2001 Lecturer: Sun-Yung Alice Chang
Nonlinear Equations in Conformal Geometry
Abstract:
Elliptic equations have been and continue to be an important tool in the study of problems in geometry. In recent decades, non-linear second order elliptic equations with critical exponents have played a special role in the solutions of several important problems in conformal geometry; e.g. the problem of prescribing Gaussian curvature and the Yamabe problem. In this talk, I will describe some recent efforts to extend the role played by second order semilinear equations to higher order semilinear equations as well as second order fully non-linear equations. A common feature essential to understanding such equations is the analysis of blow up in these equations. This analysis involves classifying entire solutions to such equations in Euclidean space. I plan to discuss examples of blowup phenomena in several such situations.
Brief Biography:
Sun-Yung Alice Chang was born in Cian, China. Her family moved to Taiwan shortly after the Chinese revolution and she grew up in Taiwan. She received her B.A. from the National Taiwan University in 1970 and attended graduate school at University of California, Berkeley, where she wrote her Ph.D. thesis in 1974 under the supervision of Donald Sarason. Since then she has held many temporary/visiting position at various universities, including the State University of New York at Buffalo; the University of California, Los Angeles; the University of Maryland, College Park; Institute for Advanced Study; Princeton University; and Mittag-Leffler Institute, Sweden. She settled down at UCLA in 1980 as an associate professor. She was promoted to full professor there in 1982 and has remained there except in 1989 when she was Professor at UC Berkeley. Since 1998, she has also been Professor at Princeton University.
In her thesis, Chang worked on problems in classical analysis, in particular the study of boundary behavior of bounded analytic functions on the unit disc. Since then her research interest has gradually shifted to problems in real harmonic analysis, then to spectral theory of the Laplacian, and further to problems in geometric analysis, using PDE methods to study problems in differential geometry. She is currently interested in the conformal geometry of a class of 4-manifolds. She is developing new techniques involving higher order partial differential equations to understand the conformal structures in four dimension.
Chang was awarded an Alfred P. Sloan Fellowship in 1979 and a Guggenheim Foundation Fellowship in 1999. She served as Vice-President of the American Mathematical Society (AMS) from 1989 to 1991 and was awarded the AMS Ruth Lyttle Satter Prize for outstanding contributions to mathematics research by a woman in 1995. She gave an invited AMS hour addresses at the Joint Mathematics Meetings in 1991 (Louisville, Kentucky) and in 2000 (Washington, D.C.) She was an invited speaker at the International Congress of Mathematics in 1986 (Berkeley, California).
Chang is a firm believer that, given a suitable environment in which to develop, women and men are equally talented in mathematics. In her undergraduate class at Taiwan, there were 12 women in a class of 40 mathematics majors. Partially due to the enriching interaction among the classmates, several went on to become successful mathematicians.”
Chang has one daughter and one son. Her husband, Paul Yang, is also a mathematician and a long term scientific collaborator of Chang. In her spare time, she enjoys reading novels, taking walks and listening to music.
