mathematics

Pham Huu Tiep

Pham Huu Tiep 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 Pham Huu Tiep rather than just read about it. In short: Pham Huu Tiep (Vietnamese: Phạm Hữu Tiệp) is a Vietnamese-American mathematician specializing in group theory and representation theory. He is currently a Joshua Barlaz Distinguished Professor of Mathematics at Rutgers University.

Key takeaways

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

Reference excerpt

Pham Huu Tiep (Vietnamese: Phạm Hữu Tiệp) is a Vietnamese-American mathematician specializing in group theory and representation theory. He is currently a Joshua Barlaz Distinguished Professor of Mathematics at Rutgers University. Pham Tiep graduated from Chu Văn An High School, and received a silver medal at the IMO in London in 1979. He received his Ph.D. at Moscow University in 1988 under supervision of Alexei Kostrikin. He gave an invited talk at the International Congress of Mathematicians in Rio de Janeiro in 2018. He is a Fellow of the American Mathematical Society, a Clay Institute Senior Scholar, and a Simons Fellow. Pham was the fifth Vietnamese mathematician invited to speak at the International Congress of Mathematicians, following Frédéric Pham (1970), Duong Hong Phong (1994), Ngô Bảo Châu (2006,2010) and Van H. Vu (2014). Pham was a member of the 2010 collaboration which completed the proof of Ore's conjecture. In a September 2024 paper, Pham, along with Gunter Malle, Gabriel Navarro and Amanda Schaeffer Fry, proved Brauer's height zero conjecture on the modular representation theory of Brauer blocks and their defect groups. Also in 2024, Pham, along with Michael Larsen and others, derived uniform character bounds for various finite classical groups, leading to substantial progress on Thompson's conjecture that each finite non-abelian simple group G = C 2 {\displaystyle G=C^{2}} for some conjugacy class C ⊆ G {\displaystyle C\subseteq G} .

Selected papers 2018: "Character bounds for finite groups of Lie type", Acta Math. 221 (2018), 1 – 57 (with Roman Bezrukavnikov, Martin Liebeck, and Aner Shalev) 2016: Huu Tiep, Pham (2016). "The α {\displaystyle \alpha } -invariant and Thompson's conjecture". Forum of Mathematics, Pi. 4. doi:10.1017/fmp.2016.3. ISSN 2050-5086. e5, 28 pages 2013: "Characters of relative p'-degree over normal subgroups", Ann. of Math. 178 (2013), 1135 – 1171 (with Gabriel Navarro) 2011: "Waring problem for finite simple groups", Ann. of Math. 174 (2011), 1885 – 1950 (with Michael Larsen and Aner Shalev) 2011: "A reduction theorem for the Alperin weight conjecture", Invent. Math. 184 (2011), 529 – 565 (with Gabriel Navarro) 2010: "The Ore conjecture", Journal of the European Mathematical Society (with Martin Liebeck, EA O'Brien, Aner Shalev) 2008: "Symmetric powers and a problem of Kollar and Larsen", Invent. Math. 174 (2008), 505 – 554 (with Robert M. Guralnick)

References

External links Pham Tiep's Rutgers web page Pham Huu Tiep's page at Clay Institute

Illustrations

Worked examples

Example 1 — a first encounter with Pham Huu Tiep

Start with the simplest possible case. Write down what Pham Huu Tiep 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 Pham Huu Tiep 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 Pham Huu Tiep 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 Pham Huu Tiep

In research: Pham Huu Tiep 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 Pham Huu Tiep 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: Pham Huu Tiep is common in secondary-school and first-year university syllabi. It links to neighbouring topics 20th-century Vietnamese mathematicians, 21st-century American mathematicians, Academics from Hanoi, so understanding it makes those chapters shorter.
In everyday life: Look for Pham Huu Tiep 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 Pham Huu Tiep in 20 minutes

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

Frequently asked questions

What is Pham Huu Tiep in simple terms?

Why does Pham Huu Tiep 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 Pham Huu Tiep?

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 Pham Huu Tiep.