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Sun-Yung Alice Chang

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Sun-Yung Alice Chang

In Her Own Words

That Magic Moment

My important breakthrough was in 2002, when I realized that I can learn and apply the technique of fully non-linear partial differential equations to study the geometry problem I had been pondered for a long time.

Challenges to Come

We can now gather data on the long-term asymptotic behavior of mathematical models and physical phenomena, so we need to develop an effective mathematical theory and methods to analyze the data.

With UPMC

Each time I visited, I am so impressed with the quality and devotion of colleagues working at UPMC. I look forward to more scientific cooperation.

Words for the Up & Coming

Follow your heart to do what you want, and then you will be working at full capacity.

 

professeor Sun-Yung Alice Chang

Presented by Fabrice Bethuel, professor of applied mathematics

 

It is a great honor and a great pleasure for me to present to you the work of Professor Sun-Yung Alice Chang, which earned her the title of Doctor Honoris Causa that we will bestow today. She was born in China and grew up in Taiwan, where she completed a large part of her studies. Alice Chang then moved to California where she obtained her doctorate in mathematics and began her career, becoming a professor first at Berkeley and then Los Angeles before moving in the late 90s to Princeton University, where she currently holds the Eugene Higgins Chair.

 

Her early work is in the field of harmonic analysis, the theory of analytic functions, and spectral problems for the Laplacian. One of her very first articles provided the final piece needed to resolve a famous Douglas problem; this article brought her immediate fame and established her as one of the top researchers of her generation.

 

Her work with L. Carleson was a turning point in her career. N. Trudinger and J. Moser had discovered an optimal version of the Sobolev inequality in the critical limiting case. Alice Chang and Carleson showed, to everyone’s surprise, that this inequality possesses a minimizer which is radially symmetric, even though it is the limit of inequalities which are not achieved. This optimal inequality plays a crucial role in the problem of prescribing curvature and geometric nature, which is formulated as follows: given a function on the sphere, is it the curvature of a metric which is conformally equivalent to the standard one? Kazdan and Warner gave a necessary condition. Alice Chang and Paul Yang, who later became her husband, then provided two sufficient conditions. Despite considerable progress since their article’s publication, their work represented a major breakthrough and is still considered seminal.

 

Her interest in this issue represents a turning point in her career and a transition within her classical training in analysis: geometric problems are now the focus of her research, and partial differential equations become tools to model and solve these problems. She therefore joins a tradition started by Henri Poincaré, and like Poincaré in the case of surfaces, it is the notion of curvature that is at the center of her concerns, as both a local and global perspective. She is also motivated by physics, such as general relativity in the case of varieties of the fourth dimension, which she has specifically studied.

 

Functional inequalities have led her to consider another important problem in geometry, related to the famous question: “Can you hear the shape of a drum” She has made fundamental contributions to this issue, which has disrupted research on this topic: the introduction of the use of conformal invariant operators and elliptic equations of higher order. These are related to the notion of Q-curvature and its associated operator, known in mathematical physics, but quite new for geometric analysts. These tools provide a genuinely new approach to conformal geometry, and also lead to new results for the classical Yamabe problem.

 

Conformal geometry recently brought her even closer to mathematical physics, in particular through Poincaré-Einstein metrics, which she addressed through the construction of Fefferman-Graham. Several recent articles in collaboration with Qing and Yang propose a new class of variational geometric problems that are associated with this construction. They are already important areas of research.

 

Alice Chang’s work is widely recognized, as her long list of awards will attest. She was plenary speaker at the World Congress of Mathematicians held in Beijing in 2002; she received the prestigious Ruth Lyttle Satter in 1995 and has been a member of the American Academy of Sciences since 2006. She has also held prominent positions in scientific societies, including the American Mathematical Society, of which she was vice-president from 1989 to 1991, and has participated in many prestigious scientific committees.

 

Alice Chang also created a brilliant mathematical school, whose members are among the most active researchers on these issues worldwide. She has been advisor to about fifteen doctoral candidates that include Matthew Gursky, Qing Jie, and Kai-Lin Chin—all leading researchers. Alice Chang has maintained privileged scientific contacts with France since the early 80s. She has been invited on numerous occasions, particularly to our university, first by Thierry Aubin and Haim Brezis, and then by members their schools, such as Jean-Michel Coron, Emmanuel Hebey, Frank Pacard, Frederick Hélein, Olivier Rey or myself. We have, in turn, made numerous visits to the United States, either in Los Angeles or Princeton, where she currently teaches. This year, she also spent two full months in Paris for a semester on a specific theme, organized by Matthew Gursky, Emmanuel Hebey and Frank Pacard at the Henri Poincaré Institute.

 

The distinction that we are presenting today it is therefore to recognize major work in mathematics that is impressive both for its variety than its depth, and that completely transformed our approach and insight into several major problems in geometry. It also shows our gratitude and friendship for a colleague who has always shared her passion for research and mathematics with us.



12/12/13