Past Fridays@4

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.

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.

25 January 2019
Maurice Chiodo

Teaching ethics to the mathematicians who need it most
For the last 20 years it has become increasingly obvious, and increasingly pressing, that mathematicians should be taught some ethical awareness so as to realise the impact of their work. This extends even to those more highly trained, like graduate students and postdocs. But which mathematicians should we be teaching this to, what should we be teaching them, and how should we do it? In this talk I’ll explore the idea that all mathematicians will, at some stage, be faced with ethical challenges stemming from their work, and yet few are ever told beforehand.

18 January 2019
Mohit Dalwadi and Thomas Prince

Thomas Prince The double life of the number 24.

The number 24 appears in a somewhat surprising result in the study of polyhedra with integer lattice points. In a different setting, the number 24 is the Euler characteristic of a K3 surface: a four (real) dimensional object which plays a central role in algebraic geometry. We will hint at why both instances of 24 are in fact the same, and suggest that integral affine geometry can be used to interpolate between the realm of integral polytopes and the world of complex algebraic geometry.

Mohit Dalwadi A multiscale mathematical model of bacterial nutrient uptake

In mathematical models that include nutrient delivery to bacteria, it is prohibitively expensive to include many small bacterial regions acting as volumetric nutrient sinks. To combat this problem, such models often impose an effective uptake instead. However, it is not immediately clear how to relate properties on the bacterial scale with this effective result. For example, one may intuitively expect the effective uptake to scale with bacterial volume for weak first-order uptake, and with bacterial surface area for strong first-order uptake. I will present a general model for bacterial nutrient uptake, and upscale the system using homogenization theory to determine how the effective uptake depends on the microscale bacterial properties. This will show us when the intuitive volume and surface area scalings are each valid, as well as the correct form of the effective uptake when neither of these scalings is appropriate.