Special Event

Speaker: Dr Louise McMillan

Title: How I learned to stop worrying and love statistics: Why it's ok to leave academia and come back to it later

Abstract: I am a statistician now, but I started as a mathematician who hated stats. I had no interest in biology when I was 17, but now I'm an ecological statistician. I'm an academic with a PhD, but as late as a year before the start of my PhD I had decided that I would never do a PhD. How did I get here? I've worked in industry as well as academia, and I've enjoyed both. What did I learn from them? Come along if you don't know what to do with your life and are worried people will judge you for it. Come along if you, like me, find it hard to choose between all the different topics that interest you. Come along if you want to hear about rats and whales, Mars landers and space telescopes, and the delights of life as a consultant.

Speaker: Timotheus Keanu

Title: Mordell-Weil Groups over Elliptic Curves

Abstract: Elliptic curves is a type of algebraic curves that has many applications in number theory due to its arithmetic nature. They have lots of interesting properties. For example, the Mordell-Weil theorem tell us that an elliptic curve over the rational numbers is a finitely generated abelian group. In this talk, we will explore this result in more detail and discuss the challenges faced in the current research.

Speaker: Grace Jacobs Corban

Title: Hexaflexagons are the bestagons

Description: Lets flexigate our way to happiness with the most fun you can have on six sides! In this seminar we will introduce the most influential mathematical object of the 20th century, that some call Feynman's greatest contribution to humanity, and go over how to make a 3-sided, 6-sided, and maybe 12-sided hexaflexagon. Hexaflexagons are paper folding toys, where 'flexing' reveals a new side and a new colour. How does this work? Where do the colours come from?!?! Come along to find out 🙂

Speaker: Sam Bastida

Title: The Mathematics of Juggling

Abstract: A mathematical model of juggling, known nowadays as site swaps, was developed around 1985 independently by groups in both the United States and United Kingdom. In this model numbers are assigned to the common throws jugglers use and a sequence of such numbers describes a juggling pattern or site swap. Not all site swaps are valid and the sequences that are valid correspond to affine permutations which are relevant for the construction of affine symmetric groups. In this talk I will discuss some of the mathematical ideas behind site swaps as well as exploring the various ways they have been extended to apply to different juggling tricks, I will also give some live demonstrations.

Speaker: Mashfiqul Huq Chowdhury

Title: EM Algorithm and Gaussian Mixture Model

Abstract: We usually aim to fit a suitable probability distribution to the observed data using maximum likelihood estimation (MLE). In practice, the complex structure of the data motivates us to include latent variables in our model. However, finding the MLE of parameters, in this case, is challenging because it involves non-convex optimization. In such a setting, the EM algorithm provides an efficient approach for finding the MLE of the parameters by constructing the lower bound (ELBO) of the likelihood of the data. The EM algorithm iteratively optimizes ELBO objective function until convergence. The Gaussian mixture models (GMM) are widely used for unsupervised clustering tasks in Machine learning. The application of the EM algorithm on the GMM will also be discussed. This talk will finish by showing an illustration of GMM for clustering purposes.

Speaker: Mark Bishop

Title: Effects of observed projections on turbulence statistics in the intracluster medium

Abstract:The total mass of a cluster is one of its most fundamental properties. Measurements of the galaxy cluster mass often relies upon assuming hydrostatic equilibrium. However, this is often invalidated as the intracluster medium (ICM) is continuously disturbed by mergers, feedback processes, and motions of galaxies. These processes generate gas motions that contribute nonthermal pressure; typically turbulence, that leads to an underestimation of the mass by as much as 30\%. We can measure turbulence through indirect probes that come in the form of fluctuations in the X-ray surface brightness and Sunyaev-Zeldovich effect maps. These are projected characteristics, encoding the 3D structure of the turbulence in the ICM. This project will be an analysis of the 3D to 2D projections of the intracluster medium and its effect on the retrieved statistical measures commonly used in turbulence analysis like the power spectrum by using numerical simulations appropriate to galaxy clusters.

Speaker: Jago Edyvean

Title: Hermite Transforms and Plasma Turbulence

Abstract: Transforms are a useful and powerful method for investigating and understanding systems. In collisionless plasma turbulence, the governing equation. the Vlsov Equation, is very hard to solve numerically and so transforms reduce the complexity of this. Transforming the Vlasov equation also yields interesting physical interpretations of the system. The Hermite transform is one such method.

Speaker: Sapir Ben-Shahar

Title: Introduction to Computable Metric Spaces

Abstract: This talk will begin with an introduction to metric spaces and some notions of computability, including presentations of spaces, and computably enumerable (c.e) sets.
From there we will build up to the idea of computable metric spaces, with the goal of presenting a space that is not computable, but in an unusual, almost computable way: it has both a left-c.e presentation and a right-c.e presentation but no computable presentation. This is surprising because normally we would expect something that is both left-c.e. and right-c.e. to be computable, with the left-c.e. and right-c.e. presentations each giving us, in a sense, half of the information that we need for a computable presentation. Knowledge of computability and metric spaces is NOT assumed.

Speaker: Ben Roberts

Title: The Khmaladze Transformations

Abstract: The empirical process is the central object of goodness of fit statistical testing, with test statistics being chosen as functionals of this process. Clever construction of statistics, such as the chi-squared statistic, have the additional property of being asymptotically distribution free; their limit distribution does not depend on the particular hypothesis under consideration. An intriguing alternative is to instead transform the empirical process into some other asymptotically distribution free process. A broad class of test statistics (functionals) of this new process will then be automatically asymptotically distribution free. Such a transformation was introduced in 1981 through the Khmaladze transformation, we will consider this and another recent alternative from 2016, the Khmaladze-2 transformation. We will report on some recent work extending the applicability of the Khmaladze transformation and using the Khmaladze-2 transformation for distribution-free goodness of fit testing for discrete distributions.

Speaker: Diamant Pireva

Title: An introduction to typed set theory

Abstract: Sets are often purported to be “predicates in extension”, in that for any property, there is (or should be) a set containing all and only those things with that property as its elements. Actually formalizing this principle can quickly lead to contradiction and so one has to be careful in how they incorporate it into a theory of sets. The most common way this is done is by using a restricted axiom scheme of comprehension, so that we can only collect together sets satisfying some property as subsets of already existing sets. A less common way to do this is by introducing what are known as types. Rather than restrict comprehension by means of quantification, typed set theories restrict what formulae are considered to be well-formed in defining properties. This talk introduces the typed theories TST, TZT, and NF. We start by looking at how these theories overcome the standard paradoxes of set theory. We then look at models of said theories and comparing them. Finally, we look at consistency results coming from the scheme of typical ambiguity.

Speaker: Malcolm Jones

Title: A filter approach to groupoids

Abstract: Filters simplify the construction of groupoids used to study C*-algebras. Groupoids and inverse semigroups are both generalisations of groups. They model partial symmetry (Wagner-Preston) as opposed to groups, which model total symmetry (Cayley). Given an inverse semigroup, one can construct groupoids. Two constructions are common: the germ approach pioneered by Paterson, and the filter approach developed by Kellendonk, Lenz, Lawson, Margolis and Steinberg. We describe the equivalence between them studied in collaboration with Armstrong, Clark, an Huef and Lin. This had been known for some time by the experts, but details in the literature were scarce. The aim of the talk is to convey the elegance of a filter approach compared to the classical alternative and give some intuition as to how defining properties of filters capture the same information.

Speaker: Linus Richter

Title: On Homological Algebra, Group Extensions, and Descriptive Set Theory

Abstract: One way of thinking about group extensions is via short exact sequences in the category of groups. I will outline, using simplicial homology, how algebraic topology associates algebraic objects as topological invariants. Using cohomology and descriptive set theory, I will then briefly explain how the class of group extensions whose bonding morphisms are Borel is trivial in certain circumstances. This extends results by Kanovei and Reeken (2000).

Speaker: Rafael Pereira Lima

Title: KMS states on groupoid C*-algebras

Abstract: The theory of C*-algebras started in the study of quantum mechanics. Since then, the subject has evolved and now it interacts with several areas of mathematics. Many important examples in the theory can be described as groupoid C*-algebras. In this talk, we will introduce these concepts and see a theorem due to Neshveyev, which gives a formula for the KMS states on groupoid C*-algebras. This theorem is an example of how topological properties of the groupoid help us understand C*-algebras in more detail.

Slides: KMS-groupoid-C-algebras.pdf

Speaker: Meenu Mariya Jose

Title: Recognising Principal Transversal Matroids

Abstract: Lattice path matroids are a well-behaved subclass of transversal matroids - they are closed under minors and duality and can easily be understood geometrically. Principal transversal matroids are another subclass of transversal matroids that is closed under duality but not minors. We investigated the intersection of these classes and found that a polynomial time algorithm can determine when a lattice path matroid is also principal. This is quite the contrast to the fact that it requires a tedious process to prove that a transversal matroid is principal. No prior knowledge of matroids is assumed.

Speaker: Liam Jolliffe

Title: FI modules and their submodules

Abstract: The theory of FI modules was introduced by Church, Ellenburg and Farb in 2014. These modules occur in many different places in the wild, but our interest in them is to gain some insight into the representation theory of the symmetric group. In this talk we will briefly revisit the representation theory of the symmetric group, before defining FI modules and seeing some examples. We will conclude by looking at some families of submodules of representable FI modules and describing some future work.