UNSW Mathematics and Statistics Higher Degree Research (HDR) Seminar
The primary aim of the seminar is to give PhD/Masters (and possibly Honours/other) students an opportunity to give short 30-minute talks on a mathematical topic that interests them. For those doing research currently, it could be related to a research topic you've worked on, but we would prefer them be accessible to a general math audience in this case. Alternatively, it could also be on something mathematical that you just find interesting and fun! There is no expectation that you give a talk, however it would be greatly appreciated if you want to give one! (Shoot me an email in this case.)
Following the talk (and weather permitting), we will have a lunch BBQ/sausage sizzle (with vegetarian options). This will be held on the physics lawn — the big lawn on the other side of the Old Main Building.
Location: H13-4082, UNSW Sydney.
Schedule: 11-1PM on odd Mondays (i.e. weeks 3, 5,…) during the term. I will send out emails containing the time of the talk, the speaker, and their abstract on the mailing list in the week preceding their talk.
If you have any questions, are interested in attending/speaking, or know other people who would be interested in attending let me know! Contact me or fill out the following form to be added to the mailing list. You can find the talk titles, abstracts, speakers and slides below.
March 2, 2026: How to make $0 on average at the casino, Dante Burn (UNSW)
Abstract: This talk is about martingales. We will see how basic probability theory can be used to model betting strategies for fair games of chance, with the martingale betting strategy as an example. This will lead us into an introductory discussion of the martingale Hardy spaces: explaining why they are interesting, and comparing them with the $L^p$ function spaces. No prior knowledge is required for this talk.
March 16, 2026: Dani Morrigan (UNSW)
Abstract: TBD
September 29, 2025: Aaron Manning (UNSW)
Abstract: We all LOVE LaTeX right? Right?? Well we love the high quality output, we love that it is free and open source, we love that it is plain text and thus very easy to share, collaborate on, and version control, and we love that there are tools both for running it locally and in the web. What we don't love is the cryptic error messages (underfull HBOX badness 1000, like what the heck is that?), the verbose syntax, the long compile times on big documents, and the lack of reproducible builds depending on package availability. Well guess what, there is now an alternative! (I feel like I'm writing an infomercial here). Typst started as a CS masters thesis project, but has turned into an open source project and company, and I am one of the many people who is using and contributing to it in the hopes that one day it will be an ubiquitous an LaTeX. This talk will include an introduction to and demo of Typst, with particular focus on why mathematicians may want to consider it as an alternative to LaTeX to improve their workflow without compromising on the quality of their typesetting. Interruptions with questions are highly encouraged!
August 4, 2025: Bundles of Fun, Stanley Luk (UTS)
Abstract: Fibre bundles are a ubiquitous object appearing across many aspects of topology, geometry, and especially mathematical physics. One that serves so many varied purposes that it is the foundation of many structures and theories in these fields. From the idea of a fibre bundle one can: build more complicated topological spaces from simpler ones, generalise the graph of a function on a manifold, describe cleanly much of quantum physics, and more. In this talk, we aim to present a bestiary of fibre bundles, giving many simple examples that will serve to demonstrate the main uses of fibre bundles in a number of places. There will be one central definition, no real theorems, and lots of pictures for visualisation with the goal being to impart to you a useful intuition of what a fibre bundle is. (Especially for those who haven't heard of it before.)
July 28, 2025: Compactifications and continuous functions, Leyao Zha (UNSW)
Abstract: Given the open interval (0,2π), we can form its one-point compactification S^1, a circle, with an embedding (0,2π)→S^1 given by the complex exponential e^ix. Given a continuous function on (0,2π), if its limit at 0 and 2π exist and agree, then it naturally extends to a continuous function on S^1. The aim of the talk is to explain the duality between topological space and continuous functions on the space, compactification and extension of continuous functions, just like the example above. In particular, we will look at the Stone–Čech compactification, the 'largest' compactification of a space in which every continuous function extends.
July 21, 2025: Primes in sparse sequences, Chip Corrigan (UNSW)
Abstract: We discuss some progress on problems concerning the distribution of primes in sparse sequences.
June 30, 2025: Constructing elliptic curves of 'high' rank, Blair Butler (USYD)
Abstract: Elliptic curves are a central object of study in number theory. In this talk we introduce their group structure. Perhaps the most explored, yet least understood aspect of elliptic curves is their rank, that is, the number of free generators of the group. In an attempt to construct elliptic curves with higher and higher rank, we are naturally lead to investigate elliptic curves with coefficients defined over function fields, that is, elliptic surfaces.
June 23, 2025: A practical primer in the probabilistic method, Nye Taylor (UNSW)
Abstract: Of all the tools in the combinatorialists’ bag of tricks, the probabilistic method is perhaps the most magical. This talk gives a quick introduction via a few short proofs from ‘The Book.’ (“You don't have to believe in God, but you should believe in The Book.”) No prior knowledge is assumed.
June 16, 2025: Ribbon Categories and Reshetikhin-Turaev Invariants, Thomas Dunmore (UNSW)
Abstract: In the late 80's, Witten constructed a family of invariants of knots and 3-manifolds from special kinds of topological quantum field theories. Among these invariants were the then recently-discovered Jones polynomial and its generalizations. Shortly afterwards, Reshetikhin and Turaev offered a more mathematical formulation of Witten's construction in terms of ribbon graphs coloured by representations of quantum groups. The aim of this talk is to explain Reshetikhin and Turaev's diagrammatic approach with classical vector spaces as the running example. Given time, the Jones polynomial may make an appearance at the end.
June 2, 2025: Solving the Ising model with combinatorics, Laura Stemmler (UNSW)
Abstract: Understanding phase transitions—sudden changes in the macroscopic behavior of a system—is a central goal of statistical mechanics. The two-dimensional Ising model is a foundational model in statistical physics and a rare example of an exactly solvable model for an extended system with a phase transition. In this talk, we explore a combinatorial approach to solving the 2D Ising model by mapping the partition function to a problem of counting perfect matchings on a graph.
April 14, 2025: Geometric flows - the pretty picture, Patrick Donovan (UNSW)
Abstract: Differential geometry is the study of the geometry of smooth spaces. It is a rich area of mathematics, dating back to at least the time of ancient Greek mathematics, revitalised through the invention of calculus and reformulated in terms of intrinsic geometry through the foundational work of Gauss and Riemann. A modern focus on differential geometry is geometric analysis - the study of the intimate relationship between the geometry and topology of a space and the solutions to partial differential equations over that space. In the twenty-first century, the most success within geometric analysis, and differential geometry more generally, has been via the analysis of geometric flows. By flowing the geometry of a space in a natural way, many deep results are achievable. We shall see an introduction to, and intuition of, the Ricci flow on surfaces and how it generalises to higher dimensions. This allows us to see a very coarse overview of the proof of the crowning jewel of geometric analysis in the last 25 years - the resolution to the Poincare conjecture and more general Thurston's geometrization conjecture.
April 7, 2025: The Banach-Tarski paradox and amenability, Daniel Dunmore (UNSW)
Abstract: The Banach-Tarski paradox is a well-known result from set-theoretic geometry, being one of the more bizarre mathematical curiosities of the last century or so. Acting as a stepping stone between the paradoxes of Hausdorff and von Neumann, it tells us that any closed ball in three dimensional space can be decomposed into two exact copies of itself using only finitely many rotations and translations. In this talk, I would like to give an overview of this famous result, as well as - if time permits - its surprising connections to ergodic theory, operator algebras and algebraic topology via the notion of amenability.
March 31, 2025: Graph colouring, SO(3) webs and the B1 invariant, Victor Zhang (UNSW)
Abstract: We define a diagrammatic gadget equivalent to SO(3) representations and explore its relation to graph colouring. Within this, we may uncover a knot invariant that is to this diagrammatic category as the Jones polynomial is to the Temperley-Lieb algebra.
March 17, 2025: A tour of social choice theory, Aaron Manning (UNSW)
Abstract: Social choice theory is a branch of economics concerned with the ways in which a group of individuals can make a collective decision, such as in an election. In the 1950s, interest in social choice theory amongst mathematicians grew, leading to proofs of some unexpected and sometimes unfortunate truths about our ability to run the ideal election. This talk is a tour of some of the major results in social choice theory, the formalisms and proofs of which are of a set theoretic and combinatorial flavour. No specific domain knowledge will be assumed.
March 10, 2025: Jones technology and applications, Ryan Seelig (UNSW)
Abstract: We continue to explore the work of fields medallist Vaughan Jones. This time, we will start from quantum field theory and end up rebooting knot theory using Richard Thompson's group F instead of the braid groups. Minimal knowledge will be assumed. All are welcome.
March 3, 2025: Classifying algebraic curves and surfaces, Dominic Matan (UNSW)
Abstract: One of the ultimate goals of algebraic geometry is the attempt to classify all geometric objects obtained by systems of polynomials up to some notion of “isomorphism.” In practice, this is too difficult and so we must loosen some conditions to say anything meaningful. In this talk, I will give a very rough outline of what classification theory looks like in the case of algebraic curves and surfaces (over the complex numbers) using the weaker notion of “birational equivalence.” Minimal knowledge is assumed, and all are welcome!
February 24, 2025: This idiots introduction to the Jones Polynomial, Joseph Baine (UNSW)
Abstract: In this talk I’ll introduce the Jones Polynomial, which is a beautiful invariant of knots. I’ll explain how you can compute it, and a bit of what’s happening under the hood. Minimal knowledge will be assumed. All are welcome.