After growing up in Shanghai, Visiting Professor of Mathematics Wei-Min Wang went on to study at MIT and later at Princeton University, and is currently a research director in the Centre National de la Recherche Scientifique (CNRS) in France. Wang says joining NYU Shanghai as a visiting professor has helped her find a way to come back home.
What inspired you to become a mathematician?
I started out by studying physics, then I realized that I am more drawn to the mathematics structure behind it. So I became a mathematician instead, but I retain an interest in physics. For example, my work in mathematics is often inspired by problems in physics. My PhD thesis was on mathematical physics from Princeton University, under the guidance of Professor Tom Spencer at the nearby Institute for Advanced Study.
What are some of the big questions that your research delves into?
Recently I became excited by quasicrystals. In physics, and maybe also in real life, crystals play an important role. For example, one can think of a crystal champagne glass, which when tapped, resonates and ``sings." This is because crystals have a structure and symmetry. Often the molecules in a crystal are arranged periodically. This is, but an idealization of course, as often there are defects. The defects affect the physical properties.
Quasicrystals are one way of modeling crystals with defects. It is currently a hot topic in physics and material science. My research in mathematics is very much connected to the subject.
There is, however, another way of modeling defects, which assumes that they are random, for example, their locations. This was how the1958 Nobel prize winner in physics, Phillip Anderson, modeled it back then. It is called the Anderson model; and the subject is called Anderson Localization. I started my research by studying Anderson Localization.
Anderson had this very nice way of understanding the physical problem.It was realized shortly afterwards that there is very interesting mathematics underlying the Anderson model. In the past 40 years, mathematicians have studied Anderson Localization extensively, and have drawn some far reaching consequences.
Recently I gave a talk in the annual meeting of the Chinese Industrial and Applied Mathematics Society in Kunming and presented my work with different groups of collaborators, many of whom are in China. My talk in Kunming said, roughly speaking, that these two models lead to similar results and similar physical effects. Quasicrystals are a newer, and a difficult problem, but one may now draw on the bigger wealth of knowledge on Anderson Localization.
Quasicrystals are an important subject in material science, for example they can be used in transmission of signals. Hopefully our small steps could elucidate and contribute along the way.
How does NYU Shanghai support your research?
My research has strong connections with probability theory, which is prominent here. I often have meaningful discussions with colleagues here at NYU Shanghai. Mathematics in China has made huge progress in recent years. Being at NYU Shanghai facilitates direct interactions with Chinese colleagues, for example, it has certainly made it easier to go to Kunming this October.
What are your plans for the rest of your time as Visiting Professor?
I plan to continue initiating undergraduate students into mathematics through teaching. I also have plans to attract junior mathematicians to the NYU-ECNU Mathematics Institute to further their research.