Past Fridays@4

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.


 

28 February 2020
16:00
Elena Gal and Carolina Urzua-Torres
Abstract

Elena Gal
Categorification, Quantum groups and TQFTs

Quantum groups are mathematical objects that encode (via their "category of representations”) certain symmetries which have been found in the last several dozens of years to be connected to several areas of mathematics and physics. One famous application uses representation theory of quantum groups to construct invariants of 3-dimensional manifolds. To extend this theory to higher dimensions we need to “categorify" quantum groups - in essence to find a richer structure of symmetries. I will explain how one can approach such problem.

 

Carolina Urzua-Torres
Why you should not do boundary element methods, so I can have all the fun.

Boundary integral equations offer an attractive alternative to solve a wide range of physical phenomena, like scattering problems in unbounded domains. In this talk I will give a simple introduction to boundary integral equations arising from PDEs, and their discretization via Galerkin BEM. I will discuss some nice mathematical features of BEM, together with their computational pros and cons. I will illustrate these points with some applications and recent research developments.
 

6 December 2019
16:00
Abstract

Dr Rachel Philip will discuss her experiences working at the interface between academic mathematics and industry. Oxford University Innovation will discuss how they can help academics when interacting with industry. 

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