards. All are welcome!

• Week 24, Thursday 7th April
• Li Bingjun, Hunan University of Humanities, Science and Technology
abstract:
time: 2pm-4pm
location: HB303 (Harris)

• Week 25, Thursday 14th April
• Uğur Efem, Oxford
title: On universal specializations of non-locally modular Zariski geometries
abstract: Specializations are the key tool in proving the Trichotomy Theorem for Zariski geometries. In this talk I will concentrate on a special class of specializations, called the $\kappa$-universal specializations. The focus of the talk will be on non-locally modular Zariski geometries that only admit $\kappa$-universal specializations. Contrary to the initial intuition this is not the case for all non-locally modular Zariski geometries. I will give some conditions for certain non-locally modular Zariski geometries under which all specializations are $\kappa$-universal. I will also explain how these conditions are related to the conditions given by Serre, under which any principal bundle over an algebraic variety is locally isotrivial.
time: 2pm-4pm
location: LE111 (Leighton)

Our speaker in Week 26 is Jochen Koenigsmann, from Oxford, who is giving two talks. The first talk is to the whole Jeremiah Horrocks Institute, as part of the JHI Seminar series:

• Week 26, Wednesday 20th April (JHI Seminar)
• Jochen Koenigsmann, Oxford
title: On rational numbers
abstract: "Rational numbers are easier to handle than real numbers because with rationals you can only do algebra, whereas the reals lead you straight into calculus, differential equations, integrals and other tough business." We will contrast this widespread view with the by now well understood phenomenon that the algebra of the reals is much easier than the algebra of the rationals. To illustrate this, we will present two big open problems about the rationals (one along the lines of Hilbert's 10th problem, the other going back to Grothendieck's "anabelian geometry"), explaining very recent progress towards their solution.
time: 4pm-5pm
location: LE111 (Leighton)
The seminar is followed by Cheese and Wine in HB015 (Harris)

The second talk is part of the UCLan Model Theory Seminar:

• Week 26, Thursday 21st April
• Jochen Koenigsmann, Oxford
title: Back to the model theory of local fields
abstract: Classical model theory of non-archimedean local fields has regained momentum in recent years. We will highlight some of the new developments on issues of definability and decidability originating from old open problems, but with a view towards new arithmetically compelling challenges.
time: 2pm-4pm
location: LE111 (Leighton)

• Week 27, Thursday 28th April
• no seminar

• Week 28, Friday 6th and Saturday 7th April
• ColloquiumFest 2016
time: 11am Friday 6th of May - 5.30pm Saturday 7th of May
location: LE003/LE111 (Leighton), University of Central Lancashire

### Spring 2016

All seminars will be on Thursdays between 2pm and 4pm. The location will vary from week to week, so please see each listing below for details. We will meet beforehand for lunch from 1pm in the Scholars cafeteria, and all are welcome.

• Week 18, Thursday 14th January
• Sylvy Anscombe, UCLan
title: Henselianity in the language of rings
abstract: joint work with Franziska Jahnke
time: 2pm-4pm
location: LE002

• Week 19, Wednesday 20th -- Friday 22nd January 2016
• British Postgraduate Model Theory Conference 2016
location: Manchester

• Week 20, Thursday 28th January
• no seminar

• Week 21, Thursday 4th February
• Charlotte Kestner, UCLan
title: Non-forking formulas in distal NIP theories
abstract: tba
time: 2pm-4pm
location: HB310

• Week 22, Thursday 11th February
• Charlotte Kestner, UCLan
title: Non-forking formulas in distal NIP theories, continued
abstract: tba
time: 2pm-4pm
location: BB142a

• Week 23, Thursday 18th February
• Tom Kirk, UCLan
title: $G$, $G^{0}$, and $G^{00}$
abstract: I will talk about $G$, $G^{0}$, and $G^{00}$ and explore the action of $G$ on its type space. Then I will discuss these groups in $\mathrm{SO}(2,\mathbb{R})$ and what's known in $\mathrm{SO}(2,\mathbb{Q}_{p})$.
time: 2pm-4pm
location: HA135a

• Week 24, Thursday 25th February
• Dugald Macpherson, Leeds
title: Modey Theory of profinite groups
abstract: I will discuss recent work with Katrin Tent where we consider a profinite group $G$ as a $2$-sorted structure with a second sort which codes (as a uniformly definable family) the system of all open subgroups of $G$. The main theorem is that the theory is $\mathbf{NTP}$ (or just $\mathbf{NTP2}$) if and only if $G$ has an open subgroup which is a direct product of finitely many compact $p$-adic analytic groups (for different primes $p$).
time: 2pm-4pm
location: HB310 (Harris)

• Week 24, Friday 26th February (please note the unusal date and time)
• Franziska Jahnke, Münster
title: When does dependence transfer from a field to henselian expansions?
abstract: Let $K$ be an NIP field and let $v$ be a henselian valuation on $K$. We ask whether $(K,v)$ is NIP as a valued field. By a result of Shelah, we know that if $v$ is externally definable, then $(K,v)$ is NIP. Using the definability of the canonical $p$-henselian valuation, we show that whenever the residue field of $v$ is not separably closed, then $v$ is externally definable. Time permitting, we also discuss the case of separably closed residue fields.
time: 12pm-2pm
location: HB010 (Harris)

• Week 25, Thursday 3rd March
• Model Theory research group, UCLan
title: group discussion
abstract:
time: 2pm-4pm
location: HB303 (Harris)

• Week 26, Thursday 10th March
• Model Theory research group, UCLan
title: group discussion
abstract: tba
time: 2pm-4pm
location: FBLT4 (Foster)

• Week 26, Saturday 12th March
• Lancashire-Yorkshire Model Theory Seminar
location: Manchester

• Week 27, Thursday 17th March
• Marcus Tressl, Manchester
title: On Convex valuations of ordered fields
abstract: I will give a brief introduction to Dedekind cuts of ordered fields and explain how these can be used to understand convex valuations of ordered fields. Further I will show a method to manufacture convex subrings that are definable in a given ordered field. The talk will finish with a few applications to henselian ordered fields. (Parts of this work is joint with Lorna Gregory)
time: 2pm-4pm
location: HB303 (Harris)

### Autumn 2015

All seminars will be on Thursdays between 2pm and 4pm. The location will vary from week to week, so please see each listing below for details. We will meet beforehand for lunch from 1pm in the Scholars cafeteria, and all are welcome.

#### Schedule of seminars

• Week 1, Thursday 17th September
• Sylvy Anscombe and Lotte Kestner, UCLan
title: Martin-Pizarro and Pillay's paper Elliptic and hyperelliptic curves over supersimple fields'
time: 2pm-4pm
location: LE303

• Week 4, Thursday 8th October
• Charlotte Kestner, UCLan
title: Introduction to model theory
time: 2pm-4pm
location: LH102
abstract: In this talk I will go over the basics of model theory, starting with a first order theory and touching on the beginnings of stability theory.

• Week 5, Thursday 15th October
title: Model theory and automorphism groups
abstract: Continuing with our introductory theme, we will look at some connections between the automorphism group of a model, that is the collection of "symmetries" of a structure, and definability in that model.
time: 2pm-4pm
location: HB310

• Week 6, Thursday 22nd October
• Lorna Gregory, Manchester
title: Decidability for theories of modules of tame canonical algebras
abstract: A long standing conjecture of Mike Prest claims that a finite-dimensional algebra has decidable theory of modules if and only if it is of tame representation type. Up until recently, all known examples of finite-dimensional algebras with decidable theory of modules were of tame domestic representation type. In this seminar, I will talk about how to prove that all tame canonical algebras over algebraically closed fields have decidable theory of modules. Tame canonical algebras are tame non-domestic of linear growth. I will explain in the seminar what the terms tame, domestic and linear growth mean.
time: 2pm-4pm
location: GR347

• Week 7, Thursday 29th October
• Discussion led by Davide Penazzi, UCLan
title: Discussion of the model theory of $SL_{2}(\mathbb{R})$
abstract:
time: 2pm-4pm
location: HB159

• Week 8, Thursday 5th November
• Charlotte Kestner, UCLan
title: Introduction to the $p$-adics
abstract: We give an introduction to the $p$-adics from both an algebraic and model-theoretic point of view.
time: 2pm-4pm
location: HB234

• Week 9, Thursday 12th November
• break

• Week 10, Thursday 19th November
• Gwyneth Harrison-Shermoen, Leeds
title: Limit Independence
abstract: Given a large model $M$ of some theory $T$, I will describe a method for lifting well-behaved notions of independence from the theories of substructures of $M$ to a reasonably well-behaved notion of independence in $M$. (In essence, we take the limit of the independence relations in the substructures.) The motivating example - two-sorted theories of infinite-dimensional vector spaces over an algebraically closed field and with a bilinear form - was worked out by N. Granger in his thesis.
time: 2pm-4pm
location: HB310

• Week 11, Thursday 26th November
• Tom Kirk, UCLan
title: Subgroups of $\mathrm{SO}(2,\mathbb{Q}_{p})$
abstract: I will speak about the $p$-adic numbers and subgroups of $\mathrm{SO}(2,\mathbb{Q}_{p})$, as part of the research group's ongoing project. More concretely, we will also discuss the lifting of roots of polynomials using Hensel's Lemma.
time: 2pm-4pm
location: HB159

• Week 12, Thursday 3rd December
• Franz-Viktor Kuhlmann, University of Silesia, Katowice, Poland
title: In search of a complete axiomatization for $\mathbb{F}_{p}((t))$
abstract: I will give a survey of the attempts that have been made since the mid 1960s to find a complete recursive axiomatization of the elementary theory of ${\mathbb F}_p((t))$. This problem is still open, and I will describe the difficulties researchers have met in their search. Some new hope has been generated by Yu. Ershov's observation that ${\mathbb F}_p((t))$ is an "extremal" valued field. However, while his intuition was good, his definition of this notion was flawed. It has been corrected in a paper by Azgin, Kuhlmann and Pop, in which also a partial characterization of extremal fields was given. Further progress has been made in a recent paper, completed in joint work with S. Anscombe. The property of being an "extremal valued field" is both elementary and very natural, so it is an ideal candidate for inclusion in a (hopefully) complete recursive axiomatization for ${\mathbb F}_p((t))$. It implies an axiom scheme that was considered previously, which describes the behaviour of additive polynomials under the valuation. I will discuss why additive polynomials are crucial for the model theory of valued fields of positive characteristic. The open problems around extremal fields provide a good source of research projects of various levels of difficulty for young researchers.
time: 2pm-4pm
location: HB234

• Week 12, Saturday 5th December
• Lancashire-Yorkshire Model Theory Seminar
time: all day, beginning with arrival and coffee at 10.30am.
location: Foster Building, Lecture Theatre 2, UCLan

• Week 13, Thursday 10th December
• Davide Penazzi, UCLan
title: Local and global approaches to the topological dynamics of type spaces
time: 2pm-4pm
location: HB234