Lancashire Yorkshire Model Theory Seminar
A regular series of meetings of the model theorists in Leeds, Manchester and Preston, supported by the London Mathematical Society
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14.50  Start of the Zoom meeting  
15.0015.50  Gareth Boxall (Stellenbosch University)  Some finiteness results concerning points on a curve with a power on a curve Abstract: Let C_{1}, C_{2} ⊆ 𝔾_{m}^{N}(ℂ) be geometrically irreducible closed algebraic curves, with N ≥ 3. Suppose C_{1} is not contained in an algebraic subgroup of 𝔾_{m}^{N}(ℂ) of dimension 1 and C_{1} ∪ C_{2} is not contained in an algebraic subgroup of 𝔾_{m}^{N}(ℂ) of dimension 2. It is a conjecture that at most finitely many points x ∈ C_{1} have the property that there is a positive integer n such that x^{n} ∈ C_{2} and [n]C_{1} ⊈ C_{2}, where [n]C_{1} = {x^{n} : x ∈ C_{1}}. We prove some special cases of this conjecture. We build on work done by Bays and Habegger [3] in the case where C_{1} = C_{2} and make use of a height bound of Amoroso, Masser and Zannier [1]. We also apply work of Bays, Kirby and Wilkie [2] which gave an analogue of Schanuel’s conjecture for the operation of raising to an exponentially transcendental power. [1] Amoroso, F., Masser, D. and Zannier, U., Bounded height in pencils of finitely generated subgroups, Duke Math. J. 166 (no. 13): 2599–2642, 2017. [2] Bays, M., Kirby, J. and Wilkie, A., A Schanuel property for exponentially transcendental powers, Bull. London Math. Soc. 42 (no. 5): 917–922, 2010. [3] Bays, M. and Habegger, P., A note on divisible points of curves, Trans. Amer. Math. Soc. 367: 1313–1328, 2015. 
16.0016.50  Alexi Block Gorman (University of Illinois at UrbanaChampaign)  Definability on the Reals from Büchi Automata Abstract: Büchi automata are the natural analogue of finite automata in the context of infinite strings (indexed by the natural numbers) on a finite alphabet. We say a subset X of the reals is rregular if there is a Büchi automaton that accepts (one of) the baser representations of every element in X, and rejects the baser representations of each element in its complement. These sets often exhibit fractallike behavior—e.g., the Cantor set is 3regular. There are remarkable connections in logic to Büchi automata, particularly in model theory. In this talk, I will give a characterization of when the expansion of the real ordered additive group by a predicate for a closed rregular subset of [0,1] is modeltheoretically tame (dminimal, NIP, NTP2). Moreover, I will discuss how this coincides with geometric tameness, namely trivial fractal dimension. This will include a discussion of how the properties of definable sets vary depending on the properties of the Büchi automaton that recognizes the predicate subset. 
17.0017.50  Erik Walsberg (University of California, Irvine)  Largeness, the étale open topology, and tame topology of definable sets Abstract: Definable sets in algebraically, real, and padically closed fields are all wellbehaved with respect to the Zariski, order, and valuation topologies, respectively. In recent work with Will Johnson, Minh Chieu Tran, and Jinhe (Vincent) Ye, we have introduced the étale open topology over an arbitrary field K. This agrees with the Zariski, order, valuation topology over an algebraically, real, padically closed field, respectively. More recent work with Jinhe suggests that definable sets in basically all known modeltheoretically tame perfect fields are wellbehaved with respect to the étale open topology. I will discuss this, assuming minimal background from algebraic geometry. 
18.00  Logic Pub 
8.50  Start of the Zoom meeting  
9.009.50  Annalisa Conversano (Massey University Auckland)  Nilpotent groups definable in ominimal structures Abstract: Many authors in the past thirty years have shown strong analogies between groups definable in ominimal structures and real Lie groups, especially in the compact case. For nilpotent groups, not necessarily definably compact, it is possible to find strong similarities even with the smaller class of real algebraic groups. Some recent results about this analogy will be presented in this talk, including the fact that linear algebraic groups are the only nilpotent Lie groups that can be defined in an ominimal expansion of the real field. 
10.0010.50  Christian d'Elbée (Hebrew University of Jerusalem)  Title: Dpminimal integral domains. Abstract: (joint with Yatir Halevi) As expected from the classification of dpminimal fields, dpminimal integral domains are close to be valuation domains, but not always. The are local, divided in the sense of Akiba, and every localisation at a nonmaximal prime ideal is a valuation domain. Furthermore, a dpminimal integral domain is a valuation ring if and only if its residue field is infinite or its residue field is finite and its maximal ideal is principal. I will present these results as well as some examples of dpminimal domains which are not valuation domains. If time allows it, I will also talk about a generalisation of a result of Echi and Khalfallah on the prime spectrum of the ring of bounded elements of the hyperreals. 
11.0011.50  Tingxiang Zou (University of Münster)  Title: Geometric random graph Abstract: Geometric random graphs are graphs on a countable dense set of some underlying metric space such that locally in any ball of radius one, it is a random graph. The geometric random graphs on ℝⁿ and on circles have been studied by probabilists and graph theorists. In this talk we will present some model theoretic views. In particular, we will show that under some mild assumptions, the geometric random graphs based on a fixed metric space will have the same theory. We will also talk about some geometric properties of the underlying metric space that can be recovered from the graphs. This is a work in progress joint with Omer BenNeria and Itay Kaplan. 
12.00  Logic Lunch 
14.50  Start of the Zoom meeting  
15.0015.50  Alexander Berenstein (Universidad de los Andes)  Title: Expansions of geometric theories as measurable structures Abstract: We say that a theory T is geometric if for any model $M\models T$ the algebraic closure satisfies the exchange property and T eliminates the quantifier $\exists^{\infty}$. Examples of these theories include SUrk one theories and dense ominimal theories. In this talk I will present the basic properties of these theories and some well known expansions like Hstructures and lovely pairs. We will consider the special case where the underlying theory is measurable (in the sense of Macpherson and Steinhorn) of SUrk one. Under these assumptions, the expansion as an Hstructure can be studied as a generalized measurable structure whose dimension has values in $\omega^2$. This is joint work with García and Zou. 
16.0016.50  Gabriel Conant (Cambridge)  Title: NIP approximate groups and arithmetic regularity Abstract: I will present recent work with Anand Pillay on the structure of finite approximate groups satisfying a local NIP assumption. Our results can be seen as a unification of work of Breuillard, Green, and Tao on the structure theory of approximate groups, and the modeltheoretic study of "tame” arithmetic regularity. 
17.0017.50  Samaria Montenegro Guzman (Universidad de Costa Rica)  Title: Definable groups in PRC fields Abstract: This is a joint work with Alf Onshuus and Pierre Simon. We will study the class of pseudo real closed fields (PRCfields) from a model theoretical point of view. PRC fields were introduced by Prestel and Basarav as a generalization of real closed fields and pseudo algebraically closed fields, where we admit having several orders. We know that the complete theory of a bounded PRC field (i.e., with finitely many algebraic extensions of degree m, for each m > 1) is NTP2 and we have a good description of forking. In this talk we will focus in the groups with fgeneric types definable in bounded PRC fields. The main theorem is that such a group is isogeneous with a finite index subgroup of a quantifierfree definable groups. This generalizes similar results proved by Hrushovski and Pillay for (not necessarily fgeneric) groups definable in both pseudo finite fields and real closed fields. 
18.00  Logic Pub 
10.3011.00  Arrival and coffee  
11.0012.00  Isabel Müller (Imperial)  Stationary Independence and Symmetric Indivisibility Abstract: In 2012 Tent and Ziegler introduced the notion of a Stationary Independence Relation (SIR) and used this tool to study the normal subgroup structure of homogeneous structures. In 2016, we used the existence of an SIR to establish the universality of automorphism groups of the corresponding structures. Recently, in his PhD thesis, Meir introduced and studied lexicographic products of relational first order structures to answer questions about symmetric indivisibility. In this talk, we will introduce the notions and results mentioned above, show how they can be combined and state some open questions around the area. This is work in progress with Nadav Meir. 
12.0013.00  Bea AdamDay (Leeds)  Membership Graphs of Models of AntiFoundation Abstract: It is known that if we take a countable model of ZFC and symmetrise the membership relation, then we obtain the Random Graph. It turns out that doing so in AntiFoundational set theory yields the ``Random Loopy Graph'': the Fra\"iss\'e limit of finite graphs with selfedges. However, if one instead considers the \emph{doublemembership relation}, $x\in y\in x$, then the resulting graph is much more complicated. I will discuss properties of these graphs and their theories, presenting some results from two papers, joint with Peter Cameron and with John Howe and Rosario Mennuni. 
13.0014.30  Lunch  
14.3015.30  Gareth Jones (Manchester)  Powers are easy to avoid Abstract: Suppose that a set is definable in the expansion of the real field by restricted analytic functions, and is also definable in the expansion of the real field by the restricted exponential function together with all real power functions. Then the set is definable using just the restricted exponential function. So additional exponents can be avoided. I will discuss the general result behind this, and how it can be seen as a polynomially bounded version of an old conjecture of van den Dries and Miller. This is joint work with Olivier Le Gal. 
15.3016.00  Coffee  
16.0017.00  Sylvy Anscombe (UCLan)  A newish view of Cohen rings, complete discrete valuation rings, and NIP 
17.00  Pub and Dinner 
10.3011.00  Arrival and coffee  
11.0012.00  Jan Dobrowolski (Leeds)  Elementary Equivalence Theorem for pseudo algebraically closed structures Abstract We generalise a wellknown theorem saying that two PAC fields are elementarily equivalent if a suitable isomorphism of their Galois groups exists, to the context of pseudo algebraically closed structures. This is a joint work with D. Hoffmann and J. Lee. 
12.0013.00  Nadav Meir (Imperial)  Pseudofinite sets, pseudoominimality Abstract: Given a language L, the class of ominimal Lstructures is not elementary, e.g., an ultraproduct of ominimal structures need not be ominimal. This fact gives rise to the following notion, introduced by Hans Schoutens: Given a language L, an Lstructure is pseudoominimal if it satisfies the common theory of ominimal Lstructures. Of particular importance in pseudoominimal structures are pseudofinite sets. A definable set in an ordered structure is pseudofinite if it is closed, bounded and discrete. Many results from ominimality translate to pseudoominimality by replacing finite with pseudofinite. We will review the key role that pseudofinite sets play in pseudoominimality, as well as other firstorder properties of ominimality such as definable completeness* and local ominimality**. Finally, we will see how pseudofinite sets can be used to answer two questions by Schoutens, one of them is whether there is an axiomatization of pseudoominimality by firstorder conditions on onevariable formulae only. This also partially answers a conjecture by Antongiulio Fornasiero. * An ordered structure is definably complete if every bounded definable subset has a supremum. ** An ordered structure is locally ominimal if, for every definable subset D and every point x, there is an interval I containing x such that the intersection of D and I is a finite union of intervals and points. 
13.0014.30  Lunch  
14.3015.30  Francesco Parente (Leeds)  Saturated Boolean ultrapowers, Keisler’s order, and universality of forcing extensions Abstract: In this talk, I will discuss some recent results at the interface between model theory and set theory. The first part will be concerned with modeltheoretic properties of ultrafilters in the context of Keisler’s order. I will use the framework of ‘separation of variables’, recently developed by Malliaris and Shelah, to provide a new characterization of Keisler’s order in terms of saturation of Boolean ultrapowers. Furthermore, I will show that good ultrafilters on complete Boolean algebras are precisely the ones which capture the maximum class in Keisler’s order, answering a question posed by Benda in 1974. In the second part of the talk, I will report on joint work with Matteo Viale in which we apply the above results to the study of models of set theory. In particular, our work aims at understanding the universality properties of forcing extensions. To this end, we analyse Boolean ultrapowers of $H_{\omega_1}$ in the presence of large cardinals and give a new interpretation of Woodin’s absoluteness results in this context. 
15.3016.00  Coffee  
16.0017.00  Vincenzo Mantova (Leeds)  Some unconditional results on exponentialalgebraic closure Abstract TBA 
17.00  Pub and Dinner 
10:3011:00  Arrival and Coffee 
11:0012:00  Talk by Piotr Kowalski. Title: Model theory of free operators in positive characteristics Abstract: This is joint work with Özlem Beyarslan, Daniel Hoffmann and Moshe Kamensky. We give algebraic conditions about a finite commutative algebra B over a field of positive characteristic, which are equivalent to the companionability of the theory of fields with ``Boperators'' (i.e. the operators coming from homomorphisms into tensor products with B). The notion of a Boperator includes derivations, endomorphisms and (truncated, noniterative) HasseSchmidt derivations. We show that, in the most interesting case of a local B, these model companions admit quantifier elimination in the ``smallest possible'' language and they are strictly stable. We also describe the forking relation there. 
12:0013:00  Question proposal session 
13:0014:30  Lunch 
14:3017:00  Question answer session and discussion 
17:00  Pub and dinner 
Venue: Foster Building, lecture theatre, UCLAN. The campus map can be found here.
10.3011.00  Arrival and coffee  
11.0012.00  Ulla Karhumaki (Manchester)  Definably Simple Stable Groups with Finitary Groups of Automorphisms Abstract We prove that infinite definably simple locally finite groups of finite centraliser dimension are simple groups of Lie type over locally finite fields. Then, we axiomatise some of the key properties of Frobenius maps under the name of finitary automorphism groups. This allows us to classify definably simple stable groups in the specific case when they admit such automorphism group. 
12.0013.00  Jonathan Kirby (University of East Anglia)  Existentially closed exponential fields Abstract: We characterise the existentially closed models of the theory of exponential fields. They do not form an elementary class, but can be studied using positive logic. We find the amalgamation bases and characterise the types over them. We define a notion of independence and show that independent systems of higher dimension can also be amalgamated. We extend some notions from classification theory to positive logic and position the category of existentially closed exponential fields in the stability hierarchy as NSOP_1. This is joint work with Levon Haykazyan 
13.0014.30  Lunch  
14.3015.30  Alexander Antao (Manchester)  Partial Skolemization of the real exponential ordered field Abstract: A programme of model theory is finding "natural'" mathematical structures with the properties of quantifier elimination, or the next best thing, model completeness. Some examples expanding the set of reals:

15.3016.00  Coffee  
16.0017.00  Omar León Sánchez (Manchester)  Isolated types in totally transcendental theories 
17.00  Pub and Dinner 
11.00  12.00 
Harry Schmidt (Manchester)  Mahler functions and ManinMumford for $G_m^n$
Abstract: I will report on work in progress on connections between algebraic independence of certain Mahler functions and the ManinMumford conjecture for the multiplicative group. 
12.00  13.00 
Tom Kirk (UCLan)  Definable Topological Dynamics in Metastable Theories. Abstract: We consider a dynamical system where a definable group $G$ acts on the space of complete types $S_{G}(M)$. Specifically, we will take $G$ to be an affine algebraic group definable in a metastable theory and consider the minimal ideals of this action. We give a full description for the Minimal Flows, and Ellis Group, of $SL_2(\mathbb{C}((t)))$, and note that this is not isomorphic to $G/G^{00}$; providing a negative answer as to whether metastability is a suitable weakening of a since disproven conjecture of Newelski. Further, we discuss recent work in $ACVF$ where $G$ admits a stably dominated / $fsg$ group decomposition (possibly with nontrivial intersection) and give a description of the Ellis Group in this setting. 
13.00  14.30 
Lunch  
14.30  15.30 
Julia Wolf (Cambridge)  The structure of stable sets in finite abelian groups. Abstract: We shall begin by explaining the idea behind the socalled "arithmetic regularity lemma" pioneered by Green, which is a grouptheoretic analogue of Szemerédi's celebrated regularity lemma for graphs with wideranging applications. We will then describe recent joint work with Caroline Terry (University of Chicago), which shows that under the natural modeltheoretic assumption of stability the conclusions of the arithmetic regularity lemma can be significantly strengthened, leading to a characterisation of stable subsets of finite abelian groups. In the latter part of the talk, we survey related work by various authors including Alon, Conant, Fox, Pillay, Sanders, Sisask, Terry and Zhao, further exploring this topic from both a combinatorial and a modeltheoretic perspective. 
15.30  16.00 
Tea/Coffee  Common Room 
16.00  17.00 
Marcus Tressl (Manchester)  On closed ordered differential fields.
Abstract: An ordered differential field is an ordered field K together with a derivation d:K > K; no interaction of d with the order is assumed. Michael Singer has shown that the existentially closed ordered differential fields (denoted CODF) are axiomatisable with quantifier elimination in the language of ordered differential rings. I will give an introduction to CODFs and report on some recent developments in the model theory of CODFs and its generalizations. 
17.00  Pub and Dinner 
10.30  11.00 
Arrival and coffee will be in the Physics Research Deck.  
11.00  12.00 
Pablo Cubides Kovacsics (Caen)  On isodefinability of curves in HrushovskiLoeser spaces
Abstract: Hrushovski and Loeser introduced a modeltheoretic version of the analytification of a quasiprojective variety over a nonarchimedean valued field. Their construction gives rise to a strict prodefinable set in general and to an isodefinable set in the case of curves. In this talk I will report on a joint work with Jérôme Poineau in which, focusing on the later case, we provide an alternative approach to endow the HrushovsiLoeser analytification of an algebraic curve with a definable structure. In particular, this allows us to get a complete description of the definable subsets of such curves. 
12.00  13.00 
Laura Capuano (Oxford)  Unlikely intersections and ominimality Abstract: The theory of ominimality has made a huge remark in arithmetic geometry in the study of the so called “problem of unlikely intersections”, starting with the alternative proof of ManinMumford conjecture due to Pila and Zannier. One of the main ingredients of the proof is a result of Pila about counting rational points of bounded height on subanalytic surfaces, which is a special case and predates the celebrated PilaWilkie theorem. Since then, there has been a lot of work centred around the ZilberPink conjecture, and PilaZannier “strategy” has been used to prove several results in this area in many different settings. In my talk, I will give a general overview about these problems, with a special regard to questions of unlikely intersections inside tori and families of abelian varieties. 
13.00  14.30 
Lunch  
14.30  15.30 
Zaniar Ghadernezhad (Imperial)  Minimality of automorphism groups of free homogeneous structures. Abstract: A topological group $G$ is called minimal if every bijective continuous homomorphism from $G$ to another Hausdorff topological group is a homeomorphism or equivalently, if $G$ does not admit a strictly coarser Hausdorff group topology; $G$ is called totally minimal if every continuous surjective homomorphism to a Hausdorff topological group is open. These minimality notions have been extensively studied in topological group theory and known for some cases for example the infinite permutation group and the unitary group. Automorphism groups of countable first order structures are topological groups and one could ask whether or not they are minimal. In an interesting work BenYaacov and Tsankov proved that automorphism groups of stable, $\omega$categorical structures are totally minimal. In this talk we investigate the minimality of automorphism groups of free homogeneous structures. This is a joint work with Javier de la Nues González. 
15.30  16.00 
Tea/Coffee  
16.00  17.00 
Philip Dittmann (Oxford)  Recovering Arithmetic from Galois Theory  a ModelTheoretic Perspective
Abstract: A common task in field arithmetic is recovering information about a field, e.g. about its orderings and valuations, from Galoistheoretic data. Modeltheoretic interpretability is one way to formalise such statements. I will present such an interpretation of Stone spaces of orderings and pvaluations in suitable Galois structures, applicable to wide classes of fields, for instance the class of all pseudo real closed and pseudo padically closed fields. An important part of this is finding a good modeltheoretic language for Galois theory. 
17.00  Pub and Dinner 
10.3011.00  Arrival and coffee  
11.0012.00  Victoria Gould (York)  ℵ_{0}categoricity for semigroups Abstract may be found here. 
12.0013.00  Mike Prest (Manchester)  Nori motives and model theory Abstract: Homology and cohomology theories attach algebraic and numerical invariants to varieties and schemes. There are many such (co)homology theories and the idea (of Grothendieck) is that there should be a universal such theory  one through which all the others factor. This would be an abelian category of "motives" built from a suitable category of varieties. In the 90s Nori gave a construction of a category with some of the desired features. A recent paper of BarbieriViale, Caramello and Lafforgue gives a much more direct construction, using (topostheoretic) model theory. BarbieriViale and I subsequently described an even more direct approach using (classicalstyle) model theory. In these approaches Nori motives are imaginary sorts in an appropriate language. I will talk about this and some current work with Luca BarbieriViale and Annette Huber. 
13.0014.30  Lunch  
14.3015.30  Luck Darnière (Angers)  Lattices of closed semialgebraic sets. Abstract: Let K be a padically closed field, X a semialgebraic set of dimension d defined over K and L(X) the lattice of semialgebraic subsets of X which are closed in X. We prove that the complete theory of L(X) is decidable (contrary to what happens over a real closed field) and eliminates the quantifiers in a certain language Lasc, the Lascstructure on L(X) being an extension by definition of the lattice structure. We classify these structures up to elementary equivalence, and get in particular that the complete theory of L(K^d) only depends on d, not on K nor even on p. 
15.3016.00  Coffee  
16.0017.00  Andrew BrookeTaylor (Leeds)  Generalised model theory from a category theory perspective Abstract: Shelah introduced the framework of Abstract Elementary Classes to generalise model theory beyond the first order. Parallel to this, in category theory the notion of accessible categories was developed with a similar aim. It has recently emerged that the two approaches are intimately related to each other. In this talk I will give an overview of this connection, with a particular eye to how set theory can contribute to the mix. 
17.00  Pub and Dinner 
10.3011.00  Arrival and coffee  
11.0012.00  Sam Dean (Glasgow)  Positive primitive formulas for sheaves Abstract: Others have defined what it should mean for a sheaf to sit inside another sheaf as a pure substructure. This is done in an algebraic fashion. But in the model theory of modules, we know well that this condition can be said in terms of pp formulas. Sheaves, not usually being 1storder structures, can't obviously be approached like this. Even when we do get a nice class of sheaves which are (secretly) 1storder structures, the answer we get for what the usual notion of purity means is geometrically wrong. I will give a notion of a pp formula for sheaves which fits with the geometric notion of purity, and explain what the remaining questions are. 
12.0013.00  Sasha Borovik (Manchester)  Permutation groups of finite Morley rank Abstract: I will introduce some basic concepts and ideas of this theory, and will survey latest results by Altinel, Berkman, Borovik, Deloro, and Wiscons (in various combinations of authors). 
13.0014.30  Lunch  
14.3015.30  Gabor Elek (Lancaster)  Limits of finite graphs via ultraproducts Abstract: I will show how to obtain the LovaszSzegedy resp. BenjaminiSchramm graph limits of dense resp. sparse graphs using ultraproducts and ultralimits. 
15.3016.00  Coffee  
16.0017.00  Gareth Jones (Manchester)  Pfaffian functions and elliptic functions Abstract: I will discuss work with Harry Schmidt in which we give a pfaffian definition of Weierstrass elliptic functions, refining a result due to Macintyre. The complexity of our definition is bounded by an effective absolute constant. As an application we give an effective version of a result of Corvaja, Masser and Zannier on a sharpening of ManinMumford for nonsplit extensions of elliptic curves by the additive group. We also give a higher dimensional version of their result. 
17.00  Pub and Dinner 
10:3011:00  Arrival and Coffee 
11:0012:00  Talk by Martin Hils. Title: Model theory of compact complex manifolds with an automorphism Abstract: One may develop the model theory of compact complex manifolds (CCM) with a generic automorphism in rather close analogy to what has been done for existentially closed difference fields, in important work by Chatzidakis and Hrushovski, among others. The corresponding first order theory CCMA is supersimple, and the Zilber trichotomy holds for "finitedimensional" types of SUrank 1. In the talk, I will present some results in CCMA in the spirit of geometric simplicity. Moreover, I will discuss the issue whether a given sort of CCM is stably embedded in CCMA. This is joint work with Martin Bays and Rahiim Moosa. 
12:0013:00  Question proposal session 
13:0014:30  Lunch 
14:3017:00  Question answer session and discussion 
17:00  Pub and dinner 
10.30  11.00 
Arrival and coffee  
11.00  12.00 
Isolde Adler(Leeds)  Testing logically defined properties on structures of bounded degree
Abstract: Property testing (for a property P) asks for a given input, whether it has property P, or is "far" from having that property. A "testing algorithm" is a probabilistic algorithm that answers this question with high probability correctly, by only looking at small parts of the input. Testing algorithms are thought of as "extremely efficient", making them relevant in the context of big data. We extend the bounded degree model of property testing from graphs to relational structures, and we discuss testability of firstorder logic and monadic secondorder logic in this model. This is joint work with Frederik Harwath. 
12.00  13.00 
Omar León Sánchez (Manchester)  Conditions for finiterank types to be isolated in omegastable theories (and applications) Abstract: In omegastable theories, isolated types play a crucial role; for instance, they are known to be dense in the (Stone) type space over any set of parameters. It is thus important to understand characterizations of such types in terms of more "algebraic" conditions. One potential condition is that of weakorthogonality. We will see that weakorthogonality together with analisability (to a given definable set) imply isolation. While this does not characterize isolated types, it does yield interesting applications in the theory of differential Hopf algebras and, more generally, HopfOre extensions (these notions will be explained). This is joint work with J. Bell and R. Moosa. 
13.00  14.30 
Lunch  
14.30  15.30 
Thomas QuinnGregson (York)  Homogeneity of Inverse Semigroups Abstract: The concept of homogeneity of relational structures has connections to model theory, permutation groups and combinatorics. A number of complete classifications have been obtained, including those for graphs, semilattices and posets. We may extend this definition by naming an arbitrary structure homogeneous if every isomorphism between finitely generated subsubstructures extends to an automorphism. The key to this extension is that connections with model theoretic properties such as quantifier elimination and $\aleph_0$categoricity remain. An inverse semigroup $S$ is a semigroup in which every element has a unique inverse, that is, if $a \in S$ then there exists a unique $b \in S$ such that $a = aba$ and $b = bab$, which we denote as $a^{1}$. It is clear that groups are inverse semigroups, as indeed are semilattices with binary operation of meet. Since an inverse semigroup can be viewed as either a semigroup or as a unary semigroup (a semigroup equipped with a basic unary operation), we obtain two concepts of homogeneity; homogeneous semigroups and homogeneous inverse semigroups. We discuss how the two concepts of homogeneity differ, and how the homogeneity of an inverse semigroup effects its substructure, in particular its semilattice of idempotents and maximal subgroups. We also consider the following question: Given a homogeneous group $G$, which homogeneous inverse semigroups contains $G$ as a maximal subgroup? This will be completely answered for the case where $G$ is finite and where $G$ is Hall's universal locally finite group. 
15.30  16.00 
Tea/Coffee  
16.00  17.00 
Jan Dobrowolski (Leeds)  Polish structures
Abstract: The notion of a Polish structure is a purely topological concept (it can be thought of as a Hausdorff topological space X equipped with a continuous action of a Polish group G), which is, however, inspired by model theory. After introducing the basic concepts and explaining in what way some modeltheoretic intuitions can be transferred to this setting, I will discuss the main directions of research and open problems related to that subject. 
17.00  Pub and Dinner 
10.3011.00  Arrival and coffee  
11.0012.00  Sonia L'Innocente (Camerino)  Irreducible generalised power series Abstract: A classical tool in the study of real closed fields are the fields K[[G]] of generalised power series (i.e., formal sums with wellordered support) with coefficients in a field K of characteristic 0 and exponents in an ordered abelian group G. A fundamental result by Berarducci ensures the existence of irreducible series in the subring of K[[G]] consisting of the generalised power series with nonpositive exponents. In this work, we are able to prove that all series in this subring can be factorized as a product of irreducibles and a "small" series, first in the case when the group is the additive group of real numbers and then, in the case of arbitrary groups. 
12.0013.00  Daoud Siniora (Leeds)  Ample Generics and Fraisse limits Abstract: The automorphism group of a countably infinite first order structure becomes a topological group when endowed with the pointwise convergence topology. We then can ask whether the automorphism group has 'ample generics'? By the work of Hodges, Hodkinson, Lascar, and Shelah, and later by Kechris and Rosendal, we can answer this question in the setting of homogeneous structures, or Fraisse limits, by examining the age of the structure. In this talk I will introduce ample generics, and an approach to show their existence for homogeneous structures. Moreover, I will discuss some group theoretic consequences of the existence of ample generics including the small index property, uncountable cofinality, and the Bergman property. 
13.0014.30  Lunch  
14.3015.30  Davide Penazzi (UCLan)  Topological dynamics in the padic world Abstract: I will provide a brief introduction on topological dynamics and model theoretic applications, i.e. when the flow is that of a group G acting on its type space S_G(M). I will then focus on the study of the case of SL_2(Q_p). In a joint work with Pillay and Yao we determine its minimal flows, the Ellis group and the universal minimal flow. 
15.3016.00  Coffee  
16.0017.00  Arno Fehm (Manchester)  Existentially definable henselian valuation rings with padic residue fields Abstract: Earlier joint work with Sylvy Anscombe gave us an abstract valuation theoretic condition characterizing those fields F for which F[[t]] is existentially 0definable in F((t)). In this talk I will report on joint work with Sylvy Anscombe and Philip Dittmann in which the study of this condition leads us to some beautiful results on the border of number theory and model theory. In particular, I will present and apply a padic analogue of Lagrange's Four Squares Theorem. 
17.00  Pub and Dinner 
10.30  11.00 
Arrival and coffee  
11.00  12.00 
Dario Garcia (Leeds)  Unimodularity unified
Abstract: Unimodularity was defined by Hrushovski, in his proof that a unimodular strongly minimal set is locally modular, thus generalising Zilber’s result thata locally finite strongly minimal set is locally modular. It was claimed in the same paper that unimodularity was equivalent to an a priori weaker notion known later as functional unimodularity. In an attempt to clarify the situation, Pillay and Kestner distinguished two types of functional unimodularity one for definable sets and one for typedefinable sets and studied their relationship in the context of strongly minimal structures. In this talk, I will present joint with Wagner where we introduce yet another variant called correspondence unimodularity (for types and for definable sets) and present several results describing the relationship between the different concepts. For instance, we show the variants of unimodularity for types coincide in omegastable theories, and all variants coincide for nonmultidimensional theories where the dimension is associated to strongly minimal types (e.g. strongly minimal theories or groups of finite Morley rank). 
12.00  13.00 
Franziska Jahnke (Münster)  Henselianity in the language of rings Abstract: (Joint work with Sylvy Anscombe) We consider four properties of a field K related to the existence of (definable) henselian valuations on K and on elementarily equivalent fields and study the implications between them. Surprisingly, the full pictures look very different in equicharacteristic and mixed characteristic. 
13.00  14.30 
Lunch  
14.30  15.30 
Erick Garcia Ramirez (Leeds)  Tangent cones and stratifications in RCVF Abstract: I will talk about tangent cones of definable sets in real closed valued fields. A notion of 'tstratification' will be introduce too and I will then explain how a tstratification of a definable set induces tstratifications on tangent cones. I will also discuss further interests on this subject. 
15.30  16.00 
Tea/Coffee  
16.00  17.00 
Antongiulio Fornasiero (Parma)  Nonelementary lovely pairs
Abstract: We present Lovely Pairs: expansions of a structure M with a predicate P for a "small" set (satisfying certain additional properties). Lovely pairs (a generalization of Poizat's "Belle paires") have been studied (in several contexts and under various names) for a long time. The prototypical cases are the real field R with P denoting the real algebraic numbers, or the complex field C with P a proper algebraically closed subfield. In the classical cases, P has always been an elementary substructure of M (the "elementary" lovely pairs). However, more recent works have considered other kind of structures that resemble lovely pairs, but where P is not an elementary substructure (e.g.: P a dense transcendence basis of R, or P a transcendence basis of C, or P a dense multiplicative subgroup of R* of finite rank). We will show that such "nonelementary" lovely pairs have much in common with the elementary ones. 
17.00  Pub and Dinner 
10:3011:00  Arrival and Coffee  
11:0012:00  Fabrizio Barroero (Manchester) 
Unlikely intersections in families of powers of elliptic curves Abstract: Let E_t be the Legendre elliptic curve of equation Y^2=X(X1)(Xt). In 2010 Masser and Zannier proved that, given two points on E_t with coordinates algebraic over Q(t), there are at most finitely many specializations of t such that the two points become simultaneously torsion on the specialized elliptic curve, unless they were already generically linearly dependent. One of the main ingredients of the proof is a result of Pila about counting rational points of bounded height on subanalytic surfaces, which is a special case and predates the celebrated PilaWilkie theorem. As a natural higherdimensional analogue, we considered the case of n generically independent points on E_t with coordinates algebraic over Q(t). Then there are at most finitely many specializations of t such that two independent relations hold between the specialized points. Here one needs a more sophisticated counting theorem: relying on results of Pila, we estimate the number of points on some subanalytic surfaces lying on certain linear affine varieties defined by equations with rational coefficients of bounded height. This is joint work with L. Capuano. 
12:0013:00  Davide Penazzi (Preston)  Existence Theorems for Differential Equations Abstract: We build on the article "Existence Theorems for Systems of Implicit Differential Equations" of Grill, Knebusch and Tressl; where it was shown that given a polynomial differential ideal of R{X_1,...X_n} which is semireal, then there exists an analytic map c from an interval I in R to R^N such that c solves the differential equations of the ideal (i.e. f(c(t))=0 for all f in the ideal and t in I). Our work aims at obtaining similar results for differential equations with initial value conditions (IVPs) and in a more general context: when R is the ring of convergent power series in one variable, i.e. for differential equations with power series coefficients. I will outline the results we have obtained so far and some of the ideas behind them. 
13:0014:30  Lunch  
14:3015:30  Ivo Herzog (Ohio State)  Universal *regular rings Abstract: Using the model theory of modules, we prove that if (R,i) is a ring with involution, then there exists a morphism $u: (R,i) \to (R',i'),$ with R' a *regular ring, that is universal, in the sense that any such morphism factors in a unique way through u. Recall that an involution i of a ring R is an antiautomorphism of order 2 and that a von Neumann regular ring R with involution is called *regular if for all r in R, $i(r)r \neq 0.$ For a commutative ring equipped with the identity involution, the existence of a universal *regular ring was proved by Olivier. Suppose that L is a split semisimple Lie algebra over a field k of characteristic 0. We will use a result from J.C. Jantzen's thesis together with a theorem of HarishChandra to prove that the universal enveloping algebra U(L) may be equipped with an involution i in such a way that the morphism of (U(L),i) into its universal *regular ring is an embedding. 
15:3016:00  Coffee  
16:0017:00  Vincenzo Mantova (Leeds)  Towards a composition on surreal numbers Abstract: In a recent work with Alessandro Berarducci, we have shown that surreal numbers admit the structure of a field of transseries with a compatible "simplest" derivation. This raises the question whether surreal numbers can also be interpreted as differentiable functions, forming in fact a nonstandard Hardy fields closed under composition. I will present the early partial results on this problem, with both positive and negative answers. This is joint work with Alessandro Berarducci. 
17:00  Pub and dinner 
10.3011.00  Arrival and coffee  
11.0012.00  Daniel Wolf (Leeds)  Rmacs and Lie coordinatisation Abstract: I will present the notion of an Rmac, a generalisation of the definition of an Ndimensional asymptotic class given by Elwes, Macpherson and Steinhorn in 2007. I will then go over my current efforts to try to adapt the work of Cherlin and Hrushovski on Lie Coordinatisation to the Rmac setting. Joint work with Sylvy Anscombe (UCLan), Dugald Macpherson (Leeds) and Charles Steinhorn (Vassar) 
12.0013.00  Rosie Laking (Manchester)  Pointed morphisms and the lattice of pp formulas 
13.0014.30  Lunch  
14.3015.30  Edith VargasGarcia (Leeds)  An introduction to the reconstruction of the topology on monoids of the rationals Abstract 
15.3016.00  Coffee  
16.0017.00  Alessandro Berarducci (Pisa)  Compact domination, ominimal homotopy and Pillay's conjectures Abstract: I will report on work Hrushovski, Peterzil, Pillay and Simon on NIP theories and compact domination and develop it further, yielding a new proof of Pillay's conjectures via an ominimal "nerve theorem". This is joint work with Alessandro Achille 
17.00  Pub and Dinner 
10:3011:00  Arrival and Coffee 
11:0012:00  Talk by Amador MartinPizarro. Title: Definable and interpretable groups in pairs of algebraically closed fields. Abstract: We will provide a characterisation of definable groups in a beautiful pair (K, E) of algebraically closed fields: every definable group projects, up to isogeny, onto the subgroup of Erational points of some algebraic group defined over E with kernel an algebraic group. If time permits, we will discuss the characterisation of interpretable groups. 
12:0013:00  Question proposal session 
13:0014:30  Lunch 
14:3017:00  Question answer session and discussion 
17:00  Pub and dinner 
10.30  11.00 
Arrival and coffee  
11.00  12.00 
Dugald Macpherson (Leeds)  Pseudofinite dimension and pseudofinite structures
Abstract: I will discuss recent joint work with Garcia and Steinhorn on a notion of pseudofinite dimension for definable sets in pseudofinite structures, introduced by Hrushovski and Wagner and developed further by Hrushovski. In particular, I will discuss conditions on pseudofinite dimension which ensure that a structure is simple, or supersimple, or stable, or that forking can be characterised by dimensiondrop. I will discuss examples, and some possible applications. 
12.00  13.00 
Lovkush Agarwal (Leeds)  The 11 Reducts of the Generic Digraph Abstract: Given two structures M and N, we say that N is a reduct of M if, intuitively speaking, N is a less detailed version of M or if N is obtained from M by discarding information. In this talk, I will describe what the reducts of the generic digraph are and time permitting will describe some aspects of the proof. 
13.00  14.30 
Lunch  
14.30  15.30 
Lorna Gregory (Manchester)  Interpretation functors, wild algebras and undecidability Abstract: In this talk I will present results about uniform interpretations between module categories over finite dimensional algebras. In particular, I will focus on attempts to prove a conjecture of Prest which says that if a finitedimensional $k$algebra is of wild representation type, a notion coming from representation theory, then it uniformly interprets $ Modk\langle x,y\rangle$ and hence has undecidable theory of modules. 
15.30  16.00 
Tea/Coffee  
16.00  17.00 
Charlotte Kestner (UCLan)  Some model theory of bilinear forms
Abstract: I will give a short introduction to geometric stability theory and independence relations, focussing on the tree properties. I will then introduce one of the main examples for general measureable structures, the two sorted structure of a vector space over a field with a bilinear form. I will state some results for this structure, and give some open questions. 
17.00  Pub and Dinner 
10:3011:00  Arrival and Coffee 
11:0012:00  Talk by Pierre Simon 
12:0013:00  Question proposal session 
13:0014:30  Lunch 
14:3017:00  Question answer session and discussion 
17:00  Pub and dinner 
10.3011.00  Arrival and coffee  
11.0012.00  Mike Prest (Manchester)  TBA 
12.0013.00  Immanuel Halupczok (Leeds)  Families of definable sets in the ordered group $\mathbb{Z}$ Abstract 
13.0014.30  Lunch  
14.3015.30  Ronnie Nagloo (Leeds)  On Transformations in the Painlevé family Abstract 
15.3016.00  Coffee  
16.0017.00  Ivan Tomašić (Queen Mary)  Applications of the twisted theorem of Chebotarev Abstract 
17.00  Pub and Dinner 
10.3011.00  Arrival and coffee  
11.0012.00  Charlotte Kestner (Preston)  NIP categories 
12.0013.00  Marcus Tressl (Manchester)  Externally definable sets in real closed fields 
13.0015.00  Lunch  
15.0016.00  Tamara Servi (Lisbon)  Quantifier elimination for generalised quasianalytic classes. Abstract 
16.0017.00  Andres ArandaLopez (Leeds)  Supersimple homogeneous 3graphs 
17.00  Pub and Dinner 