“It is a great opportunity to meet people with similar research
interests and friends for life. Highly recommend doing it
at least once.”

João Vitor Pinto e Silva, University of Newcastle

Presenter Abstracts

Group 1 – Wednesday 8 January, Carslaw Lecture Theatre 275

Joseph Kwong

Isometries of the hyperbolic plane

An isometry of a metric space is a bijection of the underlying set which preserves distances. My honours project is about computing the isometries of a nice class of metric spaces. The simplest of these spaces is the hyperbolic plane. In this talk, I will define the hyperbolic plane, describe its isometries, and discuss what they tell us about the geometry of the hyperbolic plane.

Kunj Guglani

The Influence of Statistics Anxiety on Academic Learning

Statistics anxiety, a prevalent issue in education, disrupts students’ cognitive processes, performance, and engagement. This study explores its origins, including negative experiences, low confidence in math, and the perceived complexity of concepts. Through examples like Kunj, a high-achieving student whose progress was derailed by anxiety, the paper highlights its detrimental effects on motivation and practical application, with lasting academic and professional consequences if unaddressed. Innovative solutions, such as gamified learning, personalized paths, and AI-powered tools, are proposed to mitigate anxiety and foster confident, proficient learners. Addressing this issue is crucial for transforming statistics education and preparing students for future challenges

Heath Robertson

Hurwitz numbers via the infinite wedge space

How many ways can you write the identity permutation as a product of a fixed number of transpositions? The answer to this question is known as a Hurwitz number, as an equivalent version of this problem was first studied by Hurwitz in the late 19th century. Hurwitz obtained a remarkable result concerning the structure of these numbers and since then, many efforts have been made to generalise this theorem. Using the tools of the infinite wedge space, we recover and generalise Hurwitz’ original result via more modern methods.

Wei Zhang

Evolution of collective behavior from the perspective of complex networks

Networks are a mathematical representation of interacting entities. As social beings, human activities are often modeled through networks of interactions to explore the evolution of social behaviors. Rather than focusing on a single type of interaction represented by simple networks, we consider how multi-type of interactions together influence the evolution of behavior, such as whether they are globally mixing or not, whether they are signed or not, and whether they are multiplex or not. While the current work focuses on theoretical modeling, the growing availability of datasets offers the opportunity to study population structures of real social behavior.

Heath Dimsey

Modelling the Bray-Liebhafsky Oscillating Chemical Reaction

“Oscillating chemical reactions often show colour-changing temporal oscillations when stirred and form spatial patterns when left to self-diffuse. However, the Bray-Liebhafsky reaction does not produce visible changes while it oscillates. Therefore, the ability for the Bray-Liebhafsky reaction to form spatial patterns has remained largely unexplored.

During this talk, we will investigate several methods to predict the temporal and spatial behaviour observed in this reaction. We suggest a novel mathematical model to predict the reaction’s kinetic behaviour. We incorporate a spatial dimension into the system, enabling the prediction of one- and two-dimensional spatial patterns within a cylindrical and rectangular dish respectively.”

Group 2 – Wednesday 8 January, Carslaw Lecture Theatre 273

Benhao Gu

Mathematical modelling for the relationship between pyrodiversity and biodiversity

Traditionally, the relationship between pyrodiversity and biodiversity is being deduced by human observations. In this talk, we will take a novel quantitative approach to explore this relationship. The talk will be divided into three parts. We will first briefly discuss some of the key components that contribute to the fire regime, then there will be a demonstration on how to use mathematical models to construct pryodiversity and biodiversity measures for species with distinct characteristics. And finally, we will present some interesting observations based on the models of pryodiversity and biodiversity we have created from the previous part.

Kiyoshi Takeuchi

Algebraic Topology for Data Analysis of CT Scans

Homology groups on a discrete set of points are trivial for n>0. I am exploring how one uses Homological Algebra on data in a meaningful way via the so-called Persistent Homology Modules. This allows us to speak of connectivity and other topological properties under different length scales and apply these concepts to the analysis of data. For my specific research, I am investigating how these topological invariants may predict and explain some phenomena in CT scans. This is joint work with UniMelb and ANU.

James Davidson

Quivers, coherent sheaves and Beilinson’s theorem

Quivers are relatively straightforward objects with many surprising connections to the representation theory of finite dimensional algebras. On the other hand, coherent sheaves are more sophisticated objects which occupy a central role in algebraic geometry. Though these two notions seem unrelated at first, a celebrated theorem of Beilinson in 1978 draws a surprising link between the coherent sheaf theory of projective n-space and representations of a certain family of quivers over a field. In this talk, we give an elementary view of how this link arises in the explicit case of the projective line and the Kronecker quiver.

Yuan Sun

Statistics and Career Planning

Abstract forthcoming

Abdulaziz Albuhayri

Option Pricing Using Cos Method

“Modern financial mathematics aims for efficient and precise option pricing, which is essential, particularly in derivative markets. Established approaches, including Monte Carlo simulations and finite difference methods, often run into computational inefficiency and convergence challenges, mainly when applied to complex financial models like the Heston stochastic volatility model. Fourier-based techniques, such as the COS method known for (Fourier-Cosine Series Expansion) introduced by Fang, offer a transformative solution to these challenges. The COS method relies on the Fourier_cosine series expansion to estimate option payoff functions, enabling speed computation with exponential convergence.”

Mahdi Nouraie

Bayesian Stability Selection

Complex analysis is a compulsory undergraduate course across AustStability selection is a powerful tool for structure estimation and variable selection. We enhance it by integrating Bayesian analysis to refine inclusion probabilities, incorporating domain expertise through a two-step process to inform prior distributions. This approach uses posterior distributions and Bayesian credible intervals to improve inference and quantify uncertainty. By addressing the limitations of selection frequencies, particularly with correlated covariates, our method ensures more informed decision-making by leveraging background knowledge. Retaining stability selection’s versatility, it provides a framework for using expert knowledge to tackle complex structure estimation challenges while accounting for uncertainty in the variable selection process.

Expand your mathematical world

AMSI Summer School is not just about the classes. Check out the extra-curricular activities and meet others from around Australia