Postgraduate Seminars Autumn 2020

These seminars (unless otherwise stated) will take place on Thursdays at 1pm via Zoom on an almost weekly basis.

22 October 2020

Zoom Link: https://ucl.zoom.us/j/97623801942 

Speaker: William Jackman
Supervisor: Prof JG Esler

Title: Atmospheric Turbulence and Zonal JetsAtmospheric Turbulence and Zonal Jets

Banding the planet on lines of constant latitude, Jupiter’s unearthly jets have been known to exist at least since 1660. Since then we’ve developed beautiful pictures of its turbulent, jet-dominated weather ( http://cdn.sci-news.com/images/enlarge4/image_5797e-Jupiter.jpg ), but maybe not such beautiful mathematics to explain it. I’ll aim to give an accessible introduction to 2D turbulence models and planetary scale jet formation. There’ll be lots of pictures and simulations. OPEN TO ALL. No knowledge of fluid dynamics needed!

Wednesday 28 October 2020 at 1pm

Zoom link: https://ucl.zoom.us/j/91901680161

Speaker: Ellen Jolley
Supervisor: Prof FT Smith

Title: Particle movement in a boundary layer

Aircraft icing is serious problem in aviation safety, in which atmospheric ice particles may adhere to the surface of aircraft wings and deform the aerodynamic shape, causing serious accidents in the worst cases. Hence there is a need to investigate the behaviour of a particle which enters the thin boundary layer near an aircraft surface. Modelling assumptions on body size reduce the governing equations for the body motion to a pair of non-linear integro-ODEs which displays a wide range of solutions, including eventual collision with the wall (`crash'), escape to infinity (`fly away') and repeatedly travelling far from the wall and back again without ever colliding or escaping (`bouncing'). I will derive the equations governing the fluid-body interaction leading to this dynamical system, and give a survey of the variety of particle behaviour.

05 November 2020

Zoom link: https://ucl.zoom.us/j/97293397403

Speaker: Corvin Paul
Supervisor: Prof M Singer

Title: G2-geometry and adiabatic Kovalev-Lefshetz fibrations

In this talk we'll give a short introduction to G2 metrics and how one might try to construct such a 7 dimensional metric from 4 and 3 dimensions. Keywords : G2-metrics, K3-surfaces, adiabatic limits.

Tuesday 17 November 2020 at 1pm

Zoom Link: https://ucl.zoom.us/j/91911835613

Speaker: Bishal Deb
Supervisor: Prof AD Sokal

Title: Total Positivity during distressing times

A matrix M with real entries is said to be totally positive (TP) if all its square submatrices have non-negative determinants. We can extend this definition to matrices with polynomial entries where a polynomial is said to be coefficientwise non-negative if all coefficients are non-negative and pointwise non-negative if it stays non-negative for all non-negative substitutions of its variables.

I will begin with introducing some terminology and make some historical remarks. Then I shall talk about three different types of TP which we are primarily interested in: Toeplitz total positivity, total positivity of a lower triangular matrix and Hankel total positivity. Various proof techniques will also be mentioned in this section which come from combinatorics, linear algebra, and classical analysis. The final section will be about the special case of the lower triangular matrix of Eulerian numbers whose TP was conjectured by Brenti in 1996. I shall talk about our (Xi Chen, BD, Alexander Dyachenko, Tomack Gilmore, Alan D. Sokal) partial progress and several refinements of the conjecture that we obtained along the way by using extensive computer experimentation.

No prerequisites will be necessary to follow the talk other than standard definitions from undergraduate courses in linear algebra, analysis, and combinatorics.

Wednesday 2 December 2020 at 1pm

Zoom link: https://ucl.zoom.us/j/92584613309

Speaker: Wendelin Lutz

Supervisor: Dr E Segal

Title: Classifying Fano manifolds via mirror symmetry

It turns out that mirror symmetry allows to establish a deep correspondence between Fano manifolds and certain Laurent polynomials. One might hence try to reduce the classification of Fano manifolds to the classification of these Laurent polynomials, which is a much easier problem, since it can largely be reduced to combinatorial calculations.
I will explain how this correspondence works, illustrate it with explicit examples and give an overview of what is known so far and what is still conjectural. No prior knowledge of Algebraic Geometry will be assumed.