mathematics

Hee Oh

Hee Oh 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 Hee Oh rather than just read about it. In short: Hee Oh (Korean: 오희, born 27 October 1969) is a Korean American mathematician and the Abraham Robinson Professor of Mathematics at Yale University. She has made contributions to dynamical systems, discrete subgroups of Lie groups, and their connections to geometry and number theory.

Key takeaways

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

Reference excerpt

Hee Oh (Korean: 오희, born 27 October 1969) is a Korean American mathematician and the Abraham Robinson Professor of Mathematics at Yale University. She has made contributions to dynamical systems, discrete subgroups of Lie groups, and their connections to geometry and number theory.

Career She graduated with a bachelor's degree from Seoul National University in 1992 and obtained her Ph.D. from Yale University in 1997 under the guidance of Gregory Margulis. She held several faculty positions, including ones at Princeton University, California Institute of Technology and Brown University, before joining the Department of Mathematics at Yale University in 2013 as the first female tenured professor in Mathematics there. She served as Vice President of the American Mathematical Society, February 1, 2021 – January 31, 2024.

Work She has worked extensively on counting and equidistribution for Apollonian circle packings, Sierpinski carpets and Schottky dances. Her recent work continues to be centered around the exploration and use of lie groups. More specifically, working with representations by using discrete sub groups, like Anosov Groups. Her research explores how these sub groups are useful in measuring characteristics of dynamical systems like maximal entropy.

Honours Hee Oh was an invited speaker at the International Congress of Mathematicians in Hyderabad in 2010, and gave a joint invited address at the 2012 AMS-MAA Joint Mathematics Meeting. In 2012 she became an inaugural fellow of the American Mathematical Society. She is the 2015 recipient of the Ruth Lyttle Satter Prize in Mathematics. In 2017, she was named a Guggenheim fellow. In 2018, she received the Ho-Am Prize for Science. In 2024, she was inducted into the American Academy of Arts and Sciences. She served on the Fields Medal committee at the 2018 ICM in Rio. She is on the Abel Prize committee for 2024-2026.

Selected publications with Laurent Clozel, Emmanuel Ullmo: Hecke operators and equidistribution of Hecke points, Inventiones mathematicae, vol. 144, 2001, pp. 327–351 Uniform pointwise bounds for matrix coefficients of unitary representations and applications to Kazhdan constants, Duke Mathematical Journal, vol. 113, 2002, pp. 133–192 with Alex Eskin, Shahar Mozes: On uniform exponential growth for linear groups, Inventiones mathematicae, vol. 160, 2005, pp. 1–30 Proceedings of International Congress of Mathematicians (2010): Dynamics on geometrically finite hyperbolic manifolds with applications to Apollonian circle packings and beyond arXiv:1006.2590 with Alex Kontorovich: Apollonian circle packings and closed horospheres on hyperbolic 3-manifolds, Journal of the American Mathematical Society, vol. 24, 2011, pp. 603–648 with Nimish Shah: The asymptotic distribution of circles in the orbits of Kleinian groups, Inventiones mathematicae, vol. 187, 2012, pp. 1–35 with Nimish Shah: Equidistribution and counting for orbits of geometrically finite hyperbolic groups, Journal of the American Mathematical Society, vol. 26, 2013, pp. 511–562 with Amir Mohammadi: Ergodicity of unipotent flows and Kleinian groups, Journal of the American Mathematical Society, vol. 28, 2015, pp. 531–577 with Dale Winter: Uniform exponential mixing and resonance free regions for convex cocompact congruence subgroups of SL_2(Z), Journal of the American Mathematical Society, vol. 29, 2016, pp. 1069–1115 with Curtis McMullen, Amir Mohammadi: Geodesic planes in hyperbolic 3-manifolds, Inventiones mathematicae, vol. 209, 2017, pp. 425–461 with Dale Winter: Prime number theorems and holonomies for hyperbolic rational maps, Inventiones mathematicae, vol. 208, 2017, pp. 401–440

References

External links Homepage at Yale University Video lecture at Cornell University Article in the American Scientist by Dana Mackenzie Archived 2017-04-10 at the Wayback Machine Interview with Yale News

Illustrations

Worked examples

Example 1 — a first encounter with Hee Oh

Start with the simplest possible case. Write down what Hee Oh 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 Hee Oh 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 Hee Oh 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 Hee Oh

In research: Hee Oh 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 Hee Oh 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: Hee Oh is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1969 births, 20th-century American mathematicians, 20th-century American women mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Hee Oh 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 Hee Oh in 20 minutes

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

Frequently asked questions

What is Hee Oh in simple terms?

Why does Hee Oh 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 Hee Oh?

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 Hee Oh.