While Professor Wong’s current work is theoretical, the theory has surprising applications in areas ranging from quantum physics to DNA manipulation. In short, his research is reshaping our understanding of the fundamental structures that govern the universe.
Wong’s research lies in the field of topology, a branch of pure math that explores the fundamental properties of shapes and spaces. More specifically, he works in low-dimensional topology, which focuses on the behaviour of spaces in three and four dimensions, and their intersections with contact geometry. Within this field, Wong studies Floer theory, a topological quantum field theory with deep connections to gauge theory in physics. Floer theory provides tools that have revolutionized the study of knots and manifolds over the last two decades.
In simpler terms, Wong’s work is like solving a puzzle where the pieces are abstract mathematical forms rather than just shapes. His research aims to understand how different theories in math relate to each other. While these theories come from different physics and mathematical contexts, they offer complementary insights into the structure of topological spaces. This can help mathematicians predict and compute the properties of complex shapes and spaces.
His recent work investigates a specific type of mathematical invariant known as the tau invariant, which appears in several distinct versions of Floer theory. His latest paper, “On the Tau invariants in instanton and monopole Floer theories,” was published in the Journal of Topology. In the article, Wong offers new insights into knot theory by examining the intricate relationships between various types of Floer theories. By exploring the relationships among the tau invariants, Wong’s research sheds light on deeper connections within the field. “Floer theory is a powerful tool that allows us to look at how different shapes, or ‘manifolds,’ fit together and how they can be analyzed from various perspectives,” he explains.
While Wong’s work in Floer theory is rooted in pure math, the broader field of knot theory has real-world applications, particularly in molecular biology. Knot theory offers a natural framework to study DNA and RNA structures since understanding how strands are knotted or unknotted can shed light on essential biological processes. This area, known as DNA topology, has even led to the identification of enzymes like topoisomerases as potential targets for drugs to act on. There are also more speculative connections between knot theory and fields such as quantum computing and cryptography, so the mathematical insights from Wong’s research may one day inform future developments in these areas as well.
Wong’s research exemplifies how pure math can deepen our understanding of complex structures and uncover unexpected connections across different theories. “The key goal of my research is to bridge different mathematical theories and uncover their connections,” he says. “By comparing these theories, we can gain a deeper understanding of their underlying principles and potentially solve problems that were previously out of reach.”
Outside of academia, Wong enjoys classical music and the strategic challenges of contract bridge. He often finds echoes of mathematical structure in the world around him — from the harmonies of music to the patterns in everyday life. This outlook mirrors his approach to math: uncovering elegant connections and exploring complexity with curiosity and precision.
As Wong continues his work, he remains dedicated to mentoring the next generation of mathematicians. Through his research and guidance, he’s helping to unlock new possibilities in both math and its applications in the wider world.
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