Presentation Details 

Alòs, Elisa 
On the relationship between implied volatilities and volatility swaps: a Malliavin calculus approach 
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This work is devoted to studying the difference between the fair strike of a volatility swap and the atthemoney implied volatility (ATMI) of a European call option. It is wellknown that the difference between these two quantities converges to zero as the time to maturity decreases. We make use of a Malliavin calculus approach to derive an exact expression for this difference. This representation allows us to establish that the order of the convergence is different in the correlated and in the uncorrelated case, and that it depends on the behavior of the Malliavin derivative of the volatility process. In particular, we will see that for volatilities driven by a fractional Brownian motion, this order depends on the corresponding Hurst parameter H. Moreover, in the case H ≥ 1/2, we develop a modelfree approximation formula for the of the volatility swap, in terms of the ATMI and its skew.
(Joint work with Kenichiro Shiraya, University of Tokyo) 
Antoine, Ramon 
The Cuntz semigroup for ultraproduct C*algebras 
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The Cuntz semigroup is an invariant for C*algebras constructed out of positive elements in a similar way as the Murray von Neumann Semigroup of projections. It naturally carries the ideal structure of the algebra, and hence is an appropriate candidate to address the possible classification of nonsimple C*algebras. The said invariant lies in a category of positively ordered monoids with a rich ordered topological structure.
I will present an overview of the category and its relation to C*algebras, focusing on a powerful functorial construction that leds to the description of Cu a colsed monoidal category, or also helps in the computation of the invariant for ultraproducts of C*algebras. 
Ara, Pere 
PLENARY TALK: Topological paradoxical decompositions and partial actions TALK 2 (Algebra and Applications session) Steinberg algebras and the realization problem 
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PLENARY ABSTRACT: The BanachTarski Paradox asserts that the unit ball of $mathbb R ^3$ is paradoxical with respect to the action of the group of all the isometries of $mathbb R ^3$. I will recall the general notion of paradoxicality for an action of a (discrete) group $G$ on a set $X$. An important result in the area is Tarski's Theorem, that establishes a dichotomy result for an action $Gcurvearrowright X$ as above: Given a subset $E$ of $X$, either $E$ is paradoxical or there is an invariant finitely additive measure $mu$ on $mathcal P (X)$ such that $mu (E) = 1$. Recently, the question of whether such a dichotomy holds for actions of groups by homeomorphisms on topological spaces has been raised. I will recall a recent result showing that Tarski's dichotomoy does not extend to this setting. This
uses, amongst other things, the theory of partial actions.
TALK 2 ABSTRACT: Leavitt path algebras associated to directed graphs have been used in [AB] to obtain a realization result for a class of conical
refinement monoids, as the monoids of finitely generated projective modules of von Neumann regular rings.
Steinberg algebras [Steinberg] associated to ample étale topological groupoids constitute an interesting generalization of Leavitt path algebras.
In workinprogress with J. Bosa, E. Pardo and A. Sims, we have associated an ample étale topological groupoid $mathcal G (mathbb P)$ to any
finite poset $mathbb P$, in such a way that, for any field $K$, a suitable universal localization $Sigma ^{1} A_K(mathcal G(mathbb P))$
of the Steinberg algebra $A_K(mathcal G(mathbb P))$ is von Neumann regular, and satisfies that its monoid of finitely generated projective modules
is isomorphic to the abelian monoid $M(mathbb P)$ generated by $mathbb P$ with defining relations $p+q=p$ if $q<p$. This algebra is shown to be isomorphic
to the algebra constructed in [Aposet]. We aim to generalize this construction to obtain a realization theorem for any finitely generated conical refinement monoid.
[Aposet] P. Ara, The regular algebra of a poset, Trans. Amer. Math. Soc. 362 (2010), 15051546.
[AB] P. Ara, M. Brustenga, The regular algebra of a quiver, J. Algebra 309 (2007), 207235.
[Steinberg] B. Steinberg, A groupoid approach to discrete inverse semigroup algebras, Adv. Math. 223 (2010), 689727. 
Baker, Andrew 
Realisations of the Joker 
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The Joker module is an important module over the finite subalgebra A(1)^* of the mod 2 Steenrod algebra. Amongst other things it gives
the unique torsion element of the Picard group of invertible elements of the stable A(1)^* modules.
I will discuss realisations of the Joker as A^* modules and as cohomology of spectra. If there is time I will discuss some generalisations and a
nonexistence result.
[This is partly joint work with Peter Eccles] 
Bavula, Vladimir 
Classical left regular left quotient ring of a ring and its semisimplicity criteria 
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Goldie's Theorem (1958, 1960) is a semisimplicity criterion for the classical left quotient ring of a ring. Semisimplicity criteria are given for the classical left regular left quotient ring of a ring. As a corollary, two new semisimplicity criteria for the classical left quotient ring are obtained (in the spirit of Goldie). Applications are given for the algebra of polynomial integrodifferential operators. 
Boyd, Rachael 
Homological stability for Artin groups 
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Many interesting sequences of groups satisfy the phenomenon known as "homological stability". Examples include the symmetric groups, braid groups, and mapping class groups of surfaces. I will provide an introduction to this topic and talk about my current research on homological stability for certain families of Artin groups, which extends the known cases of stability for A_n, B_n and D_n to more general families of groups. I will explain the problem and the approach I am using, which exploits geometric properties of the Artin monoid. 
Brendle, Tara 
A survey of normal subgroups of mapping class groups 
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Abstract: The mapping class group of a surface has an incredibly rich normal subgroups structure. For this reason, a traditional classification theorem for normal subgroups of mapping class groups, in the form of a complete list of isomorphism types, is almost certainly out of reach. However, we might hope to gain some insight into this structure via certain invariants of normal subgroups. In this talk, we will view the automorphism group as an invariant of normal subgroups, and give a survey of known examples providing evidence for a conjectured classification of normal subgroups, including constructions due to DahmaniGuirardelOsin and ClayMangahasMargalit, as well as recent joint work with Dan Margalit. 
Brown, Ken 
Azumaya algebras and discriminant ideals 
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I will explain how discriminant ideals can be used to describe the Azumaya locus of a prime affine kalgebra (k a field) which is a finite module over its centre. This is recent joint work with Milen Yakimov. 
Calvo Schwarzwälder, Marc 
Heat transfer and phase change at the nanoscale 
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It is widely known that heat transport at the nanoscale cannot be described in the same manner as for macroscopic objects. There exists a large number of experimental observations which show that many thermodynamic properties become sizedependent at the nanoscale and a mathematical description of this dependence is highly desired. Furthermore, most of the mathematical models describing heat transfer processes are based on Fourier's law, which states that the heat flux is proportional to the temperature gradient. However, it has been shown that the classical equations break down at the nanoscale and thus other approaches are necessary to correctly describe heat conduction at small length or short time scales. The GuyerKrumhansl equation is a very popular extension to the classical Fourier law that incorporates memory and nonlocalities, which become significant at the nanoscale. In this talk we present a new mathematical model for the melting temperature of nanoparticles. In addition, we will discuss the effect of the GuyerKrumhansl equation on solidification processes. 
Cantero Morán, Federico 
Rational homotopy theory of Thom spaces 
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In this talk we give rational homotopy models of Thom spaces of vector bundles, by showing that the Thom isomorphism descends to the level of commutative differential graded algebras, generalising work of Fèlix, Oprea and Tanrè. Then, we use this to study the cohomology of spaces of submanifolds. This is joint work with Urtzi Buijs and Joana Cirici. 
Casacuberta, Carles 
Lifting cellularizations to module spectra 
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The fact that exact localizations of spectra lift to (strict) modules over any (structured) ring spectrum was proved in 2010 by means of suitable model structures in categories of algebras over coloured operads, and later extended to cellularizations with similar methods. In a recent joint work with Oriol Raventós and Andy Tonks we give an easier proof of the same facts and show that, in fact, Acellularizations of Emodules coincide with cellularizations with respect to the smash product of A and E. This is particularly relevant when E is an EilenbergMac Lane spectrum. More generally, Acellularizations coincide with TAcellularizations whenever they lift to algebras over a monad T in a model category. 
Casals, Roger 
Legendrians, mirror symmetry and topological strings 
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In this talk we discuss the role of Legendrian submanifolds in the conifold transition and mirror symmetry. In particular we first review how symplectic field theory, incarnated in the form of Legendrian contact homology, interacts with the large N transition via the AganacicEkholmNgVafa formulation. Then we shall introduce a combinatorial algorithm that computes a class of these pseudoholomorphic Legendrians invariants in the resolved conifold, which themselves relate to the open topological strings in the deformed conifold. 
Casanellas, Marta 
Algebra, Geometry, and Phylogenetics 
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Many of the usual statistical evolutionary models can be viewed as algebraic varieties and a deep understanding of these varieties may solve open problems in phylogenetics. We show how different mathematical areas such as linear and commutative algebra, algebraic geometry, group representation theory, or numerical methods show up when one studies these varieties. Moreover, we prove that an indepth geometric study leads to improvements on phylogenetic reconstruction methods. We illustrate these improvements by showing results on simulated data and by comparing them to widely used methods in phylogenetics. In order to follow this talk it is not required a previous knowledge on algebraic varieties or phylogenetics. 
Castellana, Natalia 
Local analysis in groups and classifying spaces 
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The nature of the classifying space of a topological group allows both an homotopic and algebraic analysis from a local point of view by isolating the relevant information to a prime p. This duality is present in the notion of plocal finite group or plocal compact group introduced by Broto, Levi and Oliver. An algebraic object that contains the essential information to describe the homotopy type of their pcompleted classifying spaces. Conversely, given the classifying space one recovers the algebraic object.
In this talk I will explain how these new concepts and technology provide purely local proofs of results on the sructure of the cohomology of a finite group and therefore they extend to this more general class of spaces. 
Corcuera, José Manuel 
On the equilibrium under imperfect competition and privilege information. 
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In this talk we will discuss the different equilibrium situations arising in an order driven market model with different traders with different information.
The framework is that proposed by Kyle in 1982 in a discrete time setting and extended by Back to a continuous time setting in 1995. We will see how filtering, enlargement of filtrations and optimization under imperfect competition play a role in the equilibrium problem. The talk is based mainly in joint work with Giulia di Nunno and Bernt Oksendal. 
Cruise, James 
Electricity networks, novel challenges 
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A move towards the decarbonisation of power networks is leading to increased variability and uncertainty on the both the demand and supply side. In this talk we will introduce the audience the power network, and differences to other well studied networks. As part of this we will describe a set of open problems on a range of scales from microgrids to transmission networks. 
Davie, Alexander 
Multivariate CornishFisher expansions and optimal transport 
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For a random variable X with an approximately normal distribution, where the deviation from normality is measured by a small parameter, one often has an Edgeworthtype expansion for the distribution or density function. There is then a standard procedure for expressing X as f(Y) where Y is normal and f has an expansion, known as a CornishFisher expansion, in powers of the parameter. This expansion is determined uniquely by the Edgeworth expansion.
The extension of this theory to a random vector is complicated by the fact that the CornishFisher expansion is no longer unique. We describe a procedure for making a specific choice for this expansion, which is motivated by, and has applications to, problems in optimal transport. 
Delgado, Jorge 
Extending Stallings pullbacks 
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The classic theory of Stallings describing subgroups of the free group as automata provides a neat way of understanding the intersection of two subgroups $H_1,H_2 leqslant F_n$. Namely, the automaton describing the intersection $H_1 cap H_2$ is the core of the pullback (an easily constructible graph product) of the automata associated to $H_1$ and $H_2$. Since, the product of two finite graphs is always finite, this automatically shows Howson property for free groups. Moreover, this construction allows to easily find bases for the intersection, and provides the classic Hanna Neumann bound for its rank: $operatorname{rk}(H_1 cap H_2) 1 leqslant 2 (operatorname{rk}H_11) (operatorname{rk}H_21)$.
We extend the former description (of subgroups as automata) to freeabelian by free groups ($mathbb{Z}^m rtimes F_n$) by admitting abelian labels in the edges, and modifying consequently the folding process. This approach provides an appealing geometric description of intersections in the direct product case, which denies both Howson's property and any ``Hanna Neumannlike'' bound within this family.
*Joint work with Enric Ventura. 
Estrada, Gissell 
SHORT TALK: Fractional PatlakKellerSegel equations for chemotactic superdiffusion 
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The long range movement of certain organisms in the presence of a chemoattractant can be governed by long distance runs, according to an approximate Levy distribution. This article clarifies the form of biologically relevant model equations: We derive PatlakKellerSegellike equations involving nonlocal, fractional Laplacians from a microscopic model for cell movement. Starting from a powerlaw distribution of run times, we derive a kinetic equation in which the collision term takes into account the long range behaviour of the individuals. A fractional chemotactic equation is obtained in a biologically relevant regime. Apart from chemotaxis, our work has implications for biological diffusion in numerous processes. 
Gabe, James 
A new proof of the KirchbergPhillips theorem 
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In the mid 90's, Kirchberg and Phillips independently proved, that separable, nuclear, purely infinite, simple C*algebras in the UCT class are classified by their Ktheory. For most people, this deep theorem has been considered a black box. I will outline a new, shorter and more elementary proof of the theorem. This proof also works in the ideal related setting, and thus also reproves Kirchberg's classification of separable, nuclear, strongly purely infinite C* algebras. 
Garreta, Albert 
Systems of equations in nilpotent groups 
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Recently, there have been developments in the study of systems of equations over nilpotent groups. In 2014 it was proved by Duchin, Liang, and Shapiro that these are undecidable over any nonabelian free nilpotent group N. The underlying principle in their proof is that the ring of integers Z is interpretable by equations in N. Intuitively speaking, this means that the addition and multiplication operation of Z can be “expressed” in N using only the group operation of N. Since, by Hilbert’s 10th problem, equations over Z are undecidable, it follows that they are also undecidable over N.
In this talk I will present the following more general result: For any nonvirtually abelian nilpotent group G, there exists a ring of algebraic integers R(G) that is interpretable by equations in G. The question of whether equations over such ring are decidable is an open problem of number theory, and it is conjectured that they never are. After introducing and commenting this result, I will provide applications of it to other families of groups, and I will also address the question of when R(G) = Z.
This is joint work with Alexei Miasnikov and Denis Ovchinnikov. 
Gasull, Armengol 
Algebraic traveling wave solutions 
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In this talk we introduce the algebraic traveling wave solutions for general nth order partial differential equations. All examples of explicit traveling waves known by the speaker fall in this category. Our main result proves that algebraic traveling waves exist if and only if an associated ndimensional first order ordinary differential system has some invariant algebraic curve. As a paradigmatic application we prove that, for the celebrated FisherKolmogorov equation, the only algebraic traveling waves solutions are the ones found in 1979 by Ablowitz and Zeppetella. To the best of the speaker's knowledge, this is the first time that this type of results has been obtained. This talk is based on a joint work with Hector Giacomini. 
Gibson, Gavin 
Developing tools for statistical inference using generalised data augmentation 
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In Bayesian statistics Markov chain Monte Carlo (MCMC) is a key tool for computing posterior distributions of model parameters. For partially observed systems, MCMC is often performed using data augmentation whereby the joint posterior of parameters and unobserved data components is investigated. In this talk we outline how the ideas underpinning MCMC and data augmentation can be applied to formulate new methodological appoaches to problems in statistical inference that go beyond the Bayesian setting. Examples will include: the development of tools for model assessment that blend classical and Bayesian thinking; extensions of Fiducial inference and its connections with Bayesian methods; new perspectives on the relationship between classical point estimation and Bayesian inference. The work described is joint with Ben Hambly, George Streftaris, Stan Zachary, Max Lau and David Thong. 
Gilbert, Nick 
Geometric group theory and inverse semigroups: connections and contrasts 
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The title has been chosen to recall a masterly survey  "Groups and semigroups: connections and contrasts"  by John Meakin, given at the GroupsSt.Andrews conference in 2005. We shall look at some ideas central to geometric group theory, such as the Cayley graph, Stallings folding, formal languages in groups, and presentation 2complexes, and see how they translate into the study of inverse semigroups. We shall find some expected similarities, and some surprising differences. 
Gondzio, Jacek 
Continuation in Optimization: From interior point methods to Big Data 
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In this talk we will discuss similarities between two homotopybased approaches:
1. (inexact) primaldual interior point method for LP/QP, and
2. preconditioned Newton conjugate gradient method for big data optimization.
Both approaches rely on clever exploitation of the curvature of optimized functions and deliver efficient techniques for solving optimization problems of unprecedented sizes.
We will address both theoretical and practical aspects of these methods applied to solve various inverse problems arising in signal processing. 
Greenfeld, Be'eri 
TALK 1: Residual girth of algebras. SHORT TALK: Growth of Algebras 
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TALK 1 ABSTRACT: Residual girth of finitely generated (residually finite) groups measures how large should be finite quotients into which the nball of the Cayley graph injects. While for a general group the residual girth might grow arbitrarily fast, bounds are known for special classes of groups (e.g. nilpotent, linear etc.) We study an analogous notion for algebras. We compare the residual girth of a group with that of its group algebra, showing they need not coincide. We prove that for special classes of algebras (e.g. representable algebras) the residual girth is asymptotically equivalent to the growth in the sense of the GKdimension. Examples are constructed to show that without special assumptions on the algebra, its residual girth can be arbitrarily fast.
SHORT TALK ABSTRACT: We review some results on the possible growth rates of finitely generated algebras with special properties. In particular, we affirmatively answer a conjecture by Alahmadi, Alsulami, Jain and Zelmanov on possible growth rates of primitive algebras. Results on simple algebras are given too. 
Hamblin, Luke 
SHORT TALK: Tilings and their C*Algebras 
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A tiling is a decomposition of Euclidean space into pieces that fit together without gaps or overlaps. The most basic examples consist of periodic structures, such as a tiling by unit cubes, which can be used to model the structure of a crystal of table salt. More interesting examples can be obtained by requiring that our tiles are unable to tessellate the space in a periodic manner. Physical realisations of these aperiodic tilings are called quasicrystals and were first created in the lab in 1984, with the first naturally occurring specimen discovered in 2009. In this talk I will provide an introduction to tiling theory, and explain how to associate a C*algebra to a tiling. 
Herbera, Dolors 
Pure projective modules over (one dimensional) commutative noetherian local rings: Comparing with the completion 
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A module is pure projective if it is isomorphic to a direct summand of a direct sum of finitely presented modules. There is a big amount of work done on the study of finitely generated (hence, finitely presented) modules over commutative noetherian rings, but not so much is known on direct summands of infinite direct sums of such modules. In this talk we will give some insight on this problem.
Let $R$ be a local commutative noetherian ring. If $R$ is complete then all pure projective modules are direct sums of finitely generated modules, but we give plenty of examples showing that this is far from true in the noncomplete case. However, there is still a close relation between pureprojective $R$modules and pure projective $hat R$modules, as we can prove that two pureprojective modules $P$ and $Q$ are isomorphic as $R$modules if and only if $Potimes _Rhat Rcong Qotimes _Rhat R$ as $hat R$modules.
The difficult question is to determine which pureprojective $hat R$modules are extended from $R$modules. We will present an answer to this problem when $R$ is local, one dimensional and for direct summands of an arbitrary direct sum of copies of a single finitely generated $R$module $M$; that is we determine how are the objects of the category $mathrm{Add}, (M)$. The results by Herbera and Prihoda describing all projective modules over, non necessarily commutative, noetherian, semilocal rings, are our starting point to deal with such problems. However, the particular situation we are focusing on needs further developments and gives an interesting and intriguing richer structure.
The results presented are part of an ongoing project with Pavel Prihoda and Roger Wiegand.
This work is partially supported by the grant MINECO MTM201453644P (Spain). 
Higham, Des 
Nonbacktracking Walks for Network Science 
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The notion of a nonbacktracking walk around a graph has been introduced and studied, sometimes independently, over several decades in various areas of physics, computer science, random matrix theory, stochastic analysis, number theory and graph theory. In particular, nonbacktracking walks have recently been shown to offer advantages over traditional walks in the construction of centrality measures used by network scientists. In this talk, focusing on this network science perspective, I will discuss how the combinatorics of nonbacktracking walks, and appropriate generalizations, can lead to effective computational tools. The mathematical techniques used to develop and analyse these algorithms involve ideas from graph theory, applied linear algebra, marix polynomial theory, matrix function theory and sparse matrix computation. Illustrations will be given on real data sets. This is joint work with Francesca Arrigo (Strathclyde), Peter Grindrod (Oxford) and Vanni Noferini (Essex). 
Howie, Jim 
Cyclic symmetry in Heegard splittings of 3manifolds (Topology special session) 
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I will report on recent joint work with Gerald Williams, aimed at a classification of cyclically symmetric group presentations which are spines of 3manifolds. 
Huguet, Gemma 
Mathematical tools for phase control in transient states of neuronal oscillators 
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Oscillations are ubiquitous in the brain. Although the functional role of oscillations is still unknown, some studies have conjectured that the information transmission between two oscillating neuronal groups is more effective when they are properly phaselocked. Thus, studying phase dynamics is relevant for understanding neuronal communication.
The phase response curve (PRC) is a powerful and classical tool to study the effect of a perturbation on the phase of an oscillator, assuming that all the dynamics can be explained by the phase variable. However, factors like the rate of convergence to the oscillator, strong forcing or high stimulation frequency may invalidate the above assumption and raise the question of how is the phase variation away from an attractor.
In this talk, I will present powerful computational techniques to perform the effective computation of the phase advancement when we stimulate an oscillator which has not reached yet the asymptotic state (a limit cycle). I will show some examples of the computations we have carried out for some wellknown biological models and its possible implications for neural communication. 
Iyudu, Natalia 
Sklyanin algebras via Groebner bases and finiteness conditions for potential algebras 
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I will discuss how some questions on Sklyanin algebras can be solved using combinatorial techniques, namely, the theory of Groebner bases, and elements of homological algebra. We calculate the Poincaré series, prove Koszulity, PBW, CalabiYau, etc., depending on the parameters of the Sklyanin algebras. There was a gap in the ArtinSchelter classification of algebras of global dimension 3, where Koszulity and the Poincaré series for Sklyanin algebras were proved only generically. It was filled in the Grothendieck Festschrift paper of Artin, Tate and Van den Bergh, using the geometry of elliptic curves. Our point is that we recover these results by purely algebraic, combinatorial means. We use similar methods for generalized Sklyanin algebras, and for other potential algebras. The latter gives finiteness results for potential algebras arising as contraction algebras in noncommutative resolution of singularities. 
Kosta, Dimitra 
SHORT TALK: Maximum Likelihood estimation for groupbased phylogenetic models 
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Phylogenetic models have polynomial parametrization maps. For symmetric groupbased models, Matsen studied the polynomial inequalities that characterize the joint probabilities in the image of these parametrizations. We employ this description for maximum likelihood estimation via numerical algebraic geometry. In particular, we explore an example where the maximum likelihood estimate does not exist, which would be difficult to discover without using algebraic methods. We also study the embedding problem for symmetric groupbased models, i.e. we identify which mutation matrices are matrix exponentials of rate matrices that are invariant under a group action. 
Logan, Alan 
SHORT TALK: Examples of MakaninRazborov diagrams 
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MakaninRazborov diagrams are a way of understanding the solutions to equations in free groups. There exists an algorithm to compute these diagrams, but this algorithm is of triplyexponential complexity! We give concrete examples of MakaninRazborov diagrams, and in certain cases provide an effective procedure to compute these diagrams. 
Luo, Xiaoyu 
Soft tissue mechanics and the heart 
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In this talk, I will start with an overview of the history and the current development of soft tissue mechanics. I will focus on the invariantbased continuum mechanics for fibrereinforced soft tissues
that undergo large nonlinear deformation. I will then report how we apply it to the healthy and infarcted heart in diastole and systole; how we build patientspecific models from in vivo clinical magnetic resonance images; how we infer the material parameters inversely; and how we apply the models to clinical settings. Different levels of modelling will be shown, using phenomenological or agentbased approaches. Finally, I will briefly introduce the EPSRC funded SofTMech Centre and the ongoing research themes there. 
Mampusti, Michael 
A fractal approach to spectral triples for aperiodic substitution tilings 
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In this talk, we outline the construction of spectral triples for a C*algebra associated to twodimensional aperiodic substitution tilings. The key ingredient in our construction is a fractal tree which we endow in a substitution tiling, which uses the technology of fractal substitution tilings of Frank, Webster, and Whittaker. We use the Penrose substitution tiling to illustrate these fractal trees. These spectral triples define a geometry on the discrete hulls of such substitution tilings which respect the substitution systems. This is joint work with Mike Whittaker. 
Mao, Xuerong 
Almost Sure Exponential Stability of Stochastic Differential Delay Equations 
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It was very easy to show that the linear scalar stochastic differential equation (SDE) $dx(t) = b x(t) dB(t)$ is almost surely exponentially stable as long as $b not= 0$. However, it was nontrivial for Mohammed and Scheutzow (1997) to show if the corresponding linear scalar stochastic differential delay equation (SDDE)
$dx(t) = b x(ttau) dB(t)$ is almost surely exponentially stable for sufficiently small $tau$. There has been a very little progress in this topic since 1997. This talk will report some recent developments. 
Martin, Alexandre 
Hyperbolic aspects of certain Artin groups 
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Acylindrical hyperbolicity is a farreaching generalisation of relative hyperbolicity, and provides a common framework to study large classes of groups of geometric interest: mapping class groups of hyperbolic surfaces, many fundamental groups of 3manifolds, etc.
This talk will be a brief survey on this notion, and will present a very simple criterion to check the acylindrical hyperbolicity of groups acting on CAT(0) cube complexes, with application to certain Artin groups. (joint work with I. Chatterji) 
Miao, Zhouqian 
SHORT TALK: Front propagation in twocomponent reactiondiffusion systems with a cutoff 
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The study of front propagation has recently received a great deal of attention in reactiondiffusion systems. It is of great importance to identity the propagation speed of front solutions connecting stable and unstable steady states. We consider the sigmoidal system with TonnelierGerstner kinetics with a cutoff. In this talk, I will show some results that how the cutoff influence the front propagation speed via applying the blowup technique. 
Monk, Andrew 
SHORT TALK: Towards a Baum Connes Conjecture for Quantum Groups 
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In this talk I will explain the philosophy behind the classical BaumConnes conjecture, and report on work being done to extend this to a quantum analog of $SL(2, mathbb{C})$. 
Mulholland, Anthony 
Analysis of a Fractal Ultrasonic Transducer 
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Ultrasonic transducers are an essential tool in medical imaging, in imaging cracks in nuclear plants, and in a wide range of inverse problems.This talk will provide some theorems which can be used to predict the dynamics of a fractal ultrasound transducer whose piezoelectric components span a range of length scales. As far as we know this is the first to study waves in the complement to the Sierpinski gasket. This is an important mathematical development as the complement is formed from a broad distribution of length scales whereas the Sierpinski gasket is formed from triangles of equal size. A finite element method is used discretise the model and a renormalisation approach is then used to develop a recursion scheme that analytically describes the key components from the discrete matrices that arise. It transpires that the fractal device has a significantly higher reception sensitivity and a significantly wider bandwidth than an equivalent Euclidean (standard) device. So much so that our engineering colleagues have built the world’s first fractal ultrasonic transducer. 
Mundet i Riera, Ignasi 
TALK 1 (Geometry and Physics session): Finite subgroups of Ham. TALK 2 (Topology session): Finite subgroups of Diff 
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TALK 1 ABSTRACT (Geometry and Physics): A group H is Jordan if there exists a constant C with the property that any finite subgroup G of H has an abelian subgroup whose index in G is at most C. A classic theorem of Jordan implies that any connected finite dimensional Lie group is Jordan. I will talk about the following theorem: Hamiltonian diffeomorphism groups of compact symplectic manifolds are Jordan. In contrast, one can prove, generalizing a construction of Csikos, Pyber and Szabo, that there are many compact symplectic manifolds whose diffeomorphism group is not Jordan.
TALK 2 ABSTRACT (Topology): A group H is Jordan if there exists a constant C with the property that any finite subgroup G of H has an abelian subgroup whose index in G is at most C. A classic theorem of Jordan implies that any connected finite dimensional Lie group is Jordan. Etienne Ghys asked, about 30 years ago, whether the diffeomorphism group of every smooth compact manifold is Jordan. It has been proved that the answer to Ghys's question is positive in many cases and negative in many other ones. I will survey what is known at present. 
Myers, Tim 
Phase change at the nanoscale 
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In this talk we will discuss the mathematical modelling of phase change and how it has been adapted in the literature to deal with nanoscale effects. Specifically we will show that the accepted equations are incorrect and provide a new system. The accepted system has been shown to lose energy under the standard onephase reduction, and asymptotic reductions have been applied to resolve the issue. We will show how in the new system the reduction is obvious and leads immediately to an energy conserving system.
The models discussed will be based on Fourier’s law, which is known to fail at the nanoscale. This talk paves the way for the subsequent talk of M. Calvo, who will discuss modifications to the formulation using a different mode of heat transfer 
Neelima, Neelima 
SHORT TALK: L^pestimates and higher regularity for semilinear SPDEs with monotone semilinearity 
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We prove L^pestimates for semilinear stochastic partial differential equations on bounded domains. The semilinear term is monotone, continuous and has arbitrary polynomial growth. These L^pestimates are then used to obtain higher regularity of the solutions for such equations. This is joint work with David Siska. 
Nualart, Eulalia 
Moment bounds for some fractional stochastic heat equations on the ball 
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In this paper, we obtain upper and lower bounds for the moments of the solution to a class of fractional stochastic heat equations on the ball driven by a Gaussian noise which is white in time, and with a spatial correlation in space of Riesz kernel type. We also consider the spacetime white noise case on an interval. 
Nurtay, Anel 
A mathematical model of viral evolution and specialization 
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Understanding the dynamics of viral evolution is crucial for the development of novel medicines and treatments. Due to the global scales of viral diseases and their high mutation rates, observational studies and databased solutions would benefit from being supported by analytical methods of prediction. In this talk, we present a mathematical model to describe the infection of two types of host cells by a virus with multiple phenotypes. The model captures viral mutation and hence specialization by accounting for phenotypedependent interactions between the cells and virus. Although the developed system of deterministic partial integrodifferential equations illustrates a virus population mutating towards more successful phenotypes, our results show qualitatively different behaviour, i.e. more genetic drift or natural selection driven evolution, for varying sets of parameters.
We consider a technique to investigate the parameters using regression analysis which leads to an analytical understanding of the system. Our model provides new insights into the patterns seen in
collected data and may allow for more precise predictions. 
Oh, Tadahiro 
On singular stochastic dispersive PDEs 
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In this talk, I will describe recent development on the wellposedness theory of singular stochastic dispersive PDEs such as the stochastic nonlinear Schr"odinger equations. I will also describe future prospects in this field in conjunction with the recent development in stochastic parabolic PDEs. 
Quick, Martyn 
Presentations for Thompson's group V and its generalizations 
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Thompson's group V is one of the best known examples of an infinite finitely presented simple group. The presentation originally given by Thompson in his notes appears to have remained the best in terms of fewest generators and relations for decades. In this talk, I will give a number of different collections of generators, including a new smaller presentation, for V and for its relatives nV (introduced by Brin). These will illustrate how these groups can be viewed as an infinite analogues of the finite alternating and symmetric groups. Some of this is joint work with Collin Bleak. 
Recio Mitter, David 
SHORT TALK: Topological complexity of subgroups of the braid groups 
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Topological complexity (TC) was introduced in the early 2000s by Michael Farber in the context of topological robotics. It is a numerical homotopy invariant of a space which measures the instability of motion planning. Moreover, TC can also be defined for a (discrete) group π, as the TC of its EilenbergMac Lane space K(π,1). In particular the TC of the full braid group Bn is by definition equal to the TC of the unordered configuration space of n points on the plane.
In this talk the TC of groups will be introduced and calculated for some subgroups of the full braid groups, for instance mixed (or coloured) braid groups and congruence subgroups. The methods used in the calculations are algebraic rather than topological. This is joint work with Mark Grant. 
Saldaña, Joan 
A meanfield model for an SIR epidemic on a network with information dissemination 
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Human behavioural responses have an important impact on the spread of epidemics. To deal with them, some epidemic models consider that individuals are aware of the risk of contagion and adopt preventive measures when they learn about the existence of the disease. If the information about the infection state of a neighbour is transmitted, then it can be thought that information is disseminated over a second network with the same set of nodes where links are defined according to a certain type social relationship. An example of this second network is given by the socalled Partner Notification Programme which helps to reach partners of patients of sexually transmitted diseases and inform them that they may be at risk, and hence the need of seeking medical care.
In this talk, I will present some results of a joint work with David Juher (Universitat de Girona) about a simple epidemic model for the spread of an SIR epidemic on a twolayer network. The first layer is defined by the contact network and the second one contains those links along which information is disseminated. The model is derived in such a way that the overlap between both layers appears as a new parameter. This fact allows us to obtain analytical predictions about the initial growth and the final size of an epidemic in terms of this overlap, and check their accuracy with the output of stochastic simulations of the epidemic. 
Salkeld, William 
SHORT TALK: Large deviation principles for McKean Vlasov equations 
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The FreidlinWentzell theorem is a large deviation principle for stochastic processes which proves an upper bound for the rate of convergence in probability of the sample path of an Ito process diverging from the mean path. It is an extension of Schilders theorem for Brownian motion to more general diffusions using the Contraction Principle. Originally, the results were proved under the supremum metric. However, in 1994 G. Ben Arous and M. Ledoux extended the results to the Holder metric with parameter $alpha<0.5$ for SDE's with drift and diffusion coefficients which are bounded and Lipschitz. A McKeanVlasov process is the solution of a nonlinear SDE where the coefficients are dependent on the spacial variable plus the probability distribution of the solution. Their applications are wide and varied as they can be used to model multi particle systems with particle interaction. Large Deviation principles have been proved for these equations under the supremum metric using exponential tightness to approximate the process by a classical SDE where the distributional variable has been replaced by a delta distribution following the mean path. Here, I present an extension of previous results for FreidlinWentzell theory for Holder metric to McKean Vlasov type equations and weaken the conditions on the drift coefficient to unbounded and Locally Lipschitz. 
Schroers, Bernd 
Vortices, magnetic zero modes and Cartan connections 
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In this talk I will explain how one can obtain zero modes of the Dirac operator in three dimensions and coupled to a magnetic field from integrable vortex equations in two dimensions by relating both to (nonabelian) flat Cartan connections on the 3sphere.This talk is based on joint work with Calum Ross. 
Sierra, Susan 
Overrings of Skylanin algebras 
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Let S be a generic Sklyanin algebra, which is a certain graded deformation of the polynomial ring k[x,y,z]. It is wellknown that S has similar properties to the polynomial ring, although it is quite noncommutative. In particular, S is an Ngraded domain, has global dimension 3, and is a noetherian maximal order. The centre of S is generated by a single cubic element, g. We show that S satisfies the following maximality property: If S subseteq R subseteq Q(S), where R is a finitely graded noetherian maximal order, then R = k[S_a g^{b}] for appropriate a and b. (The analogous statement for the polynomial ring is false.) In particular, if R is contained in the localisation of S at gS, then R=S. As a corollary, we show that the "elliptic Weyl algebra" S[g^{1}]_0 is the maximal subring of its division ring of fractions which has GelfandKirillov dimension 2. This is joint work with Dan Rogalski and Toby Stafford. 
Smoktunowicz, Agata 
Onegenerator braces and indecomposable solutions of the YangBaxter equation 
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Braces are a generalisation of Jacobson radical rings, and they have been introduced by Rump as a tool to investigate involutive, nondegenerate settheoretic solutions of the YangBaxter equation. Recall that a brace is a group $G$ with two operations $+$ and $cdot $ such that $(G, +)$ is an abelian group, $(G, cdot )$ is a group, and $acirc (b+c)+a=acirc b+acirc c$ for all $a,b,cin G$. In this talk we describe connections between braces which are generated by one element and indecomposable solutions of the YangBaxter equation. 
Stewart, Peter 
Fracture phenomena in foams: upscaling to PDE models 
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Injection of a gas into a gas/liquid foam is known to give rise to instability phenomena on a variety of time and length scales. Macroscopically, one observes a propagating gasfilled structure that can display properties of liquid finger propagation as well as of fracture in solids. Using a discrete network model, which incorporates the underlying film instability as well as viscous resistance from the moving liquid structures, we describe both largescale ductile fingerlike cracks and brittle cleavage phenomena in line with experimental observations. Based on this discrete model, we then derive a continuum limit PDE description of both the ductile and brittle modes and draw analogy with SaffmanTaylor fingering in nonNewtonian continuum fluids and molecular dynamics simulations of fracture in crystalline atomic solids. 
Strachan, Ian 
Hermitian geometry on the big phase space 
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The big phase space, the geometric setting for the study of quantum cohomology with gravitational descendents, is a complex manifold and consists of an infinite number of copies of the small phase space. In this talk it will be shown how to define a Hermitian geometry on this space. Using an old idea of Dijkgraaf and Witten it is shown that various geometric structures on the small phase space and be lifted to the big phase space. The main results here is that various notions from tt＊geometry are preserved such liftings, endowing the Big Phase Space with an Hermitian structure. 
StricklandConstable, Charles 
Generalised geometry and supersymmetric solutions 
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It is wellknown that, in the absence of background fluxes, the supersymmetric Minkowski compactification manifolds of string theory are manifolds with special holonomy, such as the celebrated CalabiYau spaces. Generalised geometry is an extension of (pseudo)Riemannian geometry which provides an elegant geometrical description of the supergravity theories underlying string theory and M theory, and thus provides a formalism which includes the possible fluxes in the geometry. After a brief introduction to these topics, I will describe recent developments showing that general supersymmetric Minkowski solutions can be described as the analogue of special holonomy manifolds in this new geometry. The Killing superalgebra, which has a neat manifestation in this language, plays a key role in the proof of the result for N > 2 supersymmetry and we are able to fix its form explicitly using this technology. If time allows I will also briefly discuss the corresponding picture for supersymmetric Antide Sitter solutions. 
Terry, Alan 
Predatorprey models with component Allee effect for predator reproduction 
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We present four predatorprey models with component Allee effect for predator reproduction. Using numerical simulation results for our models, we describe how the customary definitions of component and demographic Allee effects, which work well for single species models, can be extended to predators in predatorprey models by assuming that the prey population is held fixed. We then explore our four models, analytically and numerically. Each of our models has a fixed point that represents predator extinction, which is always locally stable. We prove that the predator will always die out either if the initial predator population is sufficiently small or if the initial prey population is sufficiently small. Through numerical simulations, we explore coexistence fixed points. In addition, we demonstrate, by simulation, the existence of a stable limit cycle in one of our models. Finally, we derive analytical conditions for a coexistence trapping region in three of our models, and show that the fourth model cannot possess a particular kind of co existence trapping region. We punctuate our results with comments on their real world implications; in particular, we mention prey resurgence from mortality events, and failure in a biological pest control program. 
Vaes, Stefaan 
PLENARY TALK: Classification of von Neumann algebras. TALK 2 (Operator Algebras session): Bernoulli actions of type III and L^2cohomology 
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PLENARY TALK ABSTRACT: The theme of this talk is the dichotomy between amenability and nonamenability. Because the group of motions of the threedimensional Euclidean space is nonamenable (as a group with the discrete topology), we have the BanachTarski paradox. In dimension two, the group of motions is amenable and there is therefore no paradoxical decomposition of the disk. This dichotomy is most apparent in the theory of von Neumann algebras: the amenable ones are completely classified by the work of Connes and Haagerup, while the nonamenable ones give rise to amazing rigidity theorems, especially within Sorin Popa's deformation/rigidity theory. I will illustrate the gap between amenability and nonamenability for von Neumann algebras associated with countable groups, with locally compact groups, and with group actions on probability spaces.
TALK 2 ABSTRACT: I report on a recent joint work with Jonas Wahl. We prove that for most countable groups G, including those that admit at least one element of infinite order, G admits a Bernoulli action of Murrayvon Neumann type III if and only if G has nontrivial first L^2cohomology. 
Vives, Josep 
Option price decomposition for jumpdiffusion stochastic volatility models: price approximation and calibration 
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We will survey the recent papers [ADV15], [MV15], [MV17] and [MPSV17], where we obtain a decomposition formula for the option price for different jumpdiffusion stochastic and local volatility models. A formula of this type was first proved for the Heston model in [A12]. These types of decompositions are useful to obtain approximated closed formulas
for option prices, approximations of the implied volatility surface, and to develop new model calibration methodologies.
[A12] E. Alòs (2012): A Decomposition Formula for Option Prices in the Heston Model and Applications to Option Pricing Approximation. Finance and Stochastics 16 (3): 403422.
[ADV15] E. Alòs, R. De Santiago and J. Vives (2015): Calibration of stochastic volatility models via second order approximation: the Heston case. International Journal of Theoretical and Applied Finance 18 (6).
[MV15] R. Merino and J. Vives (2015): A generic decomposition formula for pricing vanilla options under stochastic volatility models. International Journal of Stochastic Analysis, ID 103647, 2015.
[MV17] R. Merino and J. Vives (2017): Option price decomposition in local volatility models and some applications]. To appear in International Journal of Stochastic Analysis.
[MPSV17] R. Merino, J. Pospísil, T. Sobotka and J. Vives (2017): Decomposition formula for jump diffusion models. Submitted. 
Voigt, Christian 
Complex quantum groups and the BaumConnes assembly map 
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In this talk I'll discuss a quantization of the BaumConnes assembly map for complex semisimple Lie groups. 
Watson, Stephen 
Emergent and hidden symmetries of nanofaceting crystal growth 
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Nanofaceted crystal answer the call for selfassembeld, physiochemically tailored materials, with those arising from a kinetically mediated response to the freeenergy isequilibria (theromokinetics) holding the greatest promise. To explore this, we consider a singularity perturbed, fourthorder, hyperbolicparabolic geometric partial differential equation that models the dynamics of slightly undercooled crystalmelt interfaces possessing strongly anisotropic and curvaturedependent surface energy, and evolving under attachmentdetachment limited kinetics. The fundamental nonequilibrium feature of this dynamics is explicated through our analytical discovery of 1D convex and concavetranslatingfront solutions (solitons), whose constant asympoticangles provably deviate from the thermodynamically expected (Wulff) angles in direct proportion to the degree of undercooling. These thermokinetic solitons induce a novel emergent facet dynamics which is exactly characterised via and original geometric matchedasymptotic analysis. We thereby discover an emergent parabolic symmetry which naturally implies the universal scaling law ${mathcal{L} sim t^{1/2} }$ for the growth in time of $t$ of the characteristic facet length $mathcal{L}$. Time permitting we will touch on a beyond scaling theory of coarsening that we have recently developed  Gequivariant universality  and illustrate its application through a hidden Lorentzian symmetry of the PDE's emergent facet dynamics. 
Zacharias, Joachim 
A dynamical version of the Cuntz semigroup 
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The Cuntz semigroup is an invariant for C*algebras combining refined Ktheoretical and tracial properties of the algebra in question, carrying important information but being notoriously difficult to determine. For dynamical systems we consider a dynamical version of the Cuntz semigroup which we hope to be easier to determine than the Cuntz semigroup of the crossed product and which might make it more accessible. We can define a dynamical semigroup in the setting of a discrete amenable groups acting on a semigroup. If the semigroup is the Cuntz semigroup of the coefficient algebra of a crossed product then our construction models the Cuntz semigroup of the crossed product algebra and in good cases is isomorphic to it. This can be used to establish strict comparison for certain crossed products of minimal actions on the Cantor set and provides a route to show their classifiability. 
Zapata Carratalá, Carlos 
A unifying picture for the reduction of geometric structures 
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In this talk I will present a summary of how the language of Lie Algebroids provides a way to systematically account for different examples of reduction. The classical example is symplectic reduction via an equivariant moment map, wellknown to both mathematical physicists and geometers, whence we will show how to assign specific Lie algebroids to each step of the reduction and how the associated linear Poisson algebras are related by coisotropic reduction. Although this first result could be interpreted as a reformulation of the fact that symplectic manifolds carry Poisson algebras that reduce accordingly under symplectic reduction, I will show that this idea carries over to many other, more interesting, examples of reduction of geometric structures: Poisson, presymplectic, quasiHamiltonian, contact, etc. 
Ziembowski, Michal 
The maximum dimension of a Lie nilpotent subalgebra of the full matrix algebra 
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The main result presented during the talk will be following: if $F$ is any field and $R$ any $F$subalgebra of the algebra $M_n(F)$ of $ntimes n$ matrices over $F$ with Lie nilpotence index $m$, then ${rm dim}_{F}R leqslant M(m+1,n)$ where $M(m+1,n)$ is the maximum of $frac{1}{2}left(n^{2}sum_{i=1}^{m+1}k_{i}^{2}right)+1$ subject to the constraint $sum_{i=1}^{m+1}k_{i}=n$ and $k_{1},k_{2},ldots,k_{m+1}$ nonnegative integers. This answers in the affirmative a conjecture posed by van Wyk and Szigeti. The case $m=1$ reduces to a classical theorem of Schur (1905), later generalized by Jacobson (1944) to all fields, which asserts that if $F$ is an algebraically closed field of characteristic zero, and $R$ is any commutative $F$subalgebra of $M_{n}(F)$, then { dim}$_{F}R leqslant leftlfloorfrac{n^{2}}{4}rightrfloor+1$. The talk is based on a joint work with J. van den Berg, J. Szigeti and L. van Wyk. 