mathematics

Michael Handel

Michael Handel 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 Michael Handel rather than just read about it. In short: Michael Handel is an American mathematician known for his work in Geometric group theory. He is a professor in the Department of Mathematics at Lehman College of the City University of New York and a professor of mathematics at the CUNY Graduate Center.

Key takeaways

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

Reference excerpt

Michael Handel is an American mathematician known for his work in Geometric group theory. He is a professor in the Department of Mathematics at Lehman College of the City University of New York and a professor of mathematics at the CUNY Graduate Center.

Career Michael Handel graduated with a B.A. in mathematics from Brandeis University in 1971. He received his Ph.D. from University of California, Berkeley, in 1975 under the supervision of Robion Kirby. From 1975 to 1978, he was an instructor at Princeton University. He joined the faculty of Michigan State University as an assistant professor in 1978, and was promoted to associate professor in 1983. Handel was a visiting scholar at the Institute for Advanced Study from 1978 to 1979, and again from 1987 to 1988. In 1990, he joined the Mathematics Department at Lehman College. Handel is best known for developing the Train track map method in Geometric group theory in collaboration with Mladen Bestvina in 1992. Bestvina, Feighn and Handel later proved that the group Out(Fn) satisfies the Tits alternative, settling a long-standing open problem.

Awards and honors In 1984, Handel won a Sloan Research Fellowship. In 2014, he became a fellow of the American Mathematical Society.

Selected publications Handel, Michael. "One Dimensional Minimal Sets and the Seifert Conjecture ". Annals of Mathematics (2) 111 (1980), number 1, pages 35–66. DOI:10.2307/1971216 Feighn, Mark; Handel, Michael. "Mapping tori of free group automorphisms are coherent". Annals of Mathematics (2) 149 (1999), number 3, pages 1061–1077. MR 1709311 Bestvina, Mladen; Feighn, Mark; Handel, Michael. The Tits alternative for Out(Fn). I. Dynamics of exponentially-growing automorphisms. Annals of Mathematics (2), volume 151 (2000), number 2, pages 517–623 Bestvina, Mladen; Feighn, Mark; Handel, Michael. The Tits alternative for Out(Fn). II. A Kolchin type theorem. Annals of Mathematics (2), volume 161 (2005), number 1, pages 1–59 MR 2150382 Handel, Michael; Mosher, Lee. "The free splitting complex of a free group, I: hyperbolicity". Geometry & Topology 17 (2013), number 3, pages 1581–1672. MR 3073931

See also Out(Fn) Train track map Pseudo-Anosov map

References

External links Department of Mathematics - Faculty - Lehman College Instituto de Matemática Interdisciplinar

Worked examples

Example 1 — a first encounter with Michael Handel

Start with the simplest possible case. Write down what Michael Handel 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 Michael Handel 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 Michael Handel 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 Michael Handel

In research: Michael Handel 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 Michael Handel 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: Michael Handel is common in secondary-school and first-year university syllabi. It links to neighbouring topics 20th-century American mathematicians, 21st-century American mathematicians, CUNY Graduate Center faculty, so understanding it makes those chapters shorter.
In everyday life: Look for Michael Handel 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 Michael Handel in 20 minutes

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

Frequently asked questions

What is Michael Handel in simple terms?

Why does Michael Handel 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 Michael Handel?

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 Michael Handel.