Past Fridays@4

Aden Forrow and Paul Ziegler

Aden Forrow
Optimal transport and cell differentiation

Optimal transport is a rich theory for comparing distributions, with both deep mathematics and application ranging from 18th century fortification planning to computer graphics. I will tie its mathematical story to a biological one, on the differentiation of cells from pluripotency to specialized functional types. First the mathematics can support the biology: optimal transport is an apt tool for linking experimental samples across a developmental time course. Then the biology can inspire new mathematics: based on the branching structure expected in differentiation pathways, we can find a regularization method that dramatically improves the statistical performance of optimal transport.

Paul Ziegler
Geometry and Arithmetic

For a family of polynomials in several variables with integral coefficients, the Weil conjectures give a surprising relationship between the geometry of the complex-valued roots of these polynomials and the number of roots of these polynomials "modulo p". I will give an introduction to this circle of results and try to explain how they are used in modern research.

31 May 2019
Katia Babbar (AI Wealth Technologies & QuantBright), Jara Imbers (Risk Management Solutions) and Tom Hawes (Smith Institute)

A panel discussion on non-academic careers for mathematicians with PhDs, featuring Katia Babbar (AI Wealth Technologies & QuantBright), Jara Imbers (Risk Management Solutions) and Tom Hawes (Smith Institute).

24 May 2019
Philip Maini

What is the point of giving a talk?  What is the point of going to a talk?  In this presentation, which is intended to have a lot of audience participation, I would like to explore how one should prepare talks for different audiences and different occasions, and what one should try to get out of going to a talk.

17 May 2019
Valérie Voorsluijs and Matthias Nagel

Valérie Voorsluijs
Deterministic limit of intracellular calcium spikes
Abstract: In non-excitable cells, global calcium spikes emerge from the collective dynamics of clusters of calcium channels that are coupled by diffusion. Current modeling approaches have opposed stochastic descriptions of these systems to purely deterministic models, while both paradoxically appear compatible with experimental data. Combining fully stochastic simulations and mean-field analyses, we demonstrate that these two approaches can be reconciled. Our fully stochastic model generates spike sequences that can be seen as noise-perturbed oscillations of deterministic origin while displaying statistical properties in agreement with experimental data. These underlying deterministic oscillations arise from a phenomenological spike nucleation mechanism.

Matthias Nagel
Knots in dimensions three and four
Abstract: Knot theory studies the various embeddings of a circle into three-dimensional space. I will describe an equivalence relation on knots, called "concordance", which takes the fourth dimension into account. The study of concordance is intimately related with many problems at the heart of the topology of four-manifolds, such as the difference between the smooth and the topological category, and I will discuss results that illuminate this relation.

10 May 2019

Aura Raulo (Ecological and Evolutionary Dynamics) and Marie-Claire Koschowitz (Vertebrate Palaeobiology) discuss their work and its mathematical challenges.

Aura Raulo

" Aura Raulo is a graduate student in Zoology Department working on transmission of symbiotic bacteria in the social networks of their animal hosts"
Title: Heaps in networks - How we share our microbiota through kisses
Abstract: Humans, like all vertebrates have a microbiome, a diverse community of symbiotic bacteria that live in and on us and are crucial for our functioning. These bacteria help us digest food, regulate our mood and function as a key part of our immune system. Intriguingly, while they are part of us, they are, unlike our other cells, in constant flux between us, challenging the traditional definition of a biological individual. Many of these bacteria need intimate social contact to be transmitted from human to human, making social network analysis tools handy in explaining their community dynamics.What then is a recipe for a ``good microbiome”? Theories and evidence implies that the most healthy and immunologically robust microbiome composition is both diverse, semi-stable and somewhat synchronized among closely interacting individuals, but little is known about what kind of transmission landscapes determine these bacterial cocktails. In my talk, I will present humanmicrobiome as a network trait: a metacommunity of cells shaped by an equilibrium of isolation and contact among their hosts. I propose that we do notnecessarily need to think of levels of life (e.g. cells, individuals, populations) as being neatly nested inside of each other. Rather, aggregations of cooperating cells (both bacteria and human cells) can be considered as mere tighter clusters in their interaction network, dynamically creating de novo defined units of life. I will present a few game theoretical evolutionary dilemmas following from this perspective and highlight outstanding questions in mapping how network position of the host translates into community composition of bacteria in flux.

Marie Koschowitz
“Marie Koschowitz is a PhD student in the Department of Zoology and the Department of Earth Sciences, working on comparative physiology and large scale evolutionary patterns in reptiles such as crocodiles, birds and dinosaurs."
Title: Putting the maths into dinosaurs – A zoologist's perspective
Abstract: Contemporary palaeontology is a subject area that often deals with sparse data.Therefore, palaeontologists became rather inventive in pursuit of getting the most out of what is available. If we find a dinosaur’s skull that shows prominent, but puzzling, bony ridges without any apparent function, how can we make meaningful interpretations of its purpose in the living animal that was? If we are confronted with a variety of partially preserved bones from animals looking anatomically similar, but not quite alike, how can we infer relationships in the absence of genetic data?Some methods that resolve these questions, such as finite element analysis, were borrowed from engineering. Others, like comparative phylogenetics or MCMC generalised mixed effects models, are even more directly based on mathematical computations. All of these approaches help us to calculate things like a raptors bite-force and understand the ins and outsof their skulls anatomy, or why pterosaurs and plesiosaurs aren’t exactly dinosaurs. This talk aims to presents a selection of current approaches to applied mathematics which have been inspired by interdisciplinary research – and to foster awareness of all the ways how mathematicians can get involved in “dinosaur research”, if they feel inclined to do so.


3 May 2019

What actually happens when you submit an article to a journal? How does refereeing work in practice? How can you keep editors happy as an author or referee? How does one become a referee or editor? What does 'publication' mean with the internet and arXiv?

In this panel we'll discuss what happens between finishing writing a mathematical paper and its final (?) publication, looking at the various roles that people play and how they work best.

Featuring Helen Byrne, Rama Cont and Jonathan Pila.


26 April 2019
Federico Danieli and Christian Bick

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.

1 March 2019

Further Information: 

Speaker 1: Pawan Kumar
Title: Neural Network Verification
Abstract: In recent years, deep neural networks have started to find their way into safety critical application domains such as autonomous cars and personalised medicine. As the risk of an error in such applications is very high, a key step in the deployment of neural networks is their formal verification: proving that a network satisfies a desirable property, or providing a counter-example to show that it does not. In this talk, I will formulate neural network verification as an optimization problem, briefly present the existing branch-and-bound style algorithms to compute a globally optimal solution, and highlight the outstanding mathematical challenges that limit the size of problems we can currently solve.

Speaker 2: Samuel Albanie
Title: The Design of Deep Neural Network Architectures: Exploration in a High-Dimensional Search Space
Abstract: Deep Neural Networks now represent the dominant family of function approximators for tackling machine perception tasks. In this talk, I will discuss the challenges of working with the high-dimensional design space of these networks. I will describe several competing approaches that seek to fully automate the network design process and the open mathematical questions for this problem.