International Women in Mathematics Day 

Date: May 12th, 2023     -    Location: UQ St Lucia Campus - Hawken Engineering 50-N201

Host: Rossi Ruggeri (Postdoctoral Fellow in Astrophysics, UQ)

Tentative Schedule 

10:00-11:00            Work of the 2022 Fields Medal Winner Maryna Viazovska (Barbara Maenhaut, A/Prof. UQ)
Panel Discussion : Challenges and Opportunities for Women in Maths (Poh Wah Hillock, Senior Lecturer, UQ)    

11:00-11:30             Morning Tea 

11:30 - 12:10           Meagan Carney  (Lecturer, UQ)                                                    Extremal modeling in weather systems

12:10 - 12:30           Madeline Nurcombe (PhD student, UQ)                                 The Ghost Algebra                                

12:30-2:00                Lunch                                            

2:00-2:40                  Zsuzsi Dansco (A/Prof. Sydney)                                                      Knots, Graphs and Lattices

2:40-3:00                 Inna Lukyanenko (Research Associate, UQ)                           Integrable Gaudin Systems       

3:00-3:30                 Afternoon Tea

3:30-4:10                 Sophie Raynor (Lecturer, JCU)                                                       The confidence tightrope 

4:10-4:30                 Tara Kemp (PhD Student, UQ)                                                        Fuch's Problem on Latin squares and Cubes                       

Abstracts 

Zsuzsi Dansco - Knots, Graphs and Lattices

In this talk I'll tell the story of a recent breakthrough in knot theory - by Greene, 2011 - using the "Tait graph" construction and an invariant of graphs to completely distinguish between alternating knots up to "knot mutation". I will describe my and my collaborators' new results generalising this construction to knots on surfaces (virtual knots), and showing - by counterexample - that the analogous invariant is not complete up to mutation. That is, it's unable to tell some mutation classes apart. 

I will end with a brief description of the computational methods used, and a list of questions which arose from these techniques and results.

This talk does not assume specialist knowledge of topology or graph theory, and will be accessible to an audience with some general background in undergraduate mathematics. 

This talk is based on joint work with Hans Boden, Damian Lin and Tilda Wilkinson-Finch.

Madeline Nurcombe  -  The Ghost Algebra

The Temperley-Lieb algebra has many diverse applications in mathematics, from physical models of polymers and percolation in statistical mechanics, to knot theory. It is also a diagram algebra; its basis elements can be expressed as string diagrams, which are multiplied by concatenation. The one-boundary Temperley-Lieb algebra is similar, but its basis diagrams have an additional boundary line that the strings may be connected to. There is also a two-boundary Temperley-Lieb algebra, with a second boundary, but its diagrams require an even number of strings connected to each boundary, and it is infinite-dimensional, unlike the zero- and one-boundary algebras. In this talk, I will introduce the ghost algebra, a finite-dimensional two-boundary version of the Temperley-Lieb algebra that allows diagrams with odd numbers of connections to each boundary. Its diagrams contain ghosts: dots on the boundaries that act as bookkeeping devices to ensure associativity of multiplication. I will discuss the construction of this algebra, as well as its dilute generalisation, and the relationships between these algebras.

Meagan Carney Nonstationary  - Extremal modeling in weather systems

Extremes in weather can often take the form of a hurricane, flood, or heat-wave. A better understanding of how large and frequent these events will be can influence evacuation procedures and inform preventative measures. We briefly discuss modeling extremes of dynamical systems in the classical i.i.d. setting. Classical results of extreme value theory extend naturally to dependent sequences provided the distribution of the sequence is stationary. In recent years, climate variability has caused changes in the distribution of weather observations. For example, we have shown that the mean and standard deviation of summer temperature extremes in Texas and Germany is increasing over time. We finish by discussing how machine learning techniques can allow us to obtain more accurate, time-dependent extremal models in these settings.

Inna Lukyanenko  - Integerable Gaudin Systems 

Quantum integrability is based on the notion of commuting transfer matrices. In this talk I will discuss the construction of transfer matrices for integrable Gaudin systems (introduced by Gaudin in 1976), highlighting the use of the so-called "Leningrad notation" (developed in late 70s in Leningrad by Faddeev, Kulish, Sklyanin, Takhtadzhan and others).

Sophie Raynor - The confidence tightrope

Rather than telling you about my research (which is related to operad theory), I will tell you about something that has recently been distracting me from it even more than usual: namely, some disturbing demographic discrepancies that emerged when I introduced a new assessment model for a second-year subject. I will draw on conversations with students and colleagues, and my own experiences and observations (and perhaps some aspects of my research — which is related to operad theory) to highlight some of the complexities around mathematical participation and confidence, particularly in relation to demographic factors: for example, the protection (good!) that imposter syndrome (bad!) can provide, and the aggression (bad!) that mathematical confidence (good!) can provoke. 

Of course, I will also tell you what happened when we approached the assessment issue head-on! Audience comments and ideas are very welcome. 

Tara Kemp - Fuch's problem on Latin Squares and cubes

A latin square of order n is a square array in which each of n symbols occurs exactly once in every row and column, similar to a Sudoku puzzle. L. Fuchs posed a question about the existence of quasigroups with disjoint subquasigroups and this problem is equivalent to the existence of latin squares with disjoint subsquares. The existence of these latin squares is a partially solved problem and it can be extended to a problem on latin cubes with disjoint subcubes. In this talk, I will discuss the known results for the problem on latin squares and the work that has been done on the latin cube analogue.