Tue, 30 Apr 2019

14:30 - 15:30
L6

Erdős-Rothschild problem for five and six colours

Jozef Skokan
Further Information

Given positive integers n,r,k, the Erdős-Rothschild problem asks to determine the largest number of r-edge-colourings without monochromatic k-cliques a graph on n vertices can have. In the case of triangles, i.e. when k=3, the solution is known for r = 2,3,4. We investigate the problem for five and six colours.

Tue, 30 Apr 2019

14:30 - 15:00
L3

Exponential integrators for stiff PDEs

Lloyd Nick Trefethen
(Oxford)
Abstract

Many time-dependent PDEs -- KdV, Burgers, Gray-Scott, Allen-Cahn, Navier-Stokes and many others -- combine a higher-order linear term with a lower-order nonlinear term.  This talk will review the method of exponential integrators for solving such problems with better than 2nd-order accuracy in time.

Tue, 30 Apr 2019

14:00 - 14:30
L3

Computable upper error bounds for Krylov subspace approximations to matrix exponentials

Tobias Jawecki
(TU Wien)
Abstract

A defect-based a posteriori error estimate for Krylov subspace approximations to the matrix exponential is introduced. This error estimate constitutes an upper norm bound on the error and can be computed during the construction of the Krylov subspace with nearly no computational effort. The matrix exponential function itself can be understood as a time propagation with restarts. In practice, we are interested in finding time steps for which the error of the Krylov subspace approximation is smaller than a given tolerance. Finding correct time steps is a simple task with our error estimate. Apart from step size control, the upper error bound can be used on the fly to test if the dimension of the Krylov subspace is already sufficiently large to solve the problem in a single time step with the required accuracy.

Tue, 30 Apr 2019

14:00 - 15:15
L4

Single electron entanglement and the Aharonov-Bohm Effect

Vlatko Vedral
(Oxford)
Further Information

Please note the change of time (just this week)

Abstract

I will review the idea that entanglement must ultimately be understood in terms of modes, rather than in terms of particles. The most striking instance of mode entanglement is a single particle entangled state, which I will discuss both in the case of bosons as well as in the case of fermions. I then proceed to show that the Aharonov-Bohm effect can be understood by using a single electron entangled state. Finally, I will argue that this demonstrates beyond doubt that the Aharonov-Bohm effect is non non-local, contrary to what is frequently claimed in the literature.

 

Tue, 30 Apr 2019

12:00 - 13:00
C4

Spreading of Memes on Multiplex Networks

Joseph O’Brien
(University of Limerick)
Abstract

The advent of social media and the resulting ability to instantaneously communicate ideas and messages to connections worldwide is one of the great consequences arising from the telecommunications revolution over the last century. Individuals do not, however, communicate only upon a single platform; instead there exists a plethora of options available to users, many of whom are active on a number of such media. While each platform offers some unique selling point to attract users, e.g., keeping up to date with friends through messaging and statuses (Facebook), photo sharing (Instagram), seeing information from friends, celebrities and numerous other outlets (Twitter) or keeping track of the career paths of friends and past colleagues (Linkedin), the platforms are all based upon the fundamental mechanisms of connecting with other users and transmitting information to them as a result of this link.

 

In this talk a model for the spreading of online information or “memes" on multiplex networks is introduced and analyzed using branching-process methods. The model generalizes that of [Gleeson et al., Phys. Rev. X., 2016] in two ways. First, even for a monoplex (single-layer) network, the model is defined for any specific network defined by its adjacency matrix, instead of being restricted to an ensemble of random networks. Second, a multiplex version of the model is introduced to capture the behavior of users who post information from one social media platform to another. In both cases the branching process analysis demonstrates that the dynamical system is, in the limit of low innovation, poised near a critical point, which is known to lead to heavy-tailed distributions of meme popularity similar to those observed in empirical data.

 

[1] J. P. Gleeson et al. “Effects of network structure, competition and memory time on social spreading phenomena”. Physical Review X 6.2 (2016), p. 021019.

[2] J. D. O’Brien et al. "Spreading of memes on multiplex networks." New Journal of Physics 21.2 (2019): 025001.

Mon, 29 Apr 2019
16:00
L4

Measuring families of curves

Jan Maly
(Charles University Prague)
Abstract

For measuring families of curves, or, more generally, of measures, $M_p$-modulus is traditionally used. More recent studies use so-called plans on measures. In their fundamental paper Ambrosio, Di Marino and Savare proved that these two approaches are in some sense equivalent within $1<p<\infty$. We consider the limiting case $p=1$ and show that the $AM$-modulus can be obtained alternatively by the plan approach. On the way, we demonstrate unexpected behavior of the $AM$-modulus in comparison with usual capacities.

This is a joint work with Vendula Honzlov\'a Exnerov\'a, Ond\v{r}ej F.K. Kalenda and Olli Martio. Partially supported by the grant GA\,\v{C}R P201/18-07996S of the Czech Science Foundation.

Mon, 29 Apr 2019
15:45
L6

Knots, SL_2(R) representations, and a total Lin invariant

Jacob Rasmussen
(Cambridge)
Abstract

X.S. Lin defined an invariant of knots in S^3 by counting represenations 
of the knot group into SU(2) with fixed meridinal holonomy. Lin's 
invariant was subsequently shown to coincide with the Levine-Tristam 
signature. I'll define an analogous total Lin invariant which counts 
repesentations into both SU(2) and SL_2(R). Unlike the SU(2) version, this 
invariant does not (as far as I know) coincide with other known 
invariants. I'll describe some applications to left-orderability of Dehn 
fillings and branched covers, as well as a curious connection with the 
Alexander polynomial. This is joint work with Nathan Dunfield.

Mon, 29 Apr 2019

15:45 - 16:45
L3

Inference of a large rank-one matrix and Hamilton-Jacobi equations

JEAN-CHRISTOPHE MOURRAT
(ENS FRANCE)
Abstract

We observe a noisy version of a large rank-one matrix. Depending on the strength of the noise, can we recover non-trivial information on the matrix? This problem, interesting on its own, will be motivated by its link with a "spin glass" model, which is a model of statistical mechanics where a large number of variables interact with one another, with random interactions that can be positive or negative. The resolution of the initial question will involve a Hamilton-Jacobi equation

Mon, 29 Apr 2019

14:15 - 15:15
L3

Scaling limits and surface tension for gradient Gibbs measure

WEI WU
(Warwick University)
Abstract

I will discuss new results for the gradient field models with uniformly convex potential (also known as the Ginzburg-Landau field). A connection between the scaling limits of the field and elliptic homogenization was introduced by Naddaf and Spencer in 1997. We quantify the existing central limit theorems in light of recent advances in quantitative homogenization; and positively settle a conjecture of Funaki and Spohn about the surface tension. Joint work with Scott Armstrong. 

 

Mon, 29 Apr 2019

14:15 - 15:15
L4

Einstein 4-manifolds, negative curvature and smoothing cones

Joel Fine
(Universite Libre de Bruxelles)
Abstract

I will describe joint work with Bruno Premoselli which gives a new existence theorem for negatively curved Einstein 4-manifolds, which are obtained by smoothing the singularities of hyperbolic cone metrics. Let (M_k) be a sequence of compact 4-manifolds and let g_k be a hyperbolic cone metric on M_k with cone angle \alpha (independent of k) along a smooth surface S_k. We make the following assumptions:

1. The injectivity radius i(k) of M_k tends to infinity (where in defining injectivity radius we ignore those geodesics which hit the cone singularity)

2. The normal injectivity radius of S_k is at least i(k)/2.

3. The area of the singular locii satisfy A(S_k)\leq C \exp(5 i(k)/2) for some C independent of k.

When these assumptions hold, we prove that for all large k, M_k carries a smooth Einstein metric of negative curvature. The proof involves a gluing theorem and a parameter dependent implicit function theorem (where k is the parameter). As I will explain, negative curvature plays an essential role in the proof. (For those who may be aware of our arxiv preprint, https://arxiv.org/abs/1802.00608 [arxiv.org], the work
I will describe has a new feature, namely we now treat all cone angles, and not just those which are greater than 2\pi. This gives lots more examples of Einstein 4-manifolds.)

 

 

Fri, 26 Apr 2019

16:00 - 17:00
L1

Mathematics in developing countries

Federico Danieli and Christian Bick
(University of Oxford)
Abstract

How do you create a self-sustaining, flourishing academic community in a developing country? What kind of challenges need to be overcome to ensure that quality education becomes available? What can we do to help make it happen? In this talk, we will describe our experience visiting the University of Yangon in Myanmar. During the visit, we delivered a course to the academic staff, and discussed future collaborations between Oxford and Yangon, as well as further directions for Mathematical education in Myanmar, all the while marvelling at the wonders of the Burmese culture.

Fri, 26 Apr 2019

11:45 - 13:15
L4

InFoMM CDT Group Meeting

Valentin Sulzer, Federico Danieli, Jonathan Peters, James Morrill
(Mathematical Institute)
Tue, 02 Apr 2019

11:00 - 16:00
L2

MiLS Meeting on Multiscale modelling techniques and their applications in biology and medicine

Various Speakers
(Mathematical Institute)
Further Information

By Daniele Avitabile on Mar 04, 2019 09:38 pm

The ninth Mathematics in Life Sciences (MiLS) meeting will focus on "Multiscale modelling techniques and their applications in biology and medicine". It will take place on the 2nd of April 2019 from 11am to 4pm, at the University of Oxford. This is the first meeting organised in collaboration with our new members, Sarah Waters (University of Oxford), and  Alessia Annibale (King's College London).

The meeting will consist of two review talks aimed at non-experts, combined with several contributed research talks. The review talks will be given by Oliver Jensen (University of Manchester), and Patrick Farrell (University of Oxford).

Attendance to the meeting is free of charge, but we kindly ask you to register your intention to attend, by sending an email to Nicola.Kirkham@maths.ox.ac.uk

We solicit contributed talks and posters, especially from early career researchers and postgraduate students. If you are interested in giving a talk, please send a title and abstract to Sarah.Waters (waters [at] maths [dot] ox [dot] ac [dot] uk) and Daniele Avitabile (daniele [dot] avitabile [at] nottingham [dot] ac [dot] uk).

You can read more about MiLS here and here and you can subscribe to our low-traffic newsletter here.


Read in browser »

 

Mon, 01 Apr 2019

17:00 - 18:00
L5

Remarks on Euler equations

Peter Constantin
(Princeton)
Further Information


 

Abstract

I'll talk about smooth solutions of Euler equations with compactly supported velocities, and applications to other equations.

Mon, 25 Mar 2019

11:00 - 12:00
N3.12

The homotopy type of algebraic cobordism categories

Fabian Hebestreit
(Bonn)
Abstract

In this talk I want to outline the proofs our of main results, i.e. the localisation theorem and the identification of the homotopy type of Grothendieck-Witt theory in terms of K- and L-theory.
Finally, as a small application I want to present a refinement and extension of certain maps relating certain Madsen-Tillmann spectra and orthogonal/symplectic algebraic K-theory spectra of the integers.

All original material is joint work with B.Calmès, E.Dotto, Y.Harpaz, M.Land, K.Moi, D.Nardin, T.Nikolaus and W.Steimle.
 

Thu, 21 Mar 2019

11:00 - 12:00
N3.12

Poincaré categories and L-theory

Fabian Hebestreit
(Bonn)
Abstract

I will start by briefly reviewing the Tate construction and in particular, the Tate diagonal. Using these I will then illustrate Lurie’s notion of Poincaré categories by considering Poincaré structures on module categories over a ring (spectrum) in detail. In particular, I will describe the somewhat subtle genuine Poincaré structure on the category of perfect complexes of an ordinary ring, which conjecturally links the classical notion of the Grothendieck-Witt spectrum to our derived version. Finally, I will compute its associated L-groups.

Mon, 18 Mar 2019
15:45
C4

Algebraic cobordism categories and Grothendieck-Witt-theory

Fabian Hebestreit
(University of Bonn)
Abstract

I will explain how Lurie‘s approach to L-theory via Poincaré categories can be extended to yield cobordism categories of Poincaré objects à la Ranicki. These categories can be delooped by an iterated Q-construction and the resulting spectrum is a derived version of Grothendieck-Witt-theory.  Its homotopy type can be described in terms of K- and L-theory as conjectured by Hesselholt-Madsen. Furthermore, it has a clean universal property analogous to that of K-theory, localisation sequences in much greater generality than classical Grothendieck-Witt theory, gives a cycle description of Weiss-Williams‘ LA-theory and allows for maps from the geometric cobordism category, refining and unifying various known invariants.

All original material is joint work with B.Calmès, E.Dotto, Y.Harpaz, M.Land, K.Moi, D.Nardin, T.Nikolaus and W.Steimle.

Mon, 18 Mar 2019
14:15
C4

Invariants for sublinearly biLipschitz equivalence

Gabriel Pallier
(Université Paris-Sud 11)
Abstract


The large-scale features of groups and spaces are recorded by asymptotic invariants. Examples of asymptotic invariants are the asymptotic cone and, for hyperbolic groups, the Gromov boundary.
In his study of asymptotic cones of connected Lie groups, Yves Cornulier introduced a class of maps called sublinearly biLipschitz equivalences. Like the more traditionnal quasiisometries, sublinearly biLipschitz equivalences are biLipschitz on the large-scale, but unlike quasiisometries, they are generally not coarse. Sublinearly biLipschitz equivalences still induce biLipschitz homeomorphisms between asymptotic cones. In this talk, I will focus on Gromov-hyperbolic groups and show how the Gromov boundary can be used to produce invariants distinguishing them up to sublinearly biLipschitz equivalences when the asymptotic cones do not. I will especially give applications to the large-scale sublinear geometry of hyperbolic Lie groups.
 

Tue, 12 Mar 2019

14:00 - 15:00
C2

Jacob Bernoulli’s role in the history of elasticity: From a discussion with a craftsman to the discovery of the elasticity rules

Sepideh Alassi
(University of Basel)
Abstract

Jacob Bernoulli is known for his studies of the curves, infinitesimal math- ematics and statistics. However, before being a professor in mathematics, he taught experimental physics at the University of Basel. This explains his high interest in solving physical problems with newly developed Leibnizian calculus. In his scientific notebook, Meditationes, there are more than thirty notes about various mechanical problems for solving of which Bernoulli has applied Leibnizian calculus and has advanced this method along the way. A discussion with a craftsman brought Bernoulli’s attention to the problem of the strength of a beam early in his career and occupied his mind until his death. The craftsman’s narration based on his experience highlighted the flaws in Galilean-Leibnizian theory of the strength of a beam. This was the starting point of Bernoulli’s quest to mathematically find the profile of a bent beam (the Elastica Problem) and the physical laws governing it. He started a challenge to encourage other mathematicians of the time to study the problem, providing a hint hidden in an anagram. Although he published his solution of the Elastica Problem in 1694, that was not the end of the quest for him. Studying his unpublished notes in Meditationes reveals that over the last decade of his life, Bernoulli has reconsidered the problem. In my project, I demonstrate that he has found remarkable concepts such as mean tensile stress, and the notion of local stress-strain relation, etc.

Mon, 11 Mar 2019

17:00 - 18:00
L1

Marc Lackenby - Knotty Problems

Marc Lackenby
(University of Oxford)
Further Information

Knots are a familiar part of everyday life, for example tying your tie or doing up your shoe laces. They play a role in numerous physical and biological phenomena, such as the untangling of DNA when it replicates. However, knot theory is also a well-developed branch of pure mathematics.

In his talk, Marc will give an introduction to this theory and will place it in the context of the modern field of topology. This is the branch of mathematics where you are allowed to stretch and deform objects, but not tear them. He will explain how topological techniques can be used to prove some surprising facts about knots. He will also give some problems about knots that mathematicians haven't yet been able to solve.

Marc Lackenby is a Professor of Mathematics in Oxford and a Fellow of St Catherine's College.

5.00pm-6.00pm, Mathematical Institute, Oxford

Please email @email to register.

Watch live:

https://www.facebook.com/OxfordMathematics
https://livestream.com/oxuni/lackenby

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

Fri, 08 Mar 2019

16:00 - 17:00
L1

False theta functions and their modular properties CANCELLED

Kathrin Bringmann
(University of Cologne)
Further Information

THIS TALK HAS BEEN CANCELLED

Abstract

In my talk I will discuss modular properties of false theta functions. Due to a wrong sign factor these are not directly seen to be modular, however there are ways to repair this. I will report about this in my talk.

 

Fri, 08 Mar 2019

14:00 - 15:00
C2

Generation of large-scale flows in mixed turbulent and stably stratified fluids

Louis Couston
(British Antarctic Survey)
Abstract

Energy transfers from small-scale turbulence and waves to large-scale flows are ubiquituous in oceans, atmospheres, planetary cores and stars.

Therefore, turbulence and waves have a direct effect on the large-scale organization of geophysical and astrophysical fluids and can affect their long-term dynamics.

In this talk I will discuss recent direct numerical simulation (DNS) results of two upscale energy transfer mechanisms that emerge from the dynamics of a fluid that is self-organized in a turbulent layer next to a stably-stratified one. This self-organization in an adjacent "two-layer" turbulent-stratified system is ubiquituous in nature and is representative of e.g. Earth's troposphere-stratosphere system, the oceans' surface mixed layer-thermocline system, and stars' convective-radiative interiors. The first set of DNS results will demonstrate how turbulent motions can generate internal waves, which then force a slowly-reversing large-scale flow, akin to Earth's Quasi-Biennial Oscillation (QBO). The second set of DNS results will show how the stratified layer regulates the emergence of large-scale vortices (LSV) in the turbulent layer under rapid rotation in the regime known as geostrophic turbulence. I will demonstrate why it is important to resolve both the turbulence and the waves, as otherwise the natural variability of the QBO is lost and LSV cannot form. I will discuss future works and highlight how the results may guide the implementation of upscale energy transfers in global earth system models.