Guofang Wei
Encyclopedia
Guofang Wei is a mathematician in the field of differential geometry. She is currently a professor at University of California, Santa Barbara
.
Dr. Wei earned a doctorate in mathematics from SUNY Stony Brook when she was only 24 years old. Her advisor was Detlef Gromoll
.
Her dissertation produced fundamental new examples of manifolds with positive
Ricci
curvature and was published in the Bulletin of the American Mathematical Society. These examples were later expanded upon by Burkard Wilking.
In addition to her work on the topology of manifolds with nonnegative Ricci curvature, she has completed work on the isometry groups of manifolds with negative
Ricci curvature with coauthors Xianzhe Dai and Zhongmin Shen. She also has major work with Peter Petersen
on manifolds with integral Ricci curvature bounds.
Starting in 2000 Wei began working with Christina Sormani on limits of manifolds with lower Ricci curvature bounds using techniques of Jeff Cheeger
and Tobias Colding
,
particularly Kenji Fukaya's metric measure convergence. The limit spaces in this setting are metric measure spaces. Wei was invited to present this work in a series of talks
at the Seminaire Borel in Switzerland. Sormani and Wei also developed a notion called the covering spectrum of a Riemannian manifold.
Most recently Dr. Wei has completed research with her student, Will Wylie, on smooth metric measure spaces and the Bakry-Emery Ricci tensor. She was invited to present this work at the prestigious Geometry Festival
in 2009.
In addition to conducting research, Guofang Wei has mentored the Dos Pueblos High School Math Team, which won second place in the International Shing-Tung Yau High School Math Awards competition in Beijing in 2008.
University of California, Santa Barbara
The University of California, Santa Barbara, commonly known as UCSB or UC Santa Barbara, is a public research university and one of the 10 general campuses of the University of California system. The main campus is located on a site in Goleta, California, from Santa Barbara and northwest of Los...
.
Dr. Wei earned a doctorate in mathematics from SUNY Stony Brook when she was only 24 years old. Her advisor was Detlef Gromoll
Detlef Gromoll
Detlef Gromoll was a mathematician who studied distortions of shapes in three or more dimensions. In his soul theorem, published in 1972, he and Jeff Cheeger studied the properties of surfaces that have flat regions or curves like the outside of a sphere but not regions shaped liked saddles...
.
Her dissertation produced fundamental new examples of manifolds with positive
Ricci
Ricci
Ricci is an Italian surname, and can also be a shortened version of Riccardo, as a first name and may refer to:-Surname:* Christie Ricci, American wrestler* Christina Ricci, American actress* Fausto Ricci, Italian motorcycle racer...
curvature and was published in the Bulletin of the American Mathematical Society. These examples were later expanded upon by Burkard Wilking.
In addition to her work on the topology of manifolds with nonnegative Ricci curvature, she has completed work on the isometry groups of manifolds with negative
Ricci curvature with coauthors Xianzhe Dai and Zhongmin Shen. She also has major work with Peter Petersen
Peter Petersen
Peter Petersen is a South African football defender for Maritzburg United and South Africa.-External links:* at National Football Teams...
on manifolds with integral Ricci curvature bounds.
Starting in 2000 Wei began working with Christina Sormani on limits of manifolds with lower Ricci curvature bounds using techniques of Jeff Cheeger
Jeff Cheeger
Jeff Cheeger , is a mathematician. Cheeger is professor at the Courant Institute of Mathematical Sciences at New York University in New York City. His main interests are differential geometry and its applications to topology and analysis.-Biography:He graduated from Harvard University with a B.A....
and Tobias Colding
Tobias Colding
Tobias Holck Colding is a Danish mathematician. He was born in Copenhagen, Denmark, to Torben Holck Colding and Benedicte Holck Colding. He received his Ph.D. in mathematics in 1992 at the University of Pennsylvania under Chris Croke. Since 2005 Colding has been a professor of mathematics at MIT...
,
particularly Kenji Fukaya's metric measure convergence. The limit spaces in this setting are metric measure spaces. Wei was invited to present this work in a series of talks
at the Seminaire Borel in Switzerland. Sormani and Wei also developed a notion called the covering spectrum of a Riemannian manifold.
Most recently Dr. Wei has completed research with her student, Will Wylie, on smooth metric measure spaces and the Bakry-Emery Ricci tensor. She was invited to present this work at the prestigious Geometry Festival
Geometry Festival
-1985 at Penn:* Marcel Berger* Pat Eberlein* Jost Eschenburg* Friedrich Hirzebruch* Blaine Lawson* Leon Simon* Scott Wolpert* Deane Yang-1986 at Maryland:* Uwe Abresch, Explicit constant mean curvature tori...
in 2009.
In addition to conducting research, Guofang Wei has mentored the Dos Pueblos High School Math Team, which won second place in the International Shing-Tung Yau High School Math Awards competition in Beijing in 2008.
Important Publications
- Examples of complete manifolds of positive Ricci curvature with nilpotent isometry groups, Bull. Amer. Math. Soci. Vol. 19, no. 1 (1988), 311-313.
- with X. Dai and Z. Shen, Negative Ricci curvature and isometry group, Duke Math J. 76 (1994) 59-73.
- with P. Petersen, Relative volume comparison with integral curvature bounds, GAFA 7 (1997) 1031-1045.
- with C. Sormani, The covering spectrum of a compact length space, Journal of Diff. Geom. 67 (2004) 35-77.
- with W. Wylie Comparison Geometry for the Bakry-Emery Ricci Tensor , Journal of Diff. Geom. 83, no. 2 (2009), 377-405.