Past

I will give a description of a method introduced by N. Ivanov to study the abstract commensurator of a group by using a rigid action of that group on a graph. We will sketch Ivanov's theorem regarding the abstract commensurator of a mapping class group. Time permitting, I will describe how these methods are used in some of my recent work with Horbez on outer automorphism groups of free groups.

We survey recent research related to the Extension Property of Partial Isomorhisms (EPPA, also known as Hrushovski property) and, perhaps surprisingly, relate it to structural Ramsey theory.   This is based on a joint work with David Evans, Jan Hubicka and Matej Konecny.
 

Not much is known about the Chow rings  of moduli spaces of abelian varieties or more general Shimura varieties. The tautological ring of a Shimura variety of Hodge type is a subring of its Chow ring containing many "interesting" classes. I will talk about joint work with Torsten Wedhorn on this ring as well as its characteristic p variant. The later is strongly related to the question of understanding the cycle classes of Ekedahl-Oort strata in the Chow ring.

Cluster Adjacency is a geometric principle which defines a subclass of multiple polylogarithms with analytic properties compatible with that of scattering amplitudes and Feynman loop integrals. We use this principle to a priori remove the redundances in the perturbative bootstrap approach and efficiently compute the four-loop NMHV heptagon. Moreover, cluster adjacency is naturally applied to the space of $A_n$ polylogarithms and generates numerous structures therein to be explored further.

A common strategy to solve shape optimization problems is to select an initial domain and to update it iteratively until it satisfies certain optimality crietria. In the presence of PDE-constraints, computing these updates requires solving a boundary value problem on a domain that changes at every iteration. We explain how to use isoparametric finite elements to tackle this issue. We also show how finite elements allow computing these updates without deriving shape derivative formulas by hand.

There was major progress on perfect graphs in the early 2000's: Chudnovsky, Robertson, Thomas and I proved the ``strong perfect graph theorem'' that a graph is perfect if and only if it has no odd hole or odd antihole; and Chudnovsky, Cornuejols, Liu, Vuscovic and I found a polynomial-time algorithm to test whether a graph has an odd hole or odd antihole, and thereby test if it is perfect. (A ``hole'' is an induced cycle of length at least four, and an ``antihole'' is a hole in the complement graph.)

What we couldn't do then was test whether a graph has an odd hole, and this has stayed open for the last fifteen years, despite some intensive effort. I am happy to report that in fact it can be done in poly-time (in time O(|G|^{12}) at the last count), and in this talk we explain how.

Joint work with Maria Chudnovsky, Alex Scott, and Sophie Spirkl.

The classical Dirac operator is part of an osp(1|2) realisation inside the Weyl-Clifford algebra which is Pin-invariant. This leads to a multiplicity-free decomposition of the space of spinor-valued polynomials in irreducible modules for this Howe dual pair. In this talk we review an abstract generalisation A of the Weyl algebra that retains a realisation of osp(1|2) and we determine its centraliser algebra explicitly. For the special case where A is a rational Cherednik algebra, the centralizer algebra provides a refinement of the previous decomposition whose analogue was no longer irreducible in general. As an example, for the  group S3 in specific, we will examine the finite-dimensional irreducible modules of the centraliser algebra.

In this talk, we consider solving nonlinear systems of equations and the unconstrained minimization problem using Newton’s method methods from the Halley class. The methods in this class have in general local and third order rate of convergence while Newton’s method has quadratic convergence. In the unconstrained optimization case, the Halley methods will require the second and third derivative. Third-order methods will, in most cases, use fewer iterations than a second-order method to reach the same accuracy. However, the number of arithmetic operations per iteration is higher for third-order methods than for a second-order method. We will demonstrate that for a large class of problems, the ratio of the number of arithmetic operations of Halley’s method and Newton’s method is constant per iteration (independent of the number of unknowns).

We say that the sparsity pattern of the third derivative (or tensor) is induced by the sparsity pattern of the Hessian matrix. We will discuss some datastructures for matrices where the indices of nonzero elements of the tensor can be computed. Historical notes will be merged into the talk.

Coastal vegetation has a well-known effect of attenuating waves; however, quantifiable measures of attenuation for general wave and vegetation scenarios are not well known. On the plant scale, there are extensive studies in predicting the dynamics of a single plant in an oscillatory flow. On the coastal scale however, there are yet to be compact models which capture the dynamics of both the flow and vegetation, when the latter exists in the form of a dense canopy along the bed. In this talk, we will discuss the open questions in the field and the modelling approaches involved. In particular, we investigate how micro-scale effects can be homogenised in space and how periodic motions can be averaged in time.

I will review the fishnet model, which is an integrable scalar QFT, obtained by an extreme gamma deformation of N=4 super Yang-Mills. The theory has a peculiar perturbative expansion in which many quantities at a fixed loop order are given by a single Feynman diagram. This feature allows the reinterpretation of Feynman loop integrals as integrable systems.

We examine the relationship between social structure and sentiment through the analysis of a large collection of tweets about the Irish Marriage Referendum of 2015. We obtain the sentiment of every tweet with the hashtags #marref and #marriageref that was posted in the days leading to the referendum, and construct networks to aggregate sentiment and use it to study the interactions among users. Our analysis shows that the sentiment of outgoing mention tweets is correlated with the sentiment of incoming mentions, and there are significantly more connections between users with similar sentiment scores than among users with opposite scores in the mention and follower networks. We combine the community structure of the follower and mention networks with the activity level of the users and sentiment scores to find groups that support voting ‘yes’ or ‘no’ in the referendum. There were numerous conversations between users on opposing sides of the debate in the absence of follower connections, which suggests that there were efforts by some users to establish dialogue and debate across ideological divisions. Our analysis shows that social structure can be integrated successfully with sentiment to analyse and understand the disposition of social media users around controversial or polarizing issues. These results have potential applications in the integration of data and metadata to study opinion dynamics, public opinion modelling and polling.

The Euler equation describing motion of ideal fluids goes back to 1755. 
The analysis of the equation is challenging since it is nonlinear and nonlocal. Its solutions are often unstable and spontaneously generate small scales. The fundamental question of global regularity vs finite time singularity formation 
remains open for the Euler equation in three spatial dimensions. In this lecture, I will review the history of this question and its connection with the arguably greatest unsolved problem of classical physics, turbulence. Recent results on small scale and singularity formation in two dimensions and for a number of related models will also be presented.

I will describe an extremely easy construction with formal group laws, and a 
slightly more subtle argument to show that it can be done in a coordinate-free
way with formal groups.  I will then describe connections with a range of other
phenomena in stable homotopy theory, although I still have many more 
questions than answers about these.  In particular, this should illuminate the
relationship between the Lambda algebra and the Dyer-Lashof algebra at the
prime 2, and possibly suggest better ways to think about related things at 
odd primes.  The Morava K-theory of symmetric groups is well-understood
if we quotient out by transfers, but somewhat mysterious if we do not pass
to that quotient; there are some suggestions that dilation will again be a key
ingredient in resolving this.  The ring $MU_*(\Omega^2S^3)$ is another
object for which we have quite a lot of information but it seems likely that 
important ideas are missing; dilation may also be relevant here.
 

This talk is based on joint work with Dominic Joyce and Markus Upmeier. Issues we'd like to talk about are a) the orientability of moduli spaces that
appear in various gauge-theoretic problems; and b) how to orient those moduli spaces if they are orientable. We begin with briefly mentioning backgrounds and motivation, and recall basics in gauge theory such as the Atiyah-Hitchin-Singer complex and the Kuranishi model by taking the anti-self-dual instanton moduli space as an example. We then describe the orientability and canonical orientations of the anti-self-dual instanton moduli space, and other
gauge-theoretic moduli spaces which turn up in current research interests.

 Author of Alan Turing: The Enigma, sharing his academic path and experience as activist for LGBTQ+ rights

In this talk, we show that a range of non-trivial SU(3) structures can be constructed on large classes of Calabi-Yau three-folds. Among the possible SU(3) structures we find Strominger-Hull systems, suitable for heterotic or type II string compactifications. These SU(3) structures of Strominger-Hull type have a non-vanishing and non-closed three-form flux which needs to be supported by source terms in the associated Bianchi identity. We discuss the possibility of finding such source terms and present first steps towards their explicit construction. Provided suitable sources exist, our methods lead to Calabi-Yau compactifications of string theory with a non Ricci-flat, physical metric which can be written down explicitly and in analytic form. The talk is based on the paper 1805.08499.

Thomas Prince The double life of the number 24.

The number 24 appears in a somewhat surprising result in the study of polyhedra with integer lattice points. In a different setting, the number 24 is the Euler characteristic of a K3 surface: a four (real) dimensional object which plays a central role in algebraic geometry. We will hint at why both instances of 24 are in fact the same, and suggest that integral affine geometry can be used to interpolate between the realm of integral polytopes and the world of complex algebraic geometry.

Mohit Dalwadi A multiscale mathematical model of bacterial nutrient uptake

In mathematical models that include nutrient delivery to bacteria, it is prohibitively expensive to include many small bacterial regions acting as volumetric nutrient sinks. To combat this problem, such models often impose an effective uptake instead. However, it is not immediately clear how to relate properties on the bacterial scale with this effective result. For example, one may intuitively expect the effective uptake to scale with bacterial volume for weak first-order uptake, and with bacterial surface area for strong first-order uptake. I will present a general model for bacterial nutrient uptake, and upscale the system using homogenization theory to determine how the effective uptake depends on the microscale bacterial properties. This will show us when the intuitive volume and surface area scalings are each valid, as well as the correct form of the effective uptake when neither of these scalings is appropriate.
 

Are you keen to share your love of maths with non-mathematicians, but aren’t sure where to start? Whether you're keen to get involved in outreach activities at Oxford, or you'd just like to explain to your friends and family what you do all term, there's something for everyone in our interactive hour of workshop activities, and lots of laughs along the way. Just bring plenty of enthusiasm, and come prepared with a bit of mathematics you particularly like. 

This session is open to all, and no prior outreach experience is necessary.

In this talk I will show the nature, the properties and the features of the Pareto Optimality in a diverse set of phenomena modeled as complex networks.
I will present a composite design methodology for multi-objective modeling and optimization of complex networks.  The method is based on the synergy of different algorithms and computational techniques for the analysis and modeling of natural systems (e.g., metabolic pathways in prokaryotic and eukaryotic cells) and artificial systems (e.g., traffic networks, analog circuits and solar cells).

“Pareto Optimality in Multilayer Network Growth”
G. Nicosia et al, Phys. Rev. Lett., 2018

Multiple zeta values are generalizations of the special values of Riemann's zeta function at positive integers. They satisfy a large number of algebraic relations some of which were already known to Euler. More recently, the interpretation of multiple zeta values as periods of mixed Tate motives has led to important new results. However, this interpretation seems insufficient to explain the occurrence of several phenomena related to modular forms.

The aim of this talk is to describe an analog of multiple zeta values for complex elliptic curves introduced by Enriquez. We will see that these define holomorphic functions on the upper half-plane which degenerate to multiple zeta values at cusps. If time permits, we will explain how some of the rather mysterious modular phenomena pertaining to multiple zeta values can be interpreted directly via the algebraic structure of their elliptic analogs.

We analyse the consequences of conservative portfolio compression, i.e., netting cycles in financial networks, on systemic risk.  We show that the recovery rate in case of default plays a significant role in determining whether portfolio compression is potentially beneficial.  If recovery rates of defaulting nodes are zero then compression weakly reduces systemic risk. We also provide a necessary condition under which compression strongly reduces systemic risk.  If recovery rates are positive we show that whether compression is potentially beneficial or harmful for individual institutions does not just depend on the network itself but on quantities outside the network as well. In particular we show that  portfolio compression can have negative effects both for institutions that are part of the compression cycle and for those that are not. Furthermore, we show that while a given conservative compression might be beneficial for some shocks it might be detrimental for others. In particular, the distribution of the shock over the network matters and not just its size.  

Accurate simulation of electromagnetic scattering by ice crystals in clouds is an important problem in atmospheric physics, with single scattering results feeding directly into the radiative transfer models used to predict long-term climate behaviour. The problem is challenging for numerical simulation methods because the ice crystals in a given cloud can be extremely varied in size and shape, sometimes exhibiting fractal-like geometrical characteristics and sometimes being many hundreds or thousands of wavelengths in diameter. In this talk I will focus on the latter "high-frequency" issue, describing a hybrid numerical-asymptotic boundary element method for the simplified problem of acoustic scattering by penetrable convex polygons, where high frequency asymptotic information is used to build a numerical approximation space capable of achieving fixed accuracy of approximation with frequency-independent computational cost. 

It is shown by Kashiwara and Schapira (1980s) that for every constructible sheaf on a smooth manifold, one can construct a closed conic Lagrangian subset of its cotangent bundle, called the microsupport of the sheaf. This eventually led to the equivalence of the category of constructible sheaves on a manifold and the Fukaya category of its cotangent bundle by the work of Nadler and Zaslow (2006), and Ganatra, Pardon, and Shende (2018) for partially wrapped Fukaya categories. One can try to generalise this and conjecture that Fukaya category of a Weinstein manifold can be given by constructible (microlocal) sheaves associated to its skeleton. In this talk, I will explain these concepts and confirm the conjecture for a family of Weinstein manifolds which are certain quotients of A_n-Milnor fibres. I will outline the computation of their wrapped Fukaya categories and microlocal sheaves on their skeleta, called pinwheels.

Just like optimization needs derivatives, shape optimization needs shape derivatives. Their definition and computation is a classical subject, at least concerning first order shape derivatives. Second derivatives have been studied as well, but some aspects of their theory still remains a bit mysterious for practitioners. As a result, most algorithms for shape optimization are first order methods.

To understand this situation better and in a general way, we consider first and second order shape sensitivities of integrals on smooth submanifolds using a variant of shape differentiation. Instead of computing the second derivative as the derivative of the first derivative, we choose a one-parameter family of perturbations  and compute first and second derivatives with respect to that parameter. The result is a  quadratic form in terms of a perturbation vector field that yields a second order quadratic model of the perturbed functional, which can be used as the basis of a second order shape optimization algorithm. We discuss the structure of this derivative, derive domain expressions and Hadamard forms in a general geometric framework, and give a detailed geometric interpretation of the arising terms.

Finally, we use our results to construct a second order SQP-algorithm for shape optimization that exhibits indeed local fast convergence.

In this talk I will illustrate how solutions of nonlinear nonlocal Fokker-Planck equations in a bounded domain with no-flux boundary conditions can be approximated by Cauchy problems with increasingly strong confining potentials defined outside such domain. Two different approaches are analysed, making crucial use of uniform estimates for energy and entropy functionals respectively. In both cases we prove that the problem in a bounded domain can be seen as a limit problem in the whole space involving a suitably chosen sequence of large confining potentials.
This is joint work with Maria Bruna and José Antonio Carrillo.
 

Traditionally, logic was thought of as `principles of right reason'. Early twentieth century philosophy of mathematics focused on the problem of a general foundation for all mathematics. In contrast, the last 70 years have seen model theory develop as the study and comparison of formal theories for studying specific areas of mathematics. While this shift began in work of Tarski, Robinson, Henkin, Vaught, and Morley, the decisive step came with Shelah's stability theory. After this paradigm shift there is a systematic search for a short set of syntactic conditions which divide first order theories into disjoint classes such that models of different theories in the same class have similar mathematical properties. This classification of theories makes more precise the idea of a `tame structure'. Thus, logic (specifically model theory) becomes a tool for organizing and doing mathematics with consequences for combinatorics, diophantine geometry, differential equations and other fields. I will present an account of the last 70 years in model theory that illustrates this shift. This reports material in my recent book published by Cambridge: Formalization without Foundationalism: Model Theory and the Philosophy of Mathematical Practice.

Euler sums and p-adic L-functions

Abstract:  It is a central question in the theory of infinite relational structures as to which structures carry analogues of Ramsey’s Theorem.  This question, of interest for several decades, has gained recent momentum as it was brought into focus by Kechris, Pestov, and Todorcevic, when they proved a deep correspondence between Ramsey theory and topological dynamics.  

In this talk, we provide background on the Ramsey theory of the Rado graph, solved by Sauer.  A longstanding open question was whether Henson graphs, the k-clique-free analogues of the Rado graph, have similar features.  We present the speaker’s recent work solving the Ramsey theory of the Henson graphs.  The techniques developed open new lines of investigation for other relational structures with forbidden configurations.  As a byproduct of these methods, we may obtain Ramsey properties for Borel colorings on copies of the Rado graph, with respect to a certain topology.

Abstract:  It is a central question in the theory of infinite relational structures as to which structures carry analogues of Ramsey’s Theorem.  This question, of interest for several decades, has gained recent momentum as it was brought into focus by Kechris, Pestov, and Todorcevic, when they proved a deep correspondence between Ramsey theory and topological dynamics.  

In this talk, we provide background on the Ramsey theory of the Rado graph, solved by Sauer.  A longstanding open question was whether Henson graphs, the k-clique-free analogues of the Rado graph, have similar features.  We present the speaker’s recent work solving the Ramsey theory of the Henson graphs.  The techniques developed open new lines of investigation for other relational structures with forbidden configurations.  As a byproduct of these methods, we may obtain Ramsey properties for Borel colorings on copies of the Rado graph, with respect to a certain topology.

Knot theory investigates the many ways of embedding a circle into the three-dimensional sphere. The study of these embeddings is not only important for understanding three-dimensional manifolds, but is also intimately related to many new and surprising phenomena appearing in dimension four. I will discuss how four-dimensional interpretations of some invariants can help us understand surfaces that bound a given link (embedding of several disjoint circles).

The Ring Learning With Errors problem (RLWE) comes in various forms. Vanilla RLWE is the decision dual-RLWE variant, consisting in distinguishing from uniform a distribution depending on a secret belonging to the dual OK^vee of the ring of integers OK of a specified number field K. In primal-RLWE, the secret instead belongs to OK. Both decision dual-RLWE and primal-RLWE enjoy search counterparts. Also widely used is (search/decision) Polynomial Learning With Errors (PLWE), which is not defined using a ring of integers OK of a number field K but a polynomial ring Z[x]/f for a monic irreducible f in Z[x]. We show that there exist reductions between all of these six problems that incur limited parameter losses. More precisely: we prove that the (decision/search) dual to primal reduction from Lyubashevsky et al. [EUROCRYPT 2010] and Peikert [SCN 2016] can be implemented with a small error rate growth for all rings (the resulting reduction is nonuniform polynomial time); we extend it to polynomial-time reductions between (decision/search) primal RLWE and PLWE that work for a family of polynomials f that is exponentially large as a function of deg f (the resulting reduction is also non-uniform polynomial time); and we exploit the recent technique from Peikert et al. [STOC 2017] to obtain a search to decision reduction for RLWE. The reductions incur error rate increases that depend on intrinsic quantities related to K and f.

Based on joint work with Miruna Roșca and Damien Stehlé.

With Gianluca Paolini (in preparation), we constructed, using a variant on the Hrushovski dimension function, for every k ≥ 3, 2^µ families of strongly minimal Steiner k systems. We study the mathematical properties of these counterexamples to Zilber’s trichotomy conjecture rather than thinking of them as merely exotic examples. In particular the long study of finite Steiner systems in reflected in results that depend on the block size k. A quasigroup is a structure with a binary operation such that for each equation xy = z the values of two of the variables determines a unique value for the third. The new Steiner 3-systems are bi-interpretable with strongly minimal Steiner quasigroups. For k > 3, we show the pure k-Steiner systems have ‘essentially unary definable closure’ and do not interpret a quasigroup. But we show that for q a prime power the Steiner q systems can be interpreted into specific sorts of quasigroups, block algebras. We extend the notion of an (a, b)-cycle graph arising in the study of finite and infinite Stein triple systems (e.g Cameron-Webb) by introducing what we call the (a, b)-path graph of a block algebra. We exhibit theories of strongly minimal block algebras where all (a, b)-paths are infinite and others in which all are finite only in the prime model. We show how to obtain combinatorial properties (e.g. 2-transitivity) by the either varying the basic collection of finite partial Steiner systems or modifying the µ function which ensures strong minimality

The Erdos-Hajnal Theorem asserts that non-universal graphs, that is, graphs that do not contain an induced copy of some fixed graph H, have homogeneous sets of size significantly larger than one can generally expect to find in a graph. We obtain two results of this flavor in the setting of r-uniform hypergraphs.

1. A theorem of R\"odl asserts that if an n-vertex graph is non-universal then it contains an almost homogeneous set (i.e one with edge density either very close to 0 or 1) of size \Omega(n). We prove that if a 3-uniform hypergraph is non-universal then it contains an almost homogeneous set of size \Omega(log n). An example of R\"odl from 1986 shows that this bound is tight.

2. Let R_r(t) denote the size of the largest non-universal r-graph G so that neither G nor its complement contain a complete r-partite subgraph with parts of size t. We prove an Erd\H{o}s--Hajnal-type stepping-up lemma, showing how to transform a lower bound for R_r(t) into a lower bound for R_{r+1}(t). As an application of this lemma, we improve a bound of Conlon-Fox-Sudakov by showing that R_3(t) \geq t^{ct).

Joint work with M. Amir and A. Shapira

Analytic continuation is ill-posed, but becomes merely ill-conditioned (though with an infinite condition number) if it is known that the function in question is bounded in a given region of the complex plane.
This classical, seemingly theoretical subject has many connections with numerical practice.  One argument indicates that if one tracks an analytic function from z=1 around a branch point at z=0 and back to z=1 again by a Weierstrass chain of disks, the number of accurate digits is divided by about exp(2 pi e) ~= 26,000,000.

The problem of authorship attribution (AA) involves matching a text of unknown authorship with its creator, found among a pool of candidate authors. In this work, we examine in detail authorship attribution methods that rely on networks of function words to detect an “authorial fingerprint” of literary works. Previous studies interpreted these word adjacency networks (WANs) as Markov chains, giving transition rates between function words, and they compared them using information-theoretic measures. Here, we apply a variety of network flow-based tools, such as role-based similarity and community detection, to perform a direct comparison of the WANs. These tools reveal an interesting relation between communities of function words and grammatical categories. Moreover, we propose two new criteria for attribution based on the comparison of connectivity patterns and the similarity of network partitions. The results are positive, but importantly, we observe that the attribution context is an important limiting factor that is often overlooked in the field's literature. Furthermore, we give important new directions that deserve further consideration.

We study solutions to stationary Navier-Stokes system in two dimensional exterior domains, namely, existence of these solutions and their asymptotical behavior. The talk is based on the recent joint papers with K. Pileckas and R. Russo where the uniform boundedness and uniform convergence at infinity for arbitrary solution with finite Dirichlet integral were established. Here  no restrictions on smallness of fluxes are assumed, etc.  In the proofs we develop the ideas of the classical papers of Gilbarg & H.F. Weinberger (Ann. Scuola Norm.Pisa 1978) and Amick (Acta Math. 1988).

We address the problem of pricing and hedging general exotic derivatives. We study this problem in the scenario when one has access to limited price data of other exotic derivatives. In this presentation I explore a nonparametric approach to pricing exotic payoffs using market prices of other exotic derivatives using signatures.

The lower central series of a group $G$ is defined by $\gamma_1=G$ and $\gamma_n = [G,\gamma_{n-1}]$. The "dimension series", introduced by Magnus, is defined using the group algebra over the integers: $\delta_n = \{g: g-1\text{ belongs to the $n$-th power of the augmentation ideal}\}$.

It has been, for the last 80 years, a fundamental problem of group theory to relate these two series. One always has $\delta_n\ge\gamma_n$, and a conjecture by Magnus, with false proofs by Cohn, Losey, etc., claims that they coincide; but Rips constructed an example with $\delta_4/\gamma_4$ cyclic of order 2. On the positive side, Sjogren showed that $\delta_n/\gamma_n$ is always a torsion group, of exponent bounded by a function of $n$. Furthermore, it was believed (and falsely proven by Gupta) that only $2$-torsion may occur.
In joint work with Roman Mikhailov, we prove however that for every prime $p$ there is a group with $p$-torsion in some quotient $\delta_n/\gamma_n$.
Even more interestingly, I will show that the dimension quotient $\delta_n/gamma_n$ is related to the difference between homotopy and homology: our construction is fundamentally based on the order-$p$ element in the homotopy group $\pi_{2p}(S^2)$ due to Serre.
 

Abstract: Consider a gaussian field f on R^2 and a level l. One can define a random coloring of the plane by coloring a point x in black if f(x)>-l and in white otherwise. The topology of this coloring is interesting in many respects. One can study the "small scale" topology by counting connected components with fixed topology, or study the "large scale" topology by considering black crossings of large rectangles. I will present results involving these quantities.

Einstein metrics are fixed points (up to scaling) of Hamilton's Ricci flow. A natural question to ask is whether a given metric is stable in the sense that the flow returns to the Einstein metric under a small perturbation. I'll give a brief survey of this area focussing on the case when the Einstein constant is positive. An interesting class of metrics where this question is not completely resolved are the compact symmetric spaces. I'll report on some recent progress with Tommy Murphy and James Waldron where we have been able to use a criterion due to Kroencke to show the Kaehler-Einstein metric on some Grassmannians and the bi-invariant metric on the Lie group G_2 are unstable.

Get to know the Mathematrix events of this term!

We were a bit too late with ordering food, so the usual sandwich lunch will only start from week 2. However, there may be some small snacks.

The zeta-function of a manifold varies with the parameters and may be evaluated in terms of the periods. For a one parameter family of CY manifolds, the periods satisfy a single 4th order differential equation. Thus there is a straight and, it turns out, readily computable path that leads from a differential operator to a zeta-function. Especially interesting are the specialisations to singular manifolds, for which the zeta-function manifests modular behaviour. We are also able to find, from the zeta function, attractor points. These correspond to special values of the parameter for which there exists a 10D spacetime for which the 6D corresponds to a CY manifold and the 4D spacetime corresponds to an extremal supersymmetric black hole. These attractor CY manifolds are believed to have special number theoretic properties. This is joint work with Xenia de la Ossa, Mohamed Elmi and Duco van Straten.

The 23rd Annual Meeting of the SIAM UKIE Section will take place on Friday 11th January 2019 at the Mathematical Institute at the University of Oxford.

The meeting will feature five invited speakers covering a broad range of industrial and applied mathematics: 

- Lisa Fauci, Tulane University, Incoming SIAM President
- Des Higham, Strathclyde University 
- Carola-Bibiane Schoenlieb (IMA sponsored speaker), University of Cambridge 
- Kirk Soodhalter, Trinity College Dublin 
- Konstantinos Zygalakis, University of Edinburgh 

There will also be a poster session, open to PhD students and postdocs. Travel support will be available for PhD students with an accepted poster presentation, and Best Poster prizes will be awarded. 

All talks will take place in room L3 in the Andrew Wiles Building (Mathematical Institute, University of Oxford). 

Programme 
09:30 - 10:00 Registration, tea/coffee 
10:00 - 10:15 Welcome 
10:15 - 11:00 Des Higham: Our Friends are Cooler than Us 
11:00 - 11:45 Lisa Fauci: Complex dynamics of fibers in flow at the microscale 
11:45 - 12:15 Poster Blitz 
12:15 - 13:30 Lunch and Poster session 
13:30 - 14:00 SIAM UKIE Business Meeting, open to all 
14:00 - 14:45 Kirk Soodhalter: Augmented Arnoldi-Tikhonov Methods for Ill-posed Problems 
14:45 - 15:30 Konstantinos Zygalakis: Explicit stabilised Runge-Kutta methods and their application to Bayesian inverse problems 
15:30 - 16:00 Tea/coffee 
16:00 - 16:45 Carola-Bibiane Schoenlieb (IMA sponsored speaker): Variational models and partial differential equations for mathematical imaging 
16:45 - 17:00 Poster prize announcement

With topics ranging from prime numbers to the lottery, from lemmings to bending balls like Beckham, Professor Marcus du Sautoy will provide an entertaining and, perhaps, unexpected approach to explain how mathematics can be used to predict the future. 

We are delighted to announce our first Oxford Mathematics Midlands Public Lecture to take place at Solihull School on 9th January 2019. 

Please email @email to register

Watch live:
https://facebook.com/OxfordMathematics
https://livestream.com/oxuni/du-Sautoy

We are very grateful to Solihull School for hosting this lecture.

The Oxford Mathematics Public Lectures are generously supported by XTX Markets.

Hannah Fry takes us on a tour of the good, the bad and the downright ugly of the algorithms that surround us. Are they really an improvement on the humans they are replacing?

Hannah Fry is a lecturer in the Mathematics of Cities at the Centre for Advanced Spatial Analysis at UCL. She is also a well-respected broadcaster and the author of several books including the recently published 'Hello World: How to be Human in the Age of the Machine.'

5.00pm-6.00pm, Mathematical Institute, Oxford

Please email @email to register

Watch live:
https://facebook.com/OxfordMathematics
https://livestream.com/oxuni/ChristmasLecture2018

The Oxford Mathematics Public Lectures are generously supported by XTX Markets

An informal session for DPhil students, ECRs and undergraduates with an interest in probability. The aim is to gain exposure to areas outside of your own research interests in an informal and accessible way.