UNSW Maths PhD/Masters Seminar
The primary aim of the seminars 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!
Following the talk, we usually have a lunch bbq/sausage sizzle or similar (with vegetarian and gluten free options).
Location: H13-4082, UNSW Sydney.
Schedule: 12-2PM Mondays 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.
June 30, 2025: Blair Butler (USYD)
Abstract: TBD
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.
Slides
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.
Slides
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.