Making the connection between Physics and Mathematics

STRING THEORIST: Dr Tan Meng Chwan The deep connection between the fields of Physics and Mathematics has been a long-standing one, and Dr Tan Meng Chwan, NUS Department of Physics, has discovered yet another far-reaching link between the two fields. He has uncovered a purely physical understanding of a recently proven mathematical conjecture on a two-dimensional geometric Langlands duality for any simply-connected A-type group; a topic at the frontier of contemporary mathematics. In fact, his work goes further to show that the duality must also hold for any non-simply-connected D-type group. This is a profound and unexpected result that has yet to be proven by any mathematician. His research paper, entitled "Five-Branes In M-Theory and A Two-Dimensional Geometric Langlands Duality", is set to be published in the most exclusive and prestigious journal of Advances in Theoretical and Mathematical Physics.

Explained Dr Tan: "For mathematicians, once they conjecture a theorem, they will have to prove it. In the case of a two-dimensional geometric Langlands duality, they were not able to prove their conjecture in all generality as it was too difficult to do so."

Illustrating how his physical results would help guide mathematicians in the right direction towards an all-encompassing proof of their conjecture, while also providing them with novel, thought-provoking insights into the issue, he gave the analogy of filling a box with many of the same irregularly-shaped object. He said: "Mathematicians were able to prove that the box could fit, say, ten of them. However, they could not say for sure how many would fit in a box that was maybe a third of the original size." The interpretation which he placed on the Langlands duality was that the number of these objects in any box is intimately tied to a physical quantity such as energy. By invoking the physics principle of conservation of energy, he was able to understand why the original box could have held only ten objects, and why the second box can only hold, say, five objects.

Recently, this physical string-theoretic interpretation of the duality received recognition from Prof. Edward Witten of the Institute for Advanced Study in Princeton, USA. Prof. Witten, who is hailed as the "greatest living physicist of all time", cited Dr Tan in his latest paper entitled "Geometric Langlands From Six Dimensions" published in High Energy Physics- Theory.

Dr Tan is currently a postdoctoral scholar at the Institute for Advanced Study and the California Institute of Technology, working alongside Prof. Edward Witten and Prof. Anton Kapustin, as part of the NUS Overseas-Postdoctoral Fellowship Scheme. Upon his return to NUS in October this year, he hopes to raise the standard of theoretical Physics to an international level and put Singapore on the world map in this area of research. He also plans to inspire more students to follow in his footsteps of studying theoretical Physics.