Fridays@4

This event will take place in L1 and on Teams. A link will be available 30 minutes before the session begins. 

It's hard to believe: I've spent nearly 40 years in STEM. In that time, much changed: we changed from typewriters to PCs, from low performance to high  performance computing, from data-supported research to data-driven research, from traditional languages such as Fortran to a plethora of programming environments. And the rate of change seems to increase constantly. Some things have stayed more or less the same, such as the (lack of) diversity of the STEM community, the level of stress and the struggles we all experience (and the joys!). In this talk, I will reflect on those years, on lessons learned and not learned or unlearned, on things I wish I understood 40 years ago, and on things I still don't understand.

Margot is a professor at Stanford University in the Department of Energy Resources Engineering (ERE) and the Institute of Computational & Mathematical Engineering (ICME). Margot was born and raised in the Netherlands. Her STEM education started in 1982. In 1990 she received a MSc in applied mathematics at Delft University and then left her home country to search for sunnier and hillier places. She moved to Colorado and a year later to California to join the PhD program in Scientific Computing and Computational Mathematics at Stanford. During her PhD, Margot spent several quarters at Oxford University (with very good memories). Before returning to Stanford as faculty member in ERE, Margot spent 5 years as lecturer at the University of Auckland, New Zealand. From 2010-2018, Margot was the director of ICME. During this directorship, she founded the Women in Data Science initiative, which is now a global organization in over 70 countries. From 2015-2020, Margot was also the Senior Associate Dean of Educational Affairs at Stanford's school of Earth, Energy & Environmental Sciences. Currently, Margot still co-directs WiDS and is the Chair of the Board of SIAM. She has since moved back to the mountains (still sunny too) and now lives in Bend, Oregon.

This session will take place live in L1 and online. A Teams link will be shared 30 minutes before the session begins.

Candida Bowtell

Title: Chess puzzles: from recreational maths to fundamental mathematical structures

Abstract:
Back in 1848, in a German chess magazine, Max Bezzel asked how many ways there are to place 8 queens on a chessboard so that no two queens can attack one another. This question caught the attention of many, including Gauss, and was subsequently generalised. What if we want to place n non-attacking queens on an n by n chessboard? What if we embed the chessboard on the surface of a torus? How many ways are there to do this? It turns out these questions are hard, but mathematically interesting, and many different strategies have been used to attack them. We'll survey some results, old and new, including progress from this year.

Joshua Bull

Title: From Cancer to Covid: topological and spatial descriptions of immune cells in disease

Abstract:
Advances in medical imaging techniques mean that we have increasingly detailed knowledge of the specific cells that are present in different diseases. The locations of certain cells, like immune cells, gives clinicians clues about which treatments might be effective against cancer, or about how the immune system reacts to a Covid infection - but the more detailed this spatial data becomes, the harder it is for medics to analyse or interpret. Instead, we can turn to tools from topological data analysis, mathematical modelling, and spatial statistics to describe and quantify the relationships between different cell types in a wide range of medical images. This talk will demonstrate how mathematics can be used as a tool to advance our understanding of medicine, with a focus on immune cells in both cancer and covid-19.

This session will take place live in L1 and online. A Teams link will be shared 30 minutes before the session begins.

How can we make maths more accessible, promote its many applications, and encourage more women to enter the field? These are the questions we aim to address with Mathematigals.

Caoimhe Rooney and Jessica Williams met in 2015 at the start of their PhDs in mathematics in Oxford, and in 2020, they co-founded Mathematigals. Mathematigals is an online platform producing content to demonstrate fun mathematical curiosities, showcase ways maths can be used in real life, and promote female mathematicians. Mathematigals primarily produces animated videos that present maths in a way that is engaging to the general public.

In this session, Jess and Caoimhe will talk about their initial motivation to begin Mathematigals, demonstrate the process behind their content creation, and describe their future visions for the platform. The session will end with an opportunity for the audience to provide feedback or ideas to help Mathematigals on their journey to encourage future mathematicians.

This session will take place live in L1 and online. A Teams link will be shared 30 minutes before the session begins.

This session will take place live in L1 and online. A Teams link will be shared 30 minutes before the session begins.

This session will take place live in L1 and online. A Teams link will be shared 30 minutes before the session begins.

This session will take place live in L1 only and not online on Teams. 

Are you interested in sharing your love of Maths with the next generation of mathematicians, but you don’t know where to start? In this session we will discuss some basic principles and top tips for creating a workshop for students aged 14–16, and get you started on developing your own. There will also be the opportunity to work on this further afterwards and potentially deliver your session as part of the Oxfordshire Maths Masterclasses (for local school students) in Hilary Term. Bring along your favourite bit of maths and a willingness to have a go.

Jaclyn Lang
Explicit Class Field Theory
Class field theory was a major achievement in number theory
about a century ago that presaged many deep connections in mathematics
that today are known as the Langlands Program.  Class field theory
associates to each number field an special extension field, called the
Hilbert class field, whose ring of integers satisfies unique
factorization, mimicking the arithmetic in the usual integers.  While
the existence of this field is always guaranteed, it is a difficult
problem to find explicit generators for the Hilbert class field in
general.  The theory of complex multiplication of elliptic curves is
essentially the only setting where there is an explicit version of class
field theory.  We will briefly introduce class field theory, highlight
what is known in the theory of complex multiplication, and end with an
example for the field given by a fifth root of 19.  There will be many
examples!

Jan Sbierski
The strength of singularities in general relativity
One of the many curious features of Einstein’s theory of general relativity is that the theory predicts its own breakdown at so-called gravitational singularities. The gravitational field in general relativity is modelled by a Lorentzian manifold — and thus a gravitational singularity is signalled by the geometry of the Lorentzian manifold becoming singular. In this talk I will first review the classical definition of a gravitational singularity along with a classification of their strengths. I will conclude with outlining newly developed techniques which capture the singularity at the level of the connection of Lorentzian manifolds.

Clemens Koppensteiner
Categorifying Heisenberg algebras

Categorification replaces set-theoretic structures with category-theoretic analogues. We discuss what this means and why it is useful. We then discuss recent work on categorifying Heisenberg algebras and their Fock space representations. In particular this gives a satisfying answer to an observation about equivariant K-theory made by Ian Grojnowski in 1996.

Aggregation-Diffusion Equations
David Gómez-Castro

The aim of this talk is to discuss an evolution problem modelling particles systems exhibiting aggregation and diffusion phenomena, and we will focus mostly on the so-called Aggregation-Diffusion Equation: ∂ρ ∂t = ∇ · (ρ ∇(U′ (ρ) + V + W ∗ ρ)) (ADE)

First, we will discuss the modelling. The famous case U′ (ρ) = log ρ and W = 0 is the famous Heat Equation. In the classical literature, the term U′(ρ) is typically deduced from Darcy’s law and models an internal energy of the system. We will show through particle systems how the term V models a confinement energy and W ∗ ρ an aggregation energy. The complete model covers many famous examples from different disciplines: Porous Media, Fokker-Plank, Keller-Segel and others. After this modelling, we discuss the mathematical treatment of (ADE). As in the case of the Heat Equation, the diffusion cases where W = V = 0 are typically studied in the Lebesgue and Sobolev spaces. However, as in the Keller-Segel problem, a Dirac measures may appear in finite time. We present the Wasserstein distance between measures, which is a natural framework for these equations, connecting with the theory of Optimal Transport. In fact, when U, V and W are convex, (ADE) can be studied as the gradient-flow of a free-energy functional (i.e. curves minimising this energy) in this Wasserstein distance, applying Calculus of Variations techniques. We will discuss the minimisation problem associated to F, with an interest to the existence of Dirac measures. Finally, we will present new results showing that indeed, in some cases besides Keller-Segel, states with a Delta can be achieved through solutions of the evolution problem