mathematics

Roger Evans Howe

Roger Evans Howe 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 Roger Evans Howe rather than just read about it. In short: Roger Evans Howe (born May 23, 1945) is the William R. Kenan, Jr.

Key takeaways

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

Reference excerpt

Roger Evans Howe (born May 23, 1945) is the William R. Kenan, Jr. Professor Emeritus of Mathematics at Yale University, and Curtis D. Robert Endowed Chair in Mathematics Education at Texas A&M University. He is known for his contributions to representation theory, in particular for the notion of a reductive dual pair and the Howe correspondence, and his contributions to mathematics education.

Biography He attended Ithaca High School, then Harvard University as an undergraduate, becoming a Putnam Fellow in 1964. He obtained his Ph.D. from University of California, Berkeley, in 1969. His thesis, titled On representations of nilpotent groups, was written under the supervision of Calvin Moore. Between 1969 and 1974, Howe taught at the State University of New York in Stony Brook before joining the Yale faculty in 1974. His doctoral students include Ju-Lee Kim, Jian-Shu Li, Zeev Rudnick, Eng-Chye Tan, and Chen-Bo Zhu. He moved to Texas A&M University in 2015. He has been a fellow of the American Academy of Arts and Sciences since 1993, and a member of the National Academy of Sciences since 1994. Howe received a Lester R. Ford Award in 1984. In 2006 he was awarded the American Mathematical Society Distinguished Public Service Award in recognition of his "multifaceted contributions to mathematics and to mathematics education." In 2012 he became a fellow of the American Mathematical Society. In 2015 he received Texas A&M University's inaugural Award for Excellence in Mathematics Education. In 2022, he received the Mary P. Dolciani Award from the Mathematical Association of America. A conference in his honor was held at the National University of Singapore in 2006, and at Yale University in 2015.

Selected works 1977: "Tamely ramified supercuspidal representations of G l n {\displaystyle Gl_{n}} ", Pacific Journal of Mathematics 73(2): 437–460. 1979: (with Calvin C. Moore) "Asymptotic properties of unitary representations", Journal of Functional Analysis 32(1): 72–96. 1979: "θ-series and invariant theory", in Automorphic forms, Representations and L-functions, Proceedings of Symposium on Pure Mathematics XXXIII, American Mathematical Society, pages 275–285. 1981: "Wave front sets of representations of Lie groups". Automorphic forms, Representation theory and Arithmetic (Bombay, 1979), pp. 117–140, Studies in Mathematics 10, Tata Institute of Fundamental Research 1982: "On a notion of rank for unitary representations of the classical groups". Harmonic analysis and group representations, 223–331, Liguori, Naples, 1982. Howe, Roger (1989), "Remarks on classical invariant theory", Transactions of the American Mathematical Society, 313 (2): 539–570, doi:10.2307/2001418, ISSN 0002-9947, JSTOR 2001418, MR 0986027 Howe, Roger (1989), "Transcending classical invariant theory", Journal of the American Mathematical Society, 2 (3): 535–552, doi:10.1090/S0894-0347-1989-0985172-6 1995: "Perspectives on invariant theory: Schur duality, multiplicity-free actions and beyond". The Schur lectures (1992) (Tel Aviv), 1–182, Israel Math. Conf. Proc., 8, Bar-Ilan University, Ramat Gan. 1992: (with Eng-Chye Tan) "Nonabelian harmonic analysis. Applications of SL(2,R)". Universitext. Springer-Verlag, ISBN 0-387-97768-6. 2007: (with William Barker) Continuous Symmetry: From Euclid to Klein, American Mathematical Society, ISBN 978-0-8218-3900-3. Robin Hartshorne (2011) Review of Continuous Symmetry, American Mathematical Monthly 118:565–8.

Illustrations

Worked examples

Example 1 — a first encounter with Roger Evans Howe

Start with the simplest possible case. Write down what Roger Evans Howe 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 Roger Evans Howe 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 Roger Evans Howe 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 Roger Evans Howe

In research: Roger Evans Howe 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 Roger Evans Howe 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: Roger Evans Howe is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1945 births, 20th-century American mathematicians, 21st-century American mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Roger Evans Howe 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 Roger Evans Howe in 20 minutes

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

Frequently asked questions

What is Roger Evans Howe in simple terms?

Roger Evans Howe (born May 23, 1945) is the William R. Kenan, Jr.

Why does Roger Evans Howe 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 Roger Evans Howe?

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 Roger Evans Howe.