Daniel Colquitt (Liverpool), Applied Mathematics

Controlling mechanical waves - cloaking, earthquake protection, and one-way waves

We will consider how the dynamic response of multi-scale mechanical systems can be controlled to achieve a range of unprecedented and astonishing phenomena in solid mechanics, including invisibility cloaking, earthquake shields, and waves that propagate in one direction only.

Riam Kanso (UCL), Conceptionx.org

Conception X: Explore entrepreneurship during your PhD

Conception X is a programme that creates deep tech startups from PhDs, during PhDs. It is designed for students who can use their skills to create products and services based on their research, becoming venture scientists. This talk will cover the rationale behind entrepreneurship as a career choice, how STEM phds have launched companies in the last two years via Conception X, and how future students can be involved. Conception X launched in UCL but is now open to students from all universities.

Zoltan Kocsis (Manchester), Proof Theory

Proof Theory and Topology

Proof theory is a branch of mathematical logic that treats proofs and demonstrations as mathematical objects, facilitating their analysis by means of mathematical techniques. Originating in Hilbert's foundational programme (early 1900s), research in proof theory has led to advances not just in mathematics, but in computer science and linguistics as well. In this talk I will explain how proof theoretic techniques bridge the gap between the study of finite and infinite topological spaces.

Daniel Loghin (Birmingham), Numerical Analysis

Numerical Analysis

Numerical Analysis is an all-pervasive field of mathematics in science and technology with many seminal past contributions and exciting current developments and opportunities. In my talk, I will aim to offer a glimpse into NA research, including a discussion of current trends and overlaps with other fields of science.

Lucy Morgan (Lancaster), Operational Research

Solving real world problems - Operational Research (OR) a tool for decision making

If you're interested in using/ developing mathematics to solve real world problems and make impactful decisions then Operational Research (OR) may be for you! Modern OR originated in WWII to improve the working of the UK's early warning radar system. Since then it has emerged in many industries including aviation, healthcare and manufacturing as a tool to aid decision making. Some classical OR problems include scheduling - how to plan flights for large scale airports, resource planning - what level of staff is needed to keep A&E waiting times down, and optimisation - how many cars should my plant make to maximise profit. In this talk I will share my experience as an early career researcher in OR and insight into some of the interesting problems my colleagues and I have worked on.

Benjamin Miller, CDT Mathematics for Real-World Systems (Warwick)

How can mathematicians help eradicate infectious diseases?

Infectious diseases are responsible for over 10 million deaths every year. The field of epidemiology requires mathematics in order to analyse, predict, and control disease outbreaks. Working in collaboration with medical doctors, biologists, and economists, mathematicians are often able to influence official policy in regards to how outbreaks are dealt with. I will introduce some vital epidemiological concepts and longstanding problems, before focusing on my research on sleeping sickness, a deadly disease endemic to sub-Saharan Africa.

Helen Ogden (Southampton), Statistics

Complex Models, Statistical Scalability and Fighting Lizards

The increase in computational power and data collection over recent decades has prompted the development of more complex and realistic statistical models to fit to this data. But this complexity presents challenges: it is often not possible to fit these models to data in a standard way, because computing the basic quantities used for statistical inference becomes computationally infeasible. This has led to a range of approximate approaches being developed, which scale well to large amounts of data, but may lack the statistical quality guarantees of the standard approaches. I will describe what these guarantees are and why they are important, and discuss how to check whether an approximate approach will still have these guarantees. I will use a model for the outcomes of fights between pairs of South African lizards as an example throughout the talk.

Jon Pitchford (York), Mathematical Ecology

Why does it all have to be so complicated?

Maths is simple, elegant and beautiful. Why does everything else in life have to be so complicated? From ecosystems to international finance, and from nuclear weapons to the internal clocks governing our toilet habits, everything seems a bit more complicated than it needs to be. I will argue that a careful mixture of maths and imagination might help to explain when complexity can be good. More importantly for this audience, I will illustrate some of the fantastic research opportunities, which a Maths degree can open up for you.

Gesine Reinert (Oxford), Applied Probability

Probability in Network Analysis

Networks are increasingly used as representations of complex data. To draw conclusions from such data, it is important to understand probabilistic models for such networks. For such models even seemingly simple questions such as the probability that the resulting network is connected are not easy to answer. Consequently, networks have inspired new results in applied probability. This talk will introduce networks, explain some of the important questions on networks, give some models for networks with some results, and state open research questions.

Louis Theran (St Andrews), Rigidity

Rigidity

Rigidity theory is interested in questions that relate extrinsic shape to intrinsic metric information. The field has its origins in classical results of Cauchy, who showed that a convex polyhedron is determined up to congruence by its combinatorial type and face shapes, and, later the characterisation of n-point Euclidean metric spaces by Schönberg and Young—Householder. I’ll talk about some current directions in the field, as well as recent applications in machine learning, condensed matter theory and multi-bounce / non-line of sight imaging.

Anitha Thillaisundaram (Lincoln), Algebra

Hausdorff dimension of pro-p groups - history and open problems

Hausdorff dimension was developed in the 1930s by Felix Hausdorff as a generalisation of our usual concept of integer dimension for sets in Euclidean space. It has been applied to fractals and was used to solved the coastline paradox. Over the past twenty years, there have been interesting and fruitful applications of Hausdorff dimension to certain infinite groups, namely profinite groups. Key results and open problems for Hausdorff dimensions of pro-p groups will be discussed.

Lynne Walling (Bristol), Number Theory

Sums of squares as an entry-way to research in number theory and modular forms

Much of number theory research is historically grounded in questions about the integers. Over the centuries, number theory has become a very rich, complex, and diverse field of research, incorporating many tools from algebra, analysis, geometry,..., with applications in mathematical physics, the digital economy,...

One historical pursuit in number theory is that of understanding sums of squares of integers, and one of the approaches to this question leads us to one of our first examples of modular forms. We introduce this example and discuss variations and extensions.

Jared White (Besançon), Abstract Analysis

Abstract Algebra Meets Analysis

We will introduce the theory of Banach algebras - a realm in which abstract algebra and analysis come together in beautiful and often surprising ways. The talk will give an overview of a few topic which nicely illustrate the interplay between algebra and analysis, in particular the so called "automatic" continuity of certain algebra homomorphisms.