“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 14 January, S3 Eastern Science Lecture Theatre, 16 Rainforest Walk

Ryan Braiden

The K(pi, 1) conjecture for Artin groups

Every Artin group has an associated geometric object called a hyperplane complement space. To these spaces we have a sequence of groups, called homotopy groups, which record some of the topological properties of the space. In this presentation, I aim to explain the K(pi, 1) conjecture which is a statement about the extent to which Artin groups determine the homotopy groups of their associated hyperplane complement space.

Nisal Karawita

A quanto-historical analysis of Renaissance Finance

This study applies modern financial mathematics concepts techniques to digitized Renaissance-era data from the Finaeon Database, focusing on Italian city-states between 1300 and 1600. By analyzing records of exchange rates, currency conversion rates, bond yields, GDP and commodity prices, I reconstruct interest rate term structures, currency arbitrage opportunities and identify the stylized properties of financial data. Additionally, I quantify the risk premiums associated with sovereign lending and demonstrate how double-entry bookkeeping facilitated sophisticated risk management, indicating the relevance to modern quantitative risk modelling. This quanto-historical approach provides empirical evidence for the structural foundations of modern global finance.

Yan Yablonovskiy

Lean 4, AI and the univalent foundations of mathematics

Roughly speaking, the univalent foundations of mathematics seeks to reframe the foundations of mathematics in terms of type theory, and thus pliable for computerisation and examination by AI.

Lean 4 contributes to this with an interactive theorem prover, based on the foundations known as the calculus of inductive constructions. Over the past year reasoning LLMs have improved to the point of contributing solutions to previously unsolved Erdős problems.

This talk tries to briefly present a crash course in the current state of affairs in mathematical computer formalisation with regards to Lean 4.

To learn more, go to:
https://lean-lang.org/
https://mathlib-initiative.org/

Osbert Bryan Villasis

A COMBSS Approach to Change Point Detection in Time Series

This ongoing research project explores the use of the Continuous Optimization-based Best Subset Selection (COMBSS) framework for detecting change points in time-series data, with a current focus on Gaussian mean-shift models. The study aims to evaluate how continuous relaxations, sparsity-inducing penalties, and smooth optimization techniques can improve the scalability and accuracy of modern change-point detection methods. Work in progress includes simulation experiments to examine detection power, false-positive behavior, and computational efficiency across varying noise and signal settings. The project seeks to refine the COMBSS approach and establish its potential for broader statistical and real-world applications.

Krish Gupta

Comparative Cascade Dynamics Across Network Topologies and Implications for Predictive Models

This project investigates how information cascades propagate across four fundamental network models: Erdős–Rényi, Watts-Strogatz, Barabási–Albert, and Holme–Kim. By simulating diffusion processes and analysing degree distributions, clustering, path lengths, and cascade size patterns, we highlight how structural differences shape diffusion speed and reach. Conceptual links to fractal-like hub emergence and scale-free behaviour provide intuitive grounding for these results. A simple visual demonstration illustrates cascades across each topology. Finally, we discuss the potential of image-based prediction via convolutional neural networks compared to graph neural networks, outlining where each approach may succeed or fail in modelling dynamic network behaviour.

Super Cao

Knots, and Diagrammatic Algebra

Your headphones get tangled; your DNA can too. In this talk I’ll explain what mathematicians mean by a knot: a closed loop in 3D space that you’re allowed to wiggle and stretch, but never cut. A key question is how to tell knots apart, a problem that has fascinated mathematicians for over a century. The twist is that we can bring in seemingly unrelated algebra to attack it.

Group 2 – Tuesday 20 January, S3 Eastern Science Lecture Theatre, 16 Rainforest Walk

Yuji Deng

Neural Network Approaches to Realised Volatility Forecasting: Evidence from the CSI 300 ETF

This project investigates whether neural network models can improve realised volatility forecasting relative to popular HAR-type benchmarks. Using high-frequency data for the CSI 300 ETF, I construct several HAR and HAR-J specifications and compare them with LSTM-, GRU-, and MLP-based models designed to capture nonlinear and long-memory features in volatility dynamics. Out-of-sample forecasts are evaluated across multiple horizons using standard loss functions. Preliminary evidence suggests that simple HAR-type models remain competitive and that neural network performance is sensitive to design choices. The talk will discuss modelling decisions, empirical results, and practical lessons for applying deep learning to volatility forecasting.

Joshua O’Callaghan

The Parity Problem

Sieve theories have had remarkable success in answering questions about the prime numbers. The parity problem is an inherent limitation of current sieve theories. If A is a set of integers that are all products of an odd (or even) number of primes then sieve theory is unable to provide nontrivial lower bounds for |A|, and any upper bound will be off by at least a factor of 2. In this talk, I’ll discuss the parity problem, why it is so, and techniques to overcome it.

Sarah Lee

Bayesian Regression and Variable Selection for Joint Ordinal-Continuous Outcomes

Mixed responses are common in social science research: survey data are often ordinal (e.g., Likert items), while related socioeconomic measures are continuous. A common practice is to average ordinal items into a continuous score, but this discards the ordered structure and loses item-level information. We propose a Bayesian multivariate regression model that preserves ordinal information via an augmented Gaussian latent variable jointly modelled with the continuous response. Spike-and-slab priors are used to simultaneously perform variable selection.

Authors & affiliations:
Sarah Lee – PhD Candidate, University of Technology Sydney (UTS), Australia
Sally Cripps – Professor and Director of Human Technology Institute​, University of Technology Sydney (UTS), Australia
Matias Quiroz – Senior Lecturer, School of Mathematical and Physical Sciences , University of Technology Sydney (UTS), Australia

Samuel Killick

The orbit method for compact Lie groups

The orbit method developed by A.Kirillov allows one to speak geometrically about irreducible representations of Lie groups. Thusly we are given a geometric interpretation of the algebraic-analytic achievements made by E.Cartan and H.Weyl in the classification of the irreducible representations of semi-simple compact Lie groups.

This talk will centre around the representation theory of SU(2), understood through the extension of the orbit method from nilpotent to compact semi-simple connected Lie groups.

Hardik Gaur

From Chaos to Coherence : Modelling Cities as Complex Systems

Modern cities are prime manifestations of complex systems. They serve as centres of trade, culture, education, and social interaction, while being dominated by intricate yet highly interconnected networks of people, built environment, and institutions. Consequently, planning a city is a complex endeavour that is both an art and a science. Here, we present an overview of city planning from a mathematical perspective, drawing on concepts from chaos theory and automata theory to characterize cities as complex adaptive systems.

Michael H.

The Converse of The Extreme Value Theorem

The Extreme Value Theorem states that continuous functions on closed and bounded intervals attain their extreme values. A topological analogue of this theorem asserts that the continuous image of a compact set is compact. We consider the converse: for a given function, when does its domain admit a compact topology that renders it continuous? We’ll introduce order-theoretic tools that illuminate necessary and sufficient constraints, explore the variant demanding a compact metrizable topology, and trace how the interaction between continuity, compactness, and metrizability influences the set of possible solutions.

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