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.

### Spring 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!

### 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!

### 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.

### 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
**

title:*
Estrada index of graphs
*

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
**David Bradley-Williams, UCLan**

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

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

- Week 15, Monday 23rd January

title:

abstract:

time: 2pm-4pm

location: LE303 (Leighton)

- Week 16, Monday 30th January

title:

abstract:

time: 3pm-5pm

location: HB206 (Harris)

- Week 17, Monday 6th February

title:

abstract:

time: 3pm-5pm

location: HB206 (Harris)

- Week 18, Monday 13th February

title:

abstract:

time: 3pm-5pm

location: HB206 (Harris)

- Week 19, Monday 20th February

title:

abstract:

time: 3pm-5pm

location: HB206 (Harris)

- Week 20, Monday 27th February

title:

abstract:

time: 2pm-4pm

location: LE303 (Leighton)

- Week 21, Monday 6th March

title:

abstract:

time: 2pm-4pm

location: LE111 (Leighton)

- Week 22, Monday 13th March

title:

abstract:

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

title:

abstract:

time: 2pm-4pm

location: LE303 (Leighton)

- Week 24, Monday 27th March

no seminar

- Week 25, Monday 3rd April

title:

abstract:

time: 2pm-4pm

location: LE303 (Leighton)

- Week 1, Monday 26th September

title:

time: 2pm-4pm

location: KM015 (Kirkham)

- Week 2, Monday 3rd October

time: 2pm-4pm

location: HB159 (Harris)

- Week 3, Monday 10th October

time: 2pm-4pm

location: HB159 (Harris)

- Week 4, Monday 17th October

time: 2pm-4pm

location: HB159 (Harris)

- Week 5, Monday 24th October

no seminar

- Week 6, Monday 31st October

time: 2pm-4pm

location: HB159 (Harris)

- Week 7, Monday 7th November

time: 2pm-4pm

location: HB159 (Harris)

- Week 8, Monday 14th November

time: 2pm-4pm

location: LH325 (Livesey)

- Week 9, Monday 21st November

time: 2pm-4pm

location: HB159 (Harris)

- Week 10, Monday 28th November

time: 2pm-4pm

location: HB159 (Harris)

- Week 11, Monday 5th December

time: 2pm-4pm

location: HB159 (Harris)

- Week 12, Monday 12th December

time: 2pm-4pm

location: HB159 (Harris)

- Week 33, Thursday 14th July

(

title:

abstract:

time: 2pm-3pm

location: LE002 (Leighton)

title:

abstract:

time: 3pm-5pm

location: LE002 (Leighton)

title:

abstract:

time: 2pm-4pm

location: HB303 (Harris)

title:

abstract:

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

title:

abstract:

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:

title:

abstract:

time: 2pm-4pm

location: LE111 (Leighton)

time: 11am Friday 6th of May - 5.30pm Saturday 7th of May

location: LE003/LE111 (Leighton), University of Central Lancashire

title:

abstract:

time: 2pm-4pm

location: LE002

location: Manchester

title:

abstract:

time: 2pm-4pm

location: HB310

title:

abstract:

time: 2pm-4pm

location: BB142a

title:

abstract:

time: 2pm-4pm

location: HA135a

title:

abstract:

time: 2pm-4pm

location: HB310 (Harris)

title:

abstract:

time: 12pm-2pm

location: HB010 (Harris)

title:

abstract:

time: 2pm-4pm

location: HB303 (Harris)

title:

abstract:

time: 2pm-4pm

location: FBLT4 (Foster)

location: Manchester

title:

abstract:

time: 2pm-4pm

location: HB303 (Harris)

title:

time: 2pm-4pm

location: LE303

title:

time: 2pm-4pm

location: LH102

abstract:

title:

abstract:

time: 2pm-4pm

location: HB310

title:

abstract:

time: 2pm-4pm

location: GR347

title:

abstract:

time: 2pm-4pm

location: HB159

title:

abstract:

time: 2pm-4pm

location: HB234

title:

abstract:

time: 2pm-4pm

location: HB310

title:

abstract:

time: 2pm-4pm

location: HB159

title:

abstract:

time: 2pm-4pm

location: HB234

time: all day, beginning with arrival and coffee at 10.30am.

location: Foster Building, Lecture Theatre 2, UCLan

title:

time: 2pm-4pm

location: HB234