Michael Ng - Mathematical Science

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An Ky Duy Nguyen

Mr

26/08/1994

PB327

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+61420581879

27 Yarmouth Ave, St Albans
Victoria
Australia

My fascination with mathematics lies in its ability to reveal profound connections across seemingly disparate fields. This passion has shaped my academic journey, from graduating with First Class Honours (94.22 WAM) to publishing research that bridges Lie theory, Riemannian geometry, and dynamical systems. Currently funded by the prestigious Australian Government Scholarship, my PhD investigates Killing tensors in symmetric spaces, uncovering deep relationships between differential geometry and physics through novel applications of representation theory, Cartan geometry, and mechanics.
The 2nd Hong Kong Laureate Forum offers an unparalleled platform to elevate my research. I am deeply inspired by Shaw Laureate Shiing-Shen Chern’s groundbreaking contributions to differential geometry, which form the foundation of my work. Furthermore, engaging with luminaries like Nigel Hitchin and George Lusztig, whose research directly aligns with my interests, would provide invaluable insights into geometric and algebraic challenges, helping me navigate the complexities of my research.
Beyond expert mentorship, the Forum presents a unique opportunity to connect with fellow researchers, exchange ideas, and stay at the forefront of scientific innovation. Attending the Forum would be a once-in-a-lifetime experience that would not only broaden my knowledge but also shape my personal growth and strengthen my commitment to becoming a professional mathematician.

Postgraduate (PhD)

Pure Mathematics

La Trobe University

Melbourne, Victoria, Australia

2024 – Present: Australian Government Research Training Program PhD Scholarship
2022: Young Researcher of Heidelberg Laureate Forum
2021: Invited Member of La Trobe Student Excellence Academy
2020 – 2022: Australian Government Research Training Program Masters Scholarship
2020: La Trobe Mathematics and Statistics Department Prize
2020: La Trobe Honours Year Grant
2020: Australian Mathematical Sciences Institute (AMSI) Vacation Research Scholarship
2020: Participation in AMSI 2020 Summer School
2019 – 2021: Peter J. Fox Memorial Scholarship
2019: La Trobe Pro Vice-Chancellor’s Commendation
2019: Member of Golden Key International Honour Society
2018: Member of La Trobe Hallmark Program

Killing vector and tensor fields are fundamental to differential geometry and mathematical physics, playing crucial roles in integrable systems, conserved quantities in classical mechanics, and exact solutions in general relativity. My current research focuses on investigating and classifying the decomposability of Killing tensors on various symmetric spaces. By analysing these tensors through the combined frameworks of representation theory, invariant theory, and Riemannian geometry, we aim to reveal deep connections between algebraic structures and geometric properties, while gaining new perspectives into the interplay between symmetry and differential equations.
We have established complete classifications for several significant cases, including SL(3)/SO(3), SO(n) (n≥5), and G2/SO(4). These findings offer insights into the underlying symmetry structures governing Killing tensors and contribute to a broader understanding of their role in mathematical physics. Our ongoing work aims to extend these classifications to develop a comprehensive theoretical framework for Killing tensors on arbitrary symmetric spaces.
This research not only advances pure mathematics but also has potential implications for theoretical physics, particularly in Hamiltonian mechanics and general relativity. Through this work, we aim to bridge the gap between abstract geometry and its physical applications, furthering our understanding of symmetry principles and conservation laws in mathematical models of the universe.