Past Fridays@4

27 November 2020
16:00
Abstract

In this session we will discuss how interviewing and being interviewed has changed now that interviews are conducted online. We will have a panel comprising Marya Bazzi, Mohit Dalwadi, Sam Cohen, Ian Griffiths and Frances Kirwan who have either experienced being interviewed online and have interviewed online and we will compare experiences with in-person interviews. 

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20 November 2020
16:00
Yuji Nakatsukasa
Abstract

In this new session a speaker tells us about how their area of mathematics can be used in different applications.

In this talk, Yuji Nakatsukasa tells us about how random matrix theory can be used in numerical linear algebra. 

 

Abstract

Randomized SVD is a topic in numerical linear algebra that draws heavily from random matrix theory. It has become an extremely successful approach for efficiently computing a low-rank approximation of matrices. In particular the paper by Halko, Martinsson, and Tropp (SIREV 2011) contains extensive analysis, and has made it a very popular method. The classical Nystrom method is much faster, but only applicable to positive semidefinite matrices. This work studies a generalization of Nystrom's method applicable to general matrices, and shows that (i) it has near-optimal approximation quality comparable to competing methods, (ii) the computational cost is the near-optimal O(mnlog n+r^3) for a rank-r approximation of dense mxn matrices, and (iii) crucially, it can be implemented in a numerically stable fashion despite the presence of an ill-conditioned pseudoinverse. Numerical experiments illustrate that generalized Nystrom can significantly outperform state-of-the-art methods. In this talk I will highlight the crucial role played by a classical result in random matrix theory, namely the Marchenko-Pastur law, and also briefly mention its other applications in least-squares problems and compressed sensing.

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13 November 2020
15:00
to
17:00
James Grime
Abstract

Talking maths on YouTube is a lot of fun. Your audience will contain maths enthusiasts, young people, and the general public. These are people who are interested in what you have to say, and want to learn something new. Maths videos on YouTube can be used to teach maths, or to just show people something interesting. Making videos doesn't have to be technically difficult, but is good practice in explaining difficult concepts in clear and succinct ways. In this session we will discuss how to make your first YouTube video, including questions about content, presentation and video making.

Dr James Grime started making his first maths YouTube videos while working as a postdoc in 2008. James has made maths videos with Cambridge University, the Royal Institution, and MathsWorldUK, and is also a presenter on the popular YouTube channel Numberphile, which now has over 3 million subscribers worldwide.

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6 November 2020
16:00
Agnese Barbensi and Wolfger Peelaers
Abstract
Agnese Barbensi
Title: Knotted biopolymers
Abstract: Many biopolymers -most notably DNA- are knotted, or present some entanglement phenomena. The geometry and topology of these biopolymers has profound effects on their functioning. Using tools coming from topology and knot theory can help understanding the relations between the spatial arrangement and the behaviour of these molecules. In this talk we will give a brief overview of some useful techniques and recent work in this area. 
 
Wolfger Peelaers
Title: Vertex operator algebraic structures in quantum field theory
Abstract: Quantum field theory was originally developed to address questions involving interacting elementary particles, but ever since it has also provided, time and again, a bridge between ideas, concepts, and structures in mathematics and observables in physics. In this talk I will describe a remarkable connection of that type between vertex operator algebras and a class of highly symmetrical quantum field theories.

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30 October 2020
16:00
Abstract

In this session we discuss techniques to get the most out of your supervision sessions and tips on how to work with different personalities and use your supervisor's skills to your advantage. The session will be run by DPhil students and discussion among students during the session is encouraged.  

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23 October 2020
16:00
Martin Gallauer and Zhaohe Dai
Abstract

Martin Gallauer (North): "Algebraic algebraic geometry"
If a space is described by algebraic equations, its algebraic invariants are endowed with additional structure. I will illustrate this with some simple examples, and speculate on the meaning of the title of my talk.

Zhaohe Dai (South): "Two-dimensional material bubbles"
Two-dimensional (2D) materials are a relatively new class of thin sheets consisting of a single layer of covalently bonded atoms and have shown a host of unique electronic properties. In 2D material electronic devices, however, bubbles often form spontaneously due to the trapping of air or ambient contaminants (such as water molecules and hydrocarbons) at sheet-substrate interfaces. Though they have been considered to be a nuisance, I will discuss that bubbles can be used to characterize 2D materials' bending rigidity after the pressure inside being well controlled. I will then focus on bubbles of relatively large deformations so that the elastic tension could drive the radial slippage of the sheet on its substrate. Finally, I will discuss that the consideration of such slippage is vital to characterize the sheet's stretching stiffness and gives new opportunities to understand the adhesive and frictional interactions between the sheet and various substrates that it contacts.
 

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12 June 2020
16:00
Paolo Aceto
Abstract

Paolo Aceto

Knot concordance and homology cobordisms of 3-manifolds 

We introduce the notion of knot concordance for knots in the 3-sphere and discuss some key problems regarding the smooth concordance group. After defining homology cobordisms of 3-manifolds we introduce the integral and rational homology cobordism groups and briefly discuss their relationship with the concordance group. We conclude stating a few recent results and open questions on the structure of these groups.

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22 May 2020
16:00
Lucie Domino and Clemens Koppensteiner
Abstract
Lucie Domino
How to build 3D shapes from flat sheets using a three-centuries old theory
 
In this talk, I’ll present some of our recent work on morphing structures. We start from flat two-dimensional sheets which have been carefully cut and transform them into three-dimensional axisymmetric structures by applying edge-loads. We base our approach on the well-known Elastica theory developed by Euler to create structures with positive, negative, and variable Gaussian curvatures. We illustrate this with famous architectural examples, and verify our theory by both numerical simulations and physical experiments.
 
 
Clemens Koppensteiner
Logarithmic Riemann-Hilbert Correspondences

The classical Riemann-Hilbert correspondence is an elegant statement linking geometry (via flat connections) and topology (via local systems). However, when one allows the connections to have even simple singularities, the naive correspondence breaks down. We will outline some work on understanding this "logarithmic" setting.

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1 May 2020
16:00
Laura McDonnell
Abstract

In this session, Laura will explain the process of applying for an EPSRC fellowship. In particular, there will be a discussion on the Future Leaders Fellowships, New Investigator Awards and Standard Grant applications. There will also be a discussion on applying for EPSRC funding more generally. Laura will answer any questions that people have. 

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13 March 2020
16:00
Thomas Oliver and Ebrahim Patel
Abstract


Speaker: Thomas Oliver

Title: Hyperbolic circles and non-trivial zeros

Abstract: L-functions can often be considered as generating series of arithmetic information. Their non-trivial zeros are the subject of many famous conjectures, which offer countless applications to number theory. Using simple geometric observations in the hyperbolic plane, we will study the relationship between the zeros of L-functions and their characterisation amongst more general Dirichlet series.
 

Speaker: Ebrahim Patel

Title: From trains to brains: Adventures in Tropical Mathematics.

Abstract: Tropical mathematics uses the max and plus operator to linearise discrete nonlinear systems; I will present its popular application to solve scheduling problems such as railway timetabling. Adding the min operator generalises the system to allow the modelling of processes on networks. Thus, I propose applications such as disease and rumour spreading as well as neuron firing behaviour.


 

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