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mathematics

Ling Xiao

Ling Xiao 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 Ling Xiao rather than just read about it. In short: Ling Xiao is a mathematician whose research concerns differential geometry, and in particular geometric flow and its associated partial differential equations. She is an associate professor of mathematics at the University of Connecticut.

Key takeaways

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

Reference excerpt

Ling Xiao is a mathematician whose research concerns differential geometry, and in particular geometric flow and its associated partial differential equations. She is an associate professor of mathematics at the University of Connecticut.

Education and career Xiao received her doctorate in mathematics from Johns Hopkins University in 2013, with the dissertation Flow Problems in Hyperbolic Space supervised by Joel Spruck. After postdoctoral research at the Simons Laufer Mathematical Sciences Institute in Berkeley, California, and postdoctoral short-term positions as a visiting assistant professor at Cornell University and Hill Assistant Professor at Rutgers University, she obtained a tenure-track assistant professorship at the University of Connecticut in 2017. She was given tenure there as an associate professor in 2023.

Recognition Xiao is the 2025 recipient of the Ruth I. Michler Memorial Prize of the Association for Women in Mathematics, given "for her research accomplishments in geometric analysis and partial differential equations", including "significant contributions to the study of curvature flows in Euclidean space and in Minkowski space, and to the asymptotic Plateau problem for constant-curvature hypersurfaces in hyperbolic space".

References

External links Home page

Worked examples

Example 1 — a first encounter with Ling Xiao

Start with the simplest possible case. Write down what Ling Xiao 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 Ling Xiao 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 Ling Xiao 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 Ling Xiao

In research
Ling Xiao 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 Ling Xiao 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
Ling Xiao is common in secondary-school and first-year university syllabi. It links to neighbouring topics 21st-century American mathematicians, American women mathematicians, Differential geometers, so understanding it makes those chapters shorter.
In everyday life
Look for Ling Xiao 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 Ling Xiao in 20 minutes

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

Frequently asked questions

What is Ling Xiao in simple terms?

Ling Xiao is a mathematician whose research concerns differential geometry, and in particular geometric flow and its associated partial differential equations. She is an associate professor of mathematics at the University of Connecticut.

Why does Ling Xiao 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 Ling Xiao?

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 Ling Xiao.

Tags

  • 21st-century American mathematicians
  • American women mathematicians
  • Differential geometers
  • Johns Hopkins University alumni
  • Living people
  • University of Connecticut faculty

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