mathematics

Lai-Sang Young

Lai-Sang Young 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 Lai-Sang Young rather than just read about it. In short: Lai-Sang Lily Young (Chinese: 楊麗笙, born 1952) is a Hong Kong-born American mathematician who holds the Henry & Lucy Moses Professorship of Science and is a professor of mathematics and neural science at the Courant Institute of Mathematical Sciences of New York University. Her research interests include dynamical systems, ergodic theory, chaos theory, probability theory, statistical mechanics, and neuroscience.

Key takeaways

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

Reference excerpt

Lai-Sang Lily Young (Chinese: 楊麗笙, born 1952) is a Hong Kong-born American mathematician who holds the Henry & Lucy Moses Professorship of Science and is a professor of mathematics and neural science at the Courant Institute of Mathematical Sciences of New York University. Her research interests include dynamical systems, ergodic theory, chaos theory, probability theory, statistical mechanics, and neuroscience. She is particularly known for introducing the method of Markov returns in 1998, which she used to prove exponential correlation delay in Sinai billiards and other hyperbolic dynamical systems.

Education and career Although born and raised in Hong Kong, Young came to the US for her education, earning a bachelor's degree from the University of Wisconsin–Madison in 1973. She moved to the University of California, Berkeley for her graduate studies, earning a master's degree in 1976 and completing her doctorate in 1978, under the supervision of Rufus Bowen. She taught at Northwestern University from 1979 to 1980, Michigan State University from 1980 to 1986, the University of Arizona from 1987 to 1990, and the University of California, Los Angeles from 1991 to 1999. She has been the Moses Professor at NYU since 1999.

Awards and honors Young became a Sloan Fellow in 1985, and a Guggenheim Fellow in 1997. In 1993, Young was given the Ruth Lyttle Satter Prize in Mathematics of the American Mathematical Society "for her leading role in the investigation of the statistical (or ergodic) properties of dynamical systems". This is a biennial award for outstanding research contributions by a female mathematician. In 2004, she was elected as a fellow of the American Academy of Arts and Sciences. Young was an invited speaker at the International Congress of Mathematicians in 1994, and an invited plenary speaker at the 2018 International Congress of Mathematicians. In 2005, she presented the Noether Lecture of the Association for Women in Mathematics; her talk was entitled "From Limit Cycles to Strange Attractors". In 2007, she presented the Sonia Kovalevsky lecture, jointly sponsored by the AWM and the Society for Industrial and Applied Mathematics. In 2020 she was elected a member of the National Academy of Sciences. She is the recipient of the 2021 Jürgen Moser Lecture prize "for her sustained and deep contributions to the theory of non-uniformly hyperbolic dynamical systems." In 2023, she was awarded the Heinz Hopf Prize and in 2024 the Rolf Schock Prize.

Selected publications Block, Louis; Guckenheimer, John; Misiurewicz, Michał; Young, Lai Sang (1980), "Periodic points and topological entropy of one-dimensional maps", Global theory of dynamical systems (Proc. Internat. Conf., Northwestern Univ., Evanston, Ill., 1979), Lecture Notes in Mathematics, vol. 819, Berlin: Springer, pp. 18–34, doi:10.1007/BFb0086977, ISBN 978-3-540-10236-6, MR 0591173. Young, Lai Sang (1982), "Dimension, entropy and Lyapunov exponents", Ergodic Theory and Dynamical Systems, 2 (1): 109–124, doi:10.1017/S0143385700009615, MR 0684248. Benedicks, Michael; Young, Lai-Sang (1993), "Sinaĭ–Bowen–Ruelle measures for certain Hénon maps", Inventiones Mathematicae, 112 (3): 541–576, Bibcode:1993InMat.112..541B, doi:10.1007/BF01232446, MR 1218323, S2CID 18642732. Young, Lai-Sang (1998), "Statistical properties of dynamical systems with some hyperbolicity", Annals of Mathematics, Second Series, 147 (3): 585–650, doi:10.2307/120960, JSTOR 120960, MR 1637655. Young, Lai-Sang (1999), "Recurrence times and rates of mixing", Israel Journal of Mathematics, 110: 153–188, doi:10.1007/BF02808180, MR 1750438, S2CID 17557828. Wang, Qiudong; Young, Lai-Sang (2001), "Strange attractors with one direction of instability", Communications in Mathematical Physics, 218 (1): 1–97, Bibcode:2001CMaPh.218....1W, doi:10.1007/s002200100379, MR 1824198, S2CID 120611205. Young, Lai-Sang (2002), "What are SRB measures, and which dynamical systems have them?", Journal of Statistical Physics, 108 (5–6): 733–754, Bibcode:2002JSP...108..733Y, doi:10.1023/A:1019762724717, MR 1933431, S2CID 14403405.

References

External links Young's Homepage "Dynamical systems evolving – Lai-Sang Young – ICM2018". YouTube. 19 September 2018. (Plenary Lecture 8) Kevin Hartnett, A Mathematical Model Unlocks the Secrets of Vision, Quanta Magazine, 21 August 2019

Illustrations

Worked examples

Example 1 — a first encounter with Lai-Sang Young

Start with the simplest possible case. Write down what Lai-Sang Young 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 Lai-Sang Young 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 Lai-Sang Young 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 Lai-Sang Young

In research: Lai-Sang Young 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 Lai-Sang Young 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: Lai-Sang Young is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1952 births, 20th-century American mathematicians, 20th-century American women mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Lai-Sang Young 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 Lai-Sang Young in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Lai-Sang Young 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 Lai-Sang Young out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Lai-Sang Young in simple terms?

Why does Lai-Sang Young 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 Lai-Sang Young?

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 Lai-Sang Young.