mathematics

He Xuhua

He Xuhua 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 He Xuhua rather than just read about it. In short: Xuhua He (Chinese: 何旭华; pinyin: Hé Xùhuá, born 1979) is a Chinese mathematician. He is a Chair Professor of Mathematics at the University of Hong Kong and has been the President of the Hong Kong Mathematical Society since 2024, serving consecutive terms for 2024–2026 and 2026–2028.

Key takeaways

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

Reference excerpt

Xuhua He (Chinese: 何旭华; pinyin: Hé Xùhuá, born 1979) is a Chinese mathematician. He is a Chair Professor of Mathematics at the University of Hong Kong and has been the President of the Hong Kong Mathematical Society since 2024, serving consecutive terms for 2024–2026 and 2026–2028. His research lies at the intersection of algebraic groups, representation theory, and arithmetic geometry.

Education and career In 2001, He graduated with a bachelor's degree in mathematics from Peking University. In 2005, he earned his PhD from the Massachusetts Institute of Technology (MIT) with the thesis Some subvarieties of the De Concini-Procesi compactification under advisor George Lusztig. As a postdoc research fellow, He was at the Institute for Advanced Study for the academic year 2005–2006 and Simons Instructor at the State University of New York at Stony Brook from 2006 to 2008. At Hong Kong University of Science and Technology he was an assistant professor from 2008 to 2012 and an associate professor from 2012 to 2014. From 2014 to 2019 he was a professor at the University of Maryland. In 2019 he became the Choh-Ming Li Professor of Mathematics at the Chinese University of Hong Kong and joined the University of Hong Kong as a Chair Professor in 2023. For the 2016–2017 academic year, He was a von Neumann Fellow at the Institute for Advanced Study. In 2017 he was a Simons Visiting Professor at the Université Sorbonne Paris Nord (Paris 13 University).

Awards and honors 2026 – Member of the Hong Kong Academy of Sciences. 2025 – Fellow of the American Mathematical Society. 2023 – New Cornerstone Investigator. 2022 – Chevalley Prize in Lie Theory (American Mathematical Society). 2020 – Xplorer Prize in Mathematics and Physics. 2018 – Invited sectional speaker at the International Congress of Mathematicians (ICM) in Rio de Janeiro. 2015 – Invited speaker at the Current Developments in Mathematics (CDM) conference at Harvard University and MIT. 2013 – Morningside Gold Medal at the International Congress of Chinese Mathematicians. 1996 – Gold medal at the International Mathematical Olympiad.

Selected publications A. J. de Jong, X. He and J. Starr, "Families of rationally simply connected varieties over surfaces and torsors for semisimple groups", Publications Mathématiques de l'IHÉS 114 (2011), 1–85. X. He and G. Lusztig, "A generalization of Steinberg's cross-section", Journal of the American Mathematical Society 25 (2012), 739–757. X. He, "Geometric and homological properties of affine Deligne–Lusztig varieties", Annals of Mathematics (2) 179 (2014), 367–404. X. He and S. Nie, "Minimal length elements of extended affine Weyl group", Compositio Mathematica 150 (2014), 1903–1927. X. He, "Cocenters of p-adic groups, I: Newton decomposition", Forum of Mathematics, Pi 6 (2018), e2. D. Ciubotaru and X. He, "Cocenters of p-adic groups, III: Elliptic cocenter and rigid cocenter", Peking Mathematical Journal 4 (2021), 159–186. U. Görtz, X. He and S. Nie, "Fully Hodge–Newton decomposable Shimura varieties", Peking Mathematical Journal 2 (2019), no. 2, 99–154. X. He and R. Zhou, "On the connected components of affine Deligne–Lusztig varieties", Duke Mathematical Journal 169 (2020), no. 14, 2697–2765. H. Bao and X. He, "Product structure and regularity theorem for totally nonnegative flag varieties", Inventiones Mathematicae 237 (2024), no. 1, 1–47. B. Dong, X. He, P. Jin, F. Schremmer, Q. Yu, "Machine learning assisted exploration for affine Deligne–Lusztig varieties", Peking Mathematical Journal 9 (2026), no. 1, 55–104.

References

External links "Xuhua He". Chinese University of Hong Kong. (with links to selected papers/preprints) "Xuhua He: Affine Hecke algebras and p-adic groups I". YouTube. Harvard Math. December 20, 2015. "Xuhua He: Affine Hecke algebras and p-adic groups II". YouTube. Harvard Math. December 20, 2015. "Basic loci of Shimura varieties – Xuhua He". YouTube. Institute for Advanced Study. April 7, 2019. "Some results on affine Deligne–Lusztig varieties – Xuhua He – ICM2018". YouTube. Rio ICM2018. October 3, 2018.

Illustrations

Worked examples

Example 1 — a first encounter with He Xuhua

Start with the simplest possible case. Write down what He Xuhua 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 He Xuhua 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 He Xuhua 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 He Xuhua

In research: He Xuhua 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 He Xuhua 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: He Xuhua is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1979 births, 20th-century Chinese mathematicians, 21st-century Chinese mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for He Xuhua 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 He Xuhua in 20 minutes

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

Frequently asked questions

What is He Xuhua in simple terms?

Why does He Xuhua 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 He Xuhua?

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 He Xuhua.