Postgraduate Seminar

The aim of the seminar is to give postgraduate students an opportunity to socialise and share their interests with their peers. As such the seminar is a mix of afternoon teas and talks.

The seminar is coordinated by grads for grads. We welcome expressions of interest in giving a talk. If you have any comments on how we can make the most of the series, then we are all ears!

To contact the grad seminar team please email timotheus.keanu@vuw.ac.nz or samuel.bastida@vuw.ac.nz. We will be in touch as soon as possible.

Grad Seminar Photo.JPG

Upcoming talks/afternoon tea/morning tea

Date Time Location Description
Monday 02nd December 2:00-3:00pm CO431 Afternoon Tea

Previous talks

Date Description

Monday

18th November 2024

Speaker:Samuel Bastida

Title: Friendship and Colouring In

Abstract: In 1941 R.L. Brooks investigated one of the most important problems that had been vexing preschoolers for centuries: "How many colours are required to colour something in?". As it turns out, answering this question in general is (to use a technical term here) "hard", however, Brooks was able to characterise when a graph with maximum degree k is k-colourable. In 2016 Stiebitz and Toft were able to expand Brooks' Theorem to characterise when a graph with maximum friendship k (sometimes called maximum local edge-connectivity k) is k-colourable. It is known that Brooks' Theorem extends to list-colouring (a more general form of colouring that is even "harder" than the original) and so we determine whether or not Stiebitz and Toft's Theorem also extends to list-colouring and obtain some rather surprising results.

Monday 14th October 2024

Speaker: Johanna Franklin

Title: Algorithmic randomness and its connections to analysis

Last time, we introduced key concepts from computability theory and used them to formalize our intuitive ideas about randomness. This time, we'll see how these formal definitions of randomness are connected to various theorems in analysis and answer a question left over from last time about infinite binary sequences that appear to be "half random.

Monday 30th September 2024

Speaker: Johanna Franklin

Title: Algorithmic randomness and its connections to analysis

Abstract: Most people have an intuitive idea of what it means for an infinite sequence of coin flips to be random, but as mathematicians, we'd like to have a formal definition for this concept. Computability theory, a subfield of mathematical logic, allows us to do this. A point in a computable probability space is said to be random if it does not have certain easily-defined measure-zero properties, and different types of properties give rise to different definitions of randomness. In recent years, the resulting notions of randomness have been used to characterize the sets of points that satisfy various theorems in analysis. I will provide an introduction to computability theory and randomness and survey some of these recent results.

Tuesday 17th September 2024

Speaker: Malcolm Jones

Title: “I can’t get no satisfaction” in polynomial time without a
non-deterministic algorithm

Abstract: Do you want to be a millionaire? It may be easier to win the
lottery, but it would be more satisfying to solve a millennium prize
problem, for example P vs NP. I will not be solving this problem in this
talk because “I can’t get no satisfaction” without a non-deterministic
polynomial time algorithm. Rather, the goals of the talk are to explain
SATISFIABILITY, non-deterministic polynomial time algorithms and the
statement of P vs NP. My intention is for the talk to be informal and
accessible to any graduate student in maths or stats. I assume that you
know what a polynomial is.

Monday 9th September 2024

Speaker: Rezwana Razzaque Angana

Title: Regularization of Shallow Water Equations: The Role of Weak Nonlinearity and Dispersion in Controlling Singular Shock Waves.

Abstract: The regularization of shallow water equations is a critical area of study aimed at enhancing the physical realism and mathematical stability of models used to describe fluid dynamics in shallow regions, such as coastal areas and rivers. This paper focuses on the impact of weakly nonlinear and dispersive effects on singular shock waves within these systems. By introducing regularization techniques, such as incorporating higher-order dispersive terms and weakly nonlinear corrections, the study seeks to smooth out sharp gradients and manage singularities that arise in traditional shock wave models. The analysis reveals how these modifications lead to the formation of weakly singular shock waves, characterized by continuous profiles with discontinuous derivatives, and explores their stability and propagation behaviour. The findings have significant implications for improving the accuracy of numerical simulations and enhancing our understanding of complex wave phenomena in shallow water environments, particularly in scenarios where traditional models fail to capture the nuanced interplay between nonlinearity, dispersion, and shock wave dynamics.

Tuesday 27th August 2024

Speaker: Ryan Thompson

Title: Wide Subsemigroups of Boolean Inverse Semigroups

Abstract: Following the construction of Paterson in his 1999 book "Inverse Semigroups, Groupoids and their Operator Algebras", we study the intrinsic action of an inverse semigroup on its space of semicharacters, and the universal groupoid that arises. We introduce a condition called "wideness", such that a Boolean subsemigroup W of an inverse semigroup S is wide if and only if the universal groupoids of W and S are homeomorphic. We then look at a few restrictions of this action, to the space of characters and Boolean characters, which give rise to the groupoid of proper germs and the groupoid of ultragerms, respectively, and the properties of these groupoids in relation to our initial data.

Tuesday 6th August 2024

Speaker: Timotheus Keanu

Title: Stone Duality

Abstract: The duality between two objects is one of the most important principles in mathematics. In this talk, we will discuss a specific example of duality between particular classes of algebraic structures and classes of topological spaces, based on Marshall Stone's works. I will explain the related algebraic and topological structures, how to construct a duality between them, and give some basic examples.

Tuesday 23rd July 2024

Speaker: Sam Bastida

Title: The P-adic Numbers

Abstract: The "real" numbers get a lot of attention for supposedly being "real". However, in every day life one rarely encounters any real numbers beyond the rationals. In fact, in reality, even when dealing with irrational numbers, in almost all cases a rational number is used as an approximation. In this talk I will investigate an alternative to the real numbers, the p-adic numbers, which offer an alternative method to complete the rational numbers. I will explain the basics of how we obtain the real numbers from the rational numbers and then explore alternative methods which will give us the p-adic numbers. I will also explore many of the topological and algebraic properties of the p-adic numbers.

Tuesday 9 July 2024

Speaker: Roy Jansen

Title: The Two-Headed Snake Groupoid: Steinberg Algebras and Ideals

Abstract: The n-headed snake groupoids are often used as examples of
non-Hausdorff groupoids. This (very casual!) talk will give
entry-level background to topological groupoids and Steinberg algebras
over a field K, with the example of the two-headed snake. We will look
at ideals of singular functions and their independence from K. If we
have time I might introduce the three-headed snake, where the
characteristic of K does weird things to the ideals ...

Tuesday 25 June 2024

Speaker: Mark Bishop

Title: Croatia vs Italy EURO 2024

Result: A last minute goal from Italy brings the score to 1 all which means Italy advances from the group stage and Croatia sadly does not (I think, I don't really know how sports works).

Monday 10 June 2024

Speaker: Ellen Hammatt

Title: Structures Computable Without Delay

Abstract: In this talk we investigate what happens when we take concepts from computable structure theory and forbid the use of unbounded search. In other words, we discuss the primitive recursive content of structure theory. This central definition is that of punctual structures, introduced by Kalimullin, Melnikov and Ng in 2017. We investigate various concepts from computable structure theory in the primitive recursive case. A common theme is that new techniques are required in the primitive recursive case. We also discuss a degree structure within punctual presentations which is induced by primitive recursive isomorphisms. This degree structure is a new concept that does not arise in computable structure theory.

Monday 20 May 2024

Speakers: Various

Title: What the heck is a teaching statement anyway?

Abstract: US academic job applications require a "teaching statement". Today we will find out what a teaching statement is and have some discussions on what it should contain. We have four special guests to help this discussion, Brendan Harding, Becky Armstrong, Lisa Orloff Clark and Mariya Soskova. Our guests will talk about their own experiences in applying for jobs and writing teaching statements as well as any experiences that they have had on the hiring side of the job process.

We will have some examples of some old teaching statements written by a couple of our special guests. There will also be an example of a statement written by ChatGPT that we can critique. We wouldn't want AI taking our jobs now, would we! We will also have a brainstorm session on some teaching philosophies to get the ideas flowing on what makes a good teacher. There will also hopefully be time for some Q&A with the guests, so please have a think about whether there is anything specific you would like to ask, but otherwise I am sure questions will arise for you throughout the session.

This session will be useful for graduates at all levels because we will also discuss what kinds of experiences could help improve your teaching statement. For those earlier in their studies, there is maybe time to think about this and look out for these sorts of opportunities in order to strengthen future applications.

Monday 6 May 2024

Speaker: Jago Edyvean

Title: Spiders?

Abstract: Spiders have long been the subject of many myths and internet rumours but are any of them actually true. These myths include "are daddy long-legs truly the most poisonous spiders?" ; "do we really swallow an average of eight spiders a year while asleep?" ; and "was Shelob right all along?" These questions and more will be asked in this talk.

Monday 22 April 2024

Speaker: Malcolm, Ellen, and Michael

Title: Netflicks presents... Physical: 100 Physics:101

Monday 8 April 2024

Speaker: Daniel Wrench

Title: Who gives a toss? The statistics of coin-flipping

Abstract: "Many people have flipped coins, but few have stopped to ponder the statistical and physical intricacies of the process." So begins the abstract to a remarkable study on coin-flipping published last year. In this seminar I will be exploring those statistical and physical intricacies, as well as the history of this iconic game. Take a chance and join me and some very meticulous experimenters on a journey of counter-intuitive probability.

Monday 18 March 2024

Speaker: Iván Ruiz Campos

Title: Lie algebras representation theory with applications to particle physics

Abstract: In the XX century, a large number of particles were discovered. In an attempt to emulate the periodic table, scientists of the time tried to classify these new particles. They discovered that it is possible to group them into families with similar properties. Gell-Mann explained this phenomenon by means of the quark model, being awarded in 1969 with the Nobel Prize in Physics for the discovery of the particle Ω¯. Gell-Mann's theory gained a lot of fame, and it has been since widely discussed and taught. However, many of the works that discuss it use a vague mathematical formalism. The objective of this talk is to provide a better formalization for the entire theory of Lie groups and representations. In addition, we will give physical motivation, something that is often ignored when studying Lie groups and that is of great scientific interest.

Monday 4 March 2024

Speaker: Ellen Hammatt

Title: The punctual degrees of the rational numbers

Abstract: In this talk, we investigate computable structure theory without unbounded search. We call such structures, punctual or informally, structures computable without delay. We use the concrete notion of primitive recursion to formalise computable without delay, this notion is nice to work with since it has a reduced version of the Church-Turing thesis. The inverse of a primitive recursive function is not necessarily primitive recursive. This induces a natural degree structure within the punctual presentations of a particular structure. We focus on investigating whether we can embed the atomless Boolean algebra into the punctual degrees of various linear orders, in particular the rational numbers.

Note that this is a talk for me to practice for an overseas conference, so it is for an expert audience. However it is a 25 min talk, so we can use the rest of the time to clarify and discuss some aspects. I will also start with an extra introduction to clarify a few definitions to hope to make the talk more understandable!

Thursday 22 February 2024

Speaker: Ryan Thompson

Title: Actions of Inverse Semigroups and their C*-Algebras

Abstract: Given an inverse semigroup S and a locally compact, Hausdorff space X, there are a number of ways to produce C*-algebras. One is to construct the groupoid of germs of the action, and then form both the full and reduced C*-algebras (which we assume to be equal). The other is to take a natural action of S on the set of continuous functions on X that vanish at infinity, and then form the crossed product. We describe these constructions and show that both methods yield isomorphic algebras.

2023
Monday 20 November 2023

Special Event: Dr Louise McMillan on '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.

Monday 13 November 2023

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.

Monday 30 October 2023

Speaker: Aleksa Vujičić

Title: Academic Experience Post-VUW

Desription: Q&A to discuss differences between graduate life at VUW and overseas.

Monday 16 October 2023

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 🙂

Monday 2 October 2023

Speaker: Grace Jacobs Corban

Title: Maths anxiety; a proof by induction

Abstract: Maths anxiety is an issue that affects New Zealand students' math performance and wellbeing and can have long-lasting effects throughout their lives, impacting career choices. What is clear is that maths anxiety is a societal issue, and that it continues to be perpetuated (by parents, teachers, and media). What is less clear is where it originated.

In this we will explore the current state of maths anxiety, as well as how it continues to be an issue, and investigate its potential origin.

Monday 18 September 2023

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.

Monday 4 September 2023

Speaker: Mashfiqul Huq Chowdhury

Title: Variational Inference, Latent Representation and Clustering

Abstract: In unsupervised learning, we aim to find the hidden structure within the data. In this talk, I will concentrate on modeling the distribution of unsupervised data using the variational inference technique. I will explain, how to simultaneously learn latent representation and clustering by leveraging a deep neural network architecture. The variational autoencoder (VAE) can be used effectively for both of these purposes. I will conclude my discussion after demonstrating an application of the VAE model.

Monday 26 June 2023

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.

Tuesday 20 June 2023

Speaker: Shonaugh Wright

Title: Topological properties of graded groupoids

Abstract: A groupoid is a generalisation of a group. I will introduce the definition of a groupoid with some examples, mainly looking at second-countable, locally compact, Hausdorff, étale groupoids. Then I will discuss the identity graded groupoid and some of the properties that it inherits from the original groupoid. I will finish by discussing how to construct a C*-algebra from a groupoid.

Monday 1 May 2023

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.

Tuesday 18 April 2023

Special Event: Dr. Brendan Harding on 'MathJobs and more'.

Abstract: I'll give an overview of mathjobs and how to use it to find and apply for jobs. I'll also give some tips on putting together an application, including things to focus on in your cover letter and some suggestions for building an academic CV. I'll show some examples of applications I have submitted in the past.

Monday 13 March 2023

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.

Monday 13 February 2023

Speaker: Daniel Wrench

Title: Intro to Bayesian Statistics

Abstract: The Bayesian approach is a very popular way of doing statistical inference and rests upon a simple theorem of conditional probability. Daniel will be discussing the basics of this mathematical method of updating your beliefs in light of new information.

Monday 30 January 2023

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.

2022
Monday 14 November 2022

Speaker: Ellen Hammatt

Title: Punctually 1-Decidable Boolean Algebras

Abstract: In my talk I will discuss my recent work on online (punctual) presentations of boolean algebras. The main result is: There exists a 1-decidable boolean algebra such that is not computably isomorphic to any punctually 1-decidable boolean algebra. All terms and definitions will be clarified in the talk.

Monday 7 November 2022

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.

Monday 7 November 2022

Speaker: Sam Bastida

Title: List Colouring and Maximal Local Edge Connectivity

Abstract: A (proper) k-colouring of a graph assigns one of k colours to each vertex such that no two adjacent vertices have the same colour. A fundamental theorem in graph theory, Brooks' Theorem, states that a graph with maximum degree k (a graph where each vertex has at most k neighbours) has a proper k-colouring unless it is a complete graph or a cycle with an odd number of vertices. More generally one can consider graphs in which each pair of vertices have at most k edge-disjoint paths between them, such graphs are said to have maximal local edge connectivity k. The question of which graphs with maximal local edge connectivity k can be k-coloured was answered by Stiebitz and Toft in 2018. One can also consider a generalisation of k-colouring where each colour must be chosen from a list of colours of size k for each vertex. A graph is k-list colourable if such a colouring exists for each assignment of lists of size k to vertices. In this talk, we describe our progress towards an attempt to extend the theorem of Stiebitz and Toft to k-list colouring. Certainly, a graph that is k-list colourable is k-colourable, but the converse may not be true - this makes the problem of characterising which graphs are k-list colourable more difficult than the problem for k-colouring.

Monday 10 October 2022

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.

Monday 12 September 2022

Speaker: Flynn Owen

Title: Finite Mixture Models - A Divide and Conquer Approach

Abstract: Within the field of data clustering, methods are commonly referred to as either ‘distance-based’ or ‘model-based’, with each having certain limitations. Distance-based methods are fast, but lack an underlying parametric model. Model-based methods are interpretable and generalise easily to distributions other than Gaussian, but are slow to estimate, especially when the number of clusters is large. In this thesis we take inspiration from divisive hierarchical clustering and develop four ‘divide and conquer’ model-based algorithms to rapidly estimate mixture models with large numbers of components. Our algorithms are: 1) The Hierarchical No Turning Back (HNTB) algorithm, 2) The Hierarchical Single Reallocation (HSR) algorithm, 3) The Hierarchical Reallocation Loop (HRL) algorithm, 4) The Hierarchical algorithm that Reallocates During execution (HRD). Using Akaike Information Criterion (AIC) as our measure of model quality, our algorithms work by recursively fitting a data matrix with R = 1 and R = 2 components, and then partitioning this data-matrix dependent on cluster membership, halting when no sub-components can be partitioned further. We then adapt the ‘E-step’ from the Expectation-Maximisation (EM) algorithm to reallocate data points across each estimated sub-component of the data matrix. We perform a series of Monte Carlo simulation studies on a series of datasets generated from the Bernoulli distribution, and compare our results against an adapted version of well known ‘Wolfe’s method’ (Wolfe, 1971). We establish that ‘divide and conquer’ mixture modelling methods are able to identify mixtures with large numbers of components at a much faster rate than our adapted version of Wolfe’s method, and approximate both the true simulated data, as well as the results from our adapted method to a good degree. Algorithms introduced in this thesis provide suitable methods to address scalability with the ever increasing magnitude of data being stored and processed, while ensuring interpretability with the increasing demand for data-driven insights.

Monday 01 August 2022

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.

Monday 18 July 2022

Speaker: Matthew Askes

Title: Strongly Online Graph Colouring

Abstract: An online algorithm is an algorithm that processes its input in pieces and must process the current piece of data before it gets the next. Online algorithms have wide-ranging applications from emergency vehicle dispatching, scheduling, and processing large data sets. In effect, any algorithm that needs to work on partial information can be represented as an online algorithm. However, online algorithms do not fully capture the nature of certain problems. Often you can see slightly ahead, or you may be able to delay an action temporarily until more data is available. In these situations the problem is not fully online. To this end, we introduce the notions of locally strongly online and strongly online presentations. In particular, we will discuss strongly online colourings of graphs and touch on the idea of strongly online path decompositions.

Monday 4 July 2022 Speaker: Aleksa Vujičić

Title: The Problem with Braid

Abstract: Braid is a puzzle game released in 2008 whose central mechanic revolves around time manipulation. The goal of any level is to manipulate different level elements so that you can reach the exit - but is this always possible to do? It turns out that answering this question in general is impossible to do, and we look at why this is the case.
2021
Tuesday 15 June 2021

Speaker: Joseph Wilson

Title: Geometric algebra and an application to special relativity

Abstract: Real Clifford algebras are affectionately called “geometric algebras” by physicists for their utility and generality. They provide an elegant framework for describing rotations in arbitrary dimensions, including 3+1 dimensional spacetime. This leads to a simple and novel formula for the composition of Lorentz transformations in terms of their infinitesimal generators.

Monday 17 May 2021

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).

2020
Monday 16 November 2020

Speaker: Linus Richter

Title: When the search for proofs turns futile

Abstract: It came as a shock when in 1931 Kurt Gödel proved that mathematics is not complete. We can find mathematical statements that are "independent"; they can neither be proven nor refuted. Surprisingly, while the original independent "Gödel sentence" is a somewhat contrived construction, meaningful mathematical questions can be independent, too.

For example, a problem long confounded set theorists: is there a subset of the real numbers that is larger than the set of integers yet smaller than the real numbers themselves?

The assertion that such intermediate sets do not exist is called the "Continuum Hypothesis" (CH), and many set out to prove CH. In 1963, Paul Cohen showed that those attempts had been futile -- he proved that CH is independent. Cohen did so by inventing the versatile method of "forcing", which has since been used to yield many more independence proofs.

I will introduce some mathematical logic, the notion of independence, and why we care about all this. Using set theory, I will then outline how forcing yields a proof of the independence of CH.

Monday 2 November 2020

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

Monday 12 October 2020

Speaker: Josh Baines

Title: The Painlevé-Gullstrand Form of Various Spacetimes

Abstract: Every spacetime is defined by its metric, the mathematical object which further defines the spacetime curvature. From the relativity principle, we have the freedom to choose which coordinate system to write our metric in. Some coordinate systems, however, are better than others. In this talk, we begin with a brief introduction into general relativity, Einstein's masterpiece theory of gravity. We then discuss some physically interesting spacetimes and the coordinate systems that the metrics of these spacetimes can be expressed in. More specifically, we discuss the existence of the rather useful Painlevé-Gullstrand coordinate system in these spacetimes. Using this useful coordinate system then allows us to conduct further analysis of these spacetimes, which we discuss.

Monday 28 September 2020

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.

Monday 31 August 2020

Speaker: Michal Salter-Duke

Title: Tangles in networks and their application to describing communities

Abstract: Communities in networks are structurally or functionally distinct subgraphs. They can be disjoint or overlapping, depending upon definition; there are several definitions of communities, and many algorithms to identify them. We present a new definition based on the graph-theoretic concept of tangles, and investigate how well it identifies subgraphs that represent cohesive parts of the network, using two protein-protein interaction networks. This requires the development of an algorithm for finding tangles in graphs. We compare our results with standard methods from the literature based on metrics that use metadata to establish communities. Our results show that tangles provide a different view of communities that complements other methods, although they are computationally expensive to identify.

Slides: MichalSalter-DukeGradTalk.pdf

Monday 10 August 2020

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.

Monday 27 July 2020

Speaker: Malcolm Jones

Title: An algebraic model in public health: the groupoid of bubbles

Abstract: Groupoids are a generalisation of groups that arose in the early 20th century in work on quadratic forms by H. Brandt. Since their inception groupoids have provided a fruitful framework in a variety of fields, including fundamental work by J. Renault in operator algebras in the 80s. Groupoids have even appeared in epidemiology as recently as 2014 as models of cognitive processes in biology. In this talk, we will review the elementary theory of groupoids, and we will discuss a widely applicable groupoid model of interactions in populations.

Monday 29 June 2020

Speaker: Jordan Mitchell Barrett

Title: Ramsey theory of semigroups

Abstract: Many fundamental results in Ramsey theory concern the structure of certain semigroups (sets with an associative binary operation). These include the Hales–Jewett theorem, the Graham–Rothschild theorem, Gowers' FINₖ theorem, and Hindman's theorem. In this talk, we will discuss and aim to understand these fundamental results. Time permitting, we will see a common generalisation of many of these theorems to the setting of arbitrary layered semigroups, as introduced by Farah, Hindman and McLeod, and further generalised in ongoing work of Barrett and Lupini.

Follow the link to see the talk: https://www.youtube.com/watch?v=FuFWwWeeu-Q

I Attachment Action Size Date Who Comment
Grad Seminar Photo.JPGJPG Grad Seminar Photo.JPG manage 58 K 08 Apr 2024 - 17:18 Main.jonesmalc Social grad seminar event
KMS-groupoid-C-algebras.pdfpdf KMS-groupoid-C-algebras.pdf manage 971 K 03 Nov 2020 - 15:19 Main.jonesmalc  
MichalSalter-DukeGradTalk.pdfpdf MichalSalter-DukeGradTalk.pdf manage 1 MB 16 Sep 2020 - 10:35 Main.jonesmalc