Mon, 28 Jan 2019
12:45
L5

Unveiling the mysteries of the E-string with Calabi-Yau geometry

Yinan Wang
(Oxford)
Abstract

The E-string theory is usually considered as the simplest among 6D (1,0) superconformal field theories. Nonetheless, we still have little information about its spectrum of operators. In this talk, I'm going to describe our recent geometric approach using F-theory compactification on an elliptic Calabi-Yau threefold. The elliptic fibration is non-flat, which means that there are complex surface components in the fiber direction. From the geometry of non-flat fiber, we read out an infinite tower of particle states in the E-string theory. I will also discuss its relevance to 4D standard model building, which is a main motivation of this work.
 

Fri, 25 Jan 2019
16:00
L1

Ethics for mathematicians

Maurice Chiodo
(Cambridge)
Abstract

Teaching ethics to the mathematicians who need it most
For the last 20 years it has become increasingly obvious, and increasingly pressing, that mathematicians should be taught some ethical awareness so as to realise the impact of their work. This extends even to those more highly trained, like graduate students and postdocs. But which mathematicians should we be teaching this to, what should we be teaching them, and how should we do it? In this talk I’ll explore the idea that all mathematicians will, at some stage, be faced with ethical challenges stemming from their work, and yet few are ever told beforehand.
 

Fri, 25 Jan 2019

14:00 - 15:00
L1

Surely there's no ethics in mathematics?

Dr Maurice Chiodo
Abstract

Mathematics is both the language and the instrument that connects our abstract understanding with the physical world, thus knowledge of mathematics quickly translates to substantial knowledge and influence on the way the world works.  But those who have the greatest ability to understand and manipulate the world hold the greatest capacity to do damage and inflict harm.  In this talk I'll explain that yes, there is ethics in mathematics, and that it is up to us as mathematicians to make good ethical choices in order to prevent our work from becoming harmful.

Fri, 25 Jan 2019

14:00 - 15:00
L3

Applied modelling of the human pulmonary system

Professor David Kay
(Dept of Computer Science University of Oxford)
Abstract

In this work we will attempt, via virtual models, to interpret how structure and body positioning impact upon the outcomes of Multi-Breath-Washout tests. 


By extrapolating data from CT images, a virtual reduced dimensional airway/vascualr network will be constructed. Using this network both airway and blood flow profiles will be calculated. These profiles will then be used to model gas transport within the lungs. The models will allow us to investigate the role of airway restriction, body position during testing and washout gas choice have on MBW measures. 
 

Fri, 25 Jan 2019

14:00 - 15:00
C2

Understanding Thermodynamic Theories

Chris Farmer
(University of Oxford)
Abstract

Many scientists, and in particular mathematicians, report difficulty in understanding thermodynamics. So why is thermodynamics so difficult? To attempt an answer, we begin by looking at the components in an exposition of a scientific theory. These include a mathematical core, a motivation for the choice of variables and equations, some historical remarks, some examples and a discussion of how variables, parameters, and functions (such as equations of state) can be inferred from experiments. There are other components too, such as an account of how a theory relates to other theories in the subject.

 

It will be suggested that theories of thermodynamics are hard to understand because (i) many expositions appear to argue from the particular to the general (ii) there are several different thermodynamic theories that have no obvious logical or mathematical equivalence (iii) each theory really is subtle and requires intense study (iv) in most expositions different theories are mixed up, and the different components of a scientific exposition are also mixed up. So, by presenting one theory at a time, and by making clear which component is being discussed, we might reduce the difficulty in understanding any individual thermodynamic theory. The key is perhaps separation of the mathematical core from the physical motivation. It is also useful to realise that a motivation is not generally the same as a proof, and that no theory is actually true.

 

By way of illustration we will attempt expositions of two of the simplest thermodynamic theories – reversible and then irreversible thermodynamics of homogeneous materials – where the mathematical core and the motivation are discussed separately. In conclusion we’ll relate these two simple theories to other, foundational and generalised, thermodynamic theories.

Fri, 25 Jan 2019

12:00 - 13:00
L4

Deep learning on graphs and manifolds: going beyond Euclidean data

Michael Bronstein
(Imperial College London)
Abstract

In the past decade, deep learning methods have achieved unprecedented performance on a broad range of problems in various fields from computer vision to speech recognition. So far research has mainly focused on developing deep learning methods for Euclidean-structured data. However, many important applications have to deal with non-Euclidean structured data, such as graphs and manifolds. Such data are becoming increasingly important in computer graphics and 3D vision, sensor networks, drug design, biomedicine, high energy physics, recommendation systems, and social media analysis. The adoption of deep learning in these fields has been lagging behind until recently, primarily since the non-Euclidean nature of objects dealt with makes the very definition of basic operations used in deep networks rather elusive. In this talk, I will introduce the emerging field of geometric deep learning on graphs and manifolds, overview existing solutions and outline the key difficulties and future research directions. As examples of applications, I will show problems from the domains of computer vision, graphics, high-energy physics, and fake news detection. 

Fri, 25 Jan 2019

11:45 - 13:15
L3

InFoMM CDT Group Meeting

Oliver Sheridan-Methven, Davin Lunz, Ellen Luckins, Victor Wang
(Mathematical Institute)
Fri, 25 Jan 2019

10:00 - 11:00
L5

Coresets for clustering very large datasets

Stephane Chretien
(NPL)
Abstract

Clustering is a very important task in data analytics and is usually addressed using (i) statistical tools based on maximum likelihood estimators for mixture models, (ii) techniques based on network models such as the stochastic block model, or (iii) relaxations of the K-means approach based on semi-definite programming (or even simpler spectral approaches). Statistical approaches of type (i) often suffer from not being solvable with sufficient guarantees, because of the non-convexity of the underlying cost function to optimise. The other two approaches (ii) and (iii) are amenable to convex programming but do not usually scale to large datasets. In the big data setting, one usually needs to resort to data subsampling, a preprocessing stage also known as "coreset selection". We will present this last approach and the problem of selecting a coreset for the special cases of K-means and spectral-type relaxations.

 

Thu, 24 Jan 2019

16:00 - 17:00
L6

Hida families of Drinfeld modular forms

Giovanni Rosso
(University of Cambridge)
Abstract

Seminal work of Hida tells us that if a modular eigenform is ordinary at p then we can always find other eigenforms, of different weights, that are congruent to our given form. Even better, it says that we can find q-expansions with coefficients in p-adic analytic function of the weight variable k that when evaluated at positive integers give the q-expansion of classical eigenforms. His construction of these families uses mainly the geometry of the modular curve and its ordinary locus.
In a joint work with Marc-Hubert Nicole, we obtained similar results for Drinfeld modular forms over function fields. After an extensive introduction to Drinfeld modules, their moduli spaces, and Drinfeld modular forms, we shall explain how to construct Hida families for ordinary Drinfeld modular forms.

Thu, 24 Jan 2019

16:00 - 17:30
L4

Contagion and Systemic Risk in Heterogeneous Financial Networks

Dr Thilo Meyer-Brandis
(University of Munich)
Abstract

 One of the most defining features of modern financial networks is their inherent complex and intertwined structure. In particular the often observed core-periphery structure plays a prominent role. Here we study and quantify the impact that the complexity of networks has on contagion effects and system stability, and our focus is on the channel of default contagion that describes the spread of initial distress via direct balance sheet exposures. We present a general approach describing the financial network by a random graph, where we distinguish vertices (institutions) of different types - for example core/periphery - and let edge probabilities and weights (exposures) depend on the types of both the receiving and the sending vertex. Our main result allows to compute explicitly the systemic damage caused by some initial local shock event, and we derive a complete characterization of resilient respectively non-resilient financial systems in terms of their global statistical characteristics. Due to the random graphs approach these results bear a considerable robustness to local uncertainties and small changes of the network structure over time. Applications of our theory demonstrate that indeed the features captured by our model can have significant impact on system stability; we derive resilience conditions for the global network based on subnetwork conditions only. 

Thu, 24 Jan 2019
16:00
C4

An overview of the SYZ conjecture

Thomas Prince
(Oxford University)
Abstract

The Strominger-Yau-Zaslow (SYZ) conjecture postulates that mirror dual Calabi-Yau manifolds carry dual special Lagrangian fibrations. Within the study of Mirror Symmetry the SYZ conjecture has provided a particularly fruitful point of convergence of ideas from Riemannian, Symplectic, Tropical, and Algebraic geometry over the last twenty years. I will attempt to provide a brief overview of this aspect of Mirror Symmetry.

Thu, 24 Jan 2019

16:00 - 17:00
L3

Instabilities in Blistering

Dr Draga Pihler-Puzović
(University of Manchester)
Abstract

Blisters form when a thin surface layer of a solid body separates/delaminates from the underlying bulk material over a finite, bounded region. It is ubiquitous in a range of industrial applications, e.g. blister test is applied to assess the strength of adhesion between thin elastic films and their solid substrates, and during natural processes, such as formation and spreading of laccoliths or retinal detachment.

We study a special case of blistering, in which a thin elastic membrane is adhered to the substrate by a thin layer of viscous fluid. In this scenario, the expansion of the newly formed blister by fluid injection occurs via a displacement flow, which peels apart the adhered surfaces through a two-way interaction between flow and deformation. If the injected fluid is less viscous than the fluid already occupying the gap, patterns of short and stubby fingers form on the propagating fluid interface in a radial geometry. This process is regulated by membrane compliance, which if increased delays the onset of fingering to higher flow rates and reduces finger amplitude. We find that the morphological features of the fingers are selected in a simple way by the local geometry of the compliant cell. In contrast, the local geometry itself is determined from a complex fluid–solid interaction, particularly in the case of rectangular blisters. Furthermore, changes to the geometry of the channel cross-section in the latter case lead to a rich variety of possible interfacial patterns. Our experiments provide a link between studies of airway reopening, Saffman-Taylor fingering and printer’s instability.   

Thu, 24 Jan 2019

14:00 - 15:00
L4

Bespoke stochastic Galerkin approximation of nearly incompressible elasticity

Prof David Silvester
(Manchester University)
Abstract

We discuss the key role that bespoke linear algebra plays in modelling PDEs with random coefficients using stochastic Galerkin approximation methods. As a specific example, we consider nearly incompressible linear elasticity problems with an uncertain spatially varying Young's modulus. The uncertainty is modelled with a finite set of parameters with prescribed probability distribution.  We introduce a novel three-field mixed variational formulation of the PDE model and and  assess the stability with respect to a weighted norm. The main focus will be  the efficient solution of the associated high-dimensional indefinite linear system of equations. Eigenvalue bounds for the preconditioned system can be  established and shown to be independent of the discretisation parameters and the Poisson ratio.  We also  discuss an associated a posteriori error estimation strategy and assess proxies for the error reduction associated with selected enrichments of the approximation spaces.  We will show by example that these proxies enable the design of efficient  adaptive solution algorithms that terminate when the estimated error falls below a user-prescribed tolerance.

This is joint work with Arbaz Khan and Catherine Powell

Thu, 24 Jan 2019

13:00 - 14:00
L4

Talks by Dphil students

Tanut Treetanthiploet and Julien Vaes (Dphil students)
Abstract

Tanut Treetanthiploet
---------------------
Exploration vs Exploitation under Statistical Uncertainty

The exploration vs Exploitation trade-off can be quantified and studied through the notion of statistical uncertainty using the theory of nonlinear expectations. The dynamic allocation problem of multi-armed bandits will be discussed. In the case of a finite state space in discrete time, we can describe the value function in terms of the solution to a discrete BSDE and obtain a similar notion to the Bellman equation. We also give an approximation scheme to evaluate decisions in the simple setting.


Julien Vaes
-----------
Optimal Execution Strategy Under Price and Volume Uncertainty

In the seminal paper on optimal execution of portfolio transactions, Almgren and Chriss define the optimal trading strategy to liquidate a fixed volume of a single security under price uncertainty. Yet there exist situations, such as in the power market, in which the volume to be traded can only be estimated and becomes more accurate when approaching a specified delivery time. To meet the need of efficient strategies in these situations, we have developed  a model that accounts for volume uncertainty and show that a risk-averse trader has benefit in delaying their trades. We show that the optimal strategy is a trade-off between early and late trades to balance risk associated to both price and volume. With the incorporation of a risk term for the volume to trade, the static optimal strategies obtained with our model avoid the explosion in the algorithmic complexity associated to dynamic programming solutions while yielding to competitive performance.

 

Thu, 24 Jan 2019
12:00
L4

On the uniqueness of graphical mean curvature flow

Mariel Saez
(Pontificia Universidad Católica de Chile)
Abstract

In this talk I will discuss recent work with P. Daskalopoulos on sufficient conditions to prove uniqueness of complete graphs evolving by mean curvature flow. It is interesting to remark that the behaviour of solutions to mean curvature flow differs from the heat equation, where non-uniqueness may occur even for smooth initial conditions if the behaviour at infinity is not prescribed for all times. 

Thu, 24 Jan 2019
11:00
L6

Kim-independence in NSOP1 theories

Itay Kaplan
(Hebrew University)
Abstract

NSOP1 is a class of first order theories containing simple theories, which contains many natural examples that somehow slip-out of the simple context.

As in simple theories, NSOP1 theories admit a natural notion of independence dubbed Kim-independence, which generalizes non-forking in simple theories and satisfies many of its properties.

In this talk I will explain all these notions, and in particular talk about recent progress (joint with Nick Ramsey) in the study of Kim-independence, showing transitivity and several consequences.

 

Wed, 23 Jan 2019
16:00
C1

Commensurator rigidity from actions on graphs

Richard Wade
(Oxford University)
Abstract

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.

Tue, 22 Jan 2019
16:00
L5

EPPA and RAMSEY

Jaroslav Nesetril
(Charles University, Prague)
Abstract

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.
 

Tue, 22 Jan 2019

15:30 - 16:30
L4

The tautological ring of Shimura varieties

Paul Ziegler
(Oxford)
Abstract

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.

Tue, 22 Jan 2019
15:00
C1

Cluster Adjacency

Dr Omer Gurdogan
(Southampton)
Abstract

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.

Tue, 22 Jan 2019

14:30 - 15:00
L5

Shape optimization with finite elements

Alberto Paganini
(Oxford)
Abstract

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.

Tue, 22 Jan 2019

14:30 - 15:30
C6

Testing for an odd hole

Paul Seymour
Abstract

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.

Tue, 22 Jan 2019
14:15
L4

Generalisations of the (Pin,osp(1|2)) Howe duality

Roy Oste
(University of Ghent)
Abstract

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.

Tue, 22 Jan 2019

14:00 - 14:30
L5

Halley and Newton are one step apart

Trond Steihaug
(Bergen)
Abstract

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.