mathematics

Guofang Wei

Guofang Wei is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Guofang Wei rather than just read about it. In short: Guofang Wei is a mathematician in the field of differential geometry. She is a professor at the University of California, Santa Barbara.

Key takeaways

Guofang Wei belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Guofang Wei to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Guofang Wei from memory before moving on to harder problems.

Reference excerpt

Guofang Wei is a mathematician in the field of differential geometry. She is a professor at the University of California, Santa Barbara.

Education Wei earned a doctorate in mathematics from the State University of New York at Stony Brook in 1989, under the supervision of 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.

Research 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. Dr. Wei has completed research with her student, Will Wylie, on smooth metric measure spaces and the Bakry–Emery Ricci tensor. Guofang Wei was twice invited to present her work at the prestigious Geometry Festival both in 1996 and 2009.

Outreach In addition to conducting research, Guofang Wei has mentored the Dos Pueblos High School Math Team Archived 2011-07-14 at the Wayback Machine, which won second place in the International Shing-Tung Yau High School Math Awards competition in Beijing in 2008.

Awards and honors In 2013 she became a fellow of the American Mathematical Society, for "contributions to global Riemannian geometry and its relation with Ricci curvature".

Selected publications "Examples of complete manifolds of positive Ricci curvature with nilpotent isometry groups", Bull. Amer. Math. Soc. Vol. 19, no. 1 (1988), 311–313. doi:10.1090/S0273-0979-1988-15653-4 with X. Dai and Z. Shen, "Negative Ricci curvature and isometry group", Duke Math J. 76 (1994), 59–73. doi:10.1215/S0012-7094-94-07603-5 with X. Dai and R. Ye, "Smoothing Riemannian manifolds with Ricci curvature bounds", MANUSCR MATH, vol. 90, no. 1 (1996), 49–61. doi:10.1007/BF02568293 with P. Petersen, "Relative volume comparison with integral curvature bounds", GAFA 7 (1997), 1031–1045. doi:10.1007/s000390050036 with C. Sormani, "The covering spectrum of a compact length space", Journal of Diff. Geom. 67 (2004), 35–77. doi:10.4310/jdg/1099587729 with X. Dai and X. Wang, "On stability of Riemannian manifold with parallel spinors", Invent Math, vol. 161, no. 1, (2005) 151–176. doi:10.1007/s00222-004-0424-x with W. Wylie, "Comparison geometry for the Bakry–Emery Ricci tensor", Journal of Diff. Geom. 83, no. 2 (2009), 377–405. doi:10.4310/jdg/1261495336

References

External links Guofang Wei at UCSB Seminaire Borel Geometry Festival 2009 Dos Pueblos High School Math Team wins Second Place in S T Yau HS Math Awards Guofang Wei at the Mathematics Genealogy Project

Worked examples

Example 1 — a first encounter with Guofang Wei

Start with the simplest possible case. Write down what Guofang Wei claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Guofang Wei before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Guofang Wei ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Guofang Wei

In research: Guofang Wei appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Guofang Wei in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Guofang Wei is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1965 births, 21st-century American mathematicians, 21st-century American women mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Guofang Wei outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Guofang Wei in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Guofang Wei means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Guofang Wei out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Guofang Wei in simple terms?

Guofang Wei is a mathematician in the field of differential geometry. She is a professor at the University of California, Santa Barbara.

Why does Guofang Wei matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Guofang Wei?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Guofang Wei.