mathematics

Martin Liebeck

Martin Liebeck 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 Martin Liebeck rather than just read about it. In short: Martin Liebeck (born 23 September 1954) is a professor of Pure Mathematics at Imperial College London whose research interests include group theory and algebraic combinatorics. Career and research Martin Liebeck studied mathematics at the University of Oxford earning a First Class BA in 1976, an MSc in 1977, and a D.Phil. in 1979, with the Dissertation Finite Permutation Groups under Peter M.

Key takeaways

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

Reference excerpt

Martin Liebeck (born 23 September 1954) is a professor of Pure Mathematics at Imperial College London whose research interests include group theory and algebraic combinatorics.

Career and research Martin Liebeck studied mathematics at the University of Oxford earning a First Class BA in 1976, an MSc in 1977, and a D.Phil. in 1979, with the Dissertation Finite Permutation Groups under Peter M. Neumann. In January 1991 he was appointed Professor at Imperial College London and became Head of the Pure Mathematics section there in 1997. Liebeck has published over 150 research articles and 10 books. His research interests include algebraic combinatorics, algebraic groups, permutation groups, and finite simple groups. He was elected Fellow of the American Mathematical Society (AMS) in 2019, and was awarded the London Mathematical Society’s Pólya Prize in 2020. In February of 2020 he and Colva Roney-Dougal organized a programme titled "Groups, Representations and Applications" at the Isaac Newton Institute for Mathematical Sciences.

Personal life Martin is the son of mathematician Hans Liebeck and mathematics educationalist Pamela Liebeck. His wife Ann is a professional musician, and they have two sons Jonathan and Matthew. Martin's main hobbies are playing tennis, especially doubles, and the violin, particularly chamber music.

Selected publications

Papers 1990: "The maximal factorizations of the finite simple groups and their automorphism groups", Memoirs Amer. Math. Soc. 86, pp. 1–151 (with C.E. Praeger and Jan Saxl) 1995: "The probability of generating a finite simple group", Geom. Dedicata 56, 103-113 (with A. Shalev) 1998: "On the subgroup structure of classical groups", Invent. Math. 134, 427-453 (with G.M. Seitz) 1999: "Simple groups, permutation groups, and probability", J. Amer. Math. Soc. 12, 497-520 (with A. Shalev) 2001: "Diameters of finite simple groups: sharp bounds and applications", Annals of Math. 154, 383-406 (with A. Shalev) 2004: "The maximal subgroups of positive dimension in exceptional algebraic groups", Memoirs Amer. Math. Soc. 169, no. 802, pp. 1–227 (with G.M. Seitz) 2010: "The Ore Conjecture", J. European Math. Soc., 12, 939–1008 (with E. O’Brien, A. Shalev, P. Tiep) 2018: "Character bounds for finite groups of Lie type", Acta Math. 221, 1–57 (with R. Bezrukavnikov, A. Shalev and P. Tiep) 2019: "Algorithms determining finite simple images of finitely presented groups", Inventiones Math. 218, 623–648 (with M. Bridson, D.M. Evans and D. Segal)

Books 1990: The Subgroup Structure of the Finite Classical Groups, London Math. Soc. Lecture Note Series No. 129, Cambridge Univ. Press, 303pp. (with P. Kleidman) 2000: A Concise Introduction to Pure Mathematics, CRC Press, 2000; Second Edition, 2005; Third Edition, 2010; Fourth Edition, 2015 2012: Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras, Math. Surveys and Monographs Series, Vol. 180, American Math. Soc., 380pp. (with G.M. Seitz)

Awards and distinctions Johnson University Prize, Oxford University, 1979 Senior Mathematical Prize, Oxford University, 1979 ISI Highly Cited Researcher, 2011 Simons Research Professor, MSRI 2018 The President's Award for Excellence in Leadership, 2019 Fellow of the American Mathematical Society, 2019 London Mathematical Society (LMS) Pólya Prize in 2020

See also O'Nan–Scott theorem Rank 3 permutation group

References

External links Martin Liebeck at the Mathematics Genealogy Project Personal web page

Illustrations

Worked examples

Example 1 — a first encounter with Martin Liebeck

Start with the simplest possible case. Write down what Martin Liebeck 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 Martin Liebeck 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 Martin Liebeck 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 Martin Liebeck

In research: Martin Liebeck 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 Martin Liebeck 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: Martin Liebeck is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1954 births, 20th-century British mathematicians, 21st-century British mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Martin Liebeck 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 Martin Liebeck in 20 minutes

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

Frequently asked questions

What is Martin Liebeck in simple terms?

Martin Liebeck (born 23 September 1954) is a professor of Pure Mathematics at Imperial College London whose research interests include group theory and algebraic combinatorics. Career and research Martin Liebeck studied mathematics at the University of Oxford earning a First Class BA in 1976, an MS…

Why does Martin Liebeck 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 Martin Liebeck?

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 Martin Liebeck.