# Benson, Dave 1955- (D.J. Benson, David J. Benson)

# Benson, Dave 1955- (D.J. Benson, David J. Benson)

## PERSONAL:

Born December 3, 1955. *Education:* Trinity College, 1974-81 (honors with distinction, 1978), Ph.D., 1981.

## ADDRESSES:

*Office—*Department of Mathematics, Meston Bldg., King's College, University of Aberdeen, Aberdeen AB24 3UE, Scotland.

## CAREER:

Yale University, New Haven, CT, Gibbs instructor, 1982-84; Northwestern University, Evanston, IL, assistant professor, 1984-86; University of Oxford, Oxford, England, lecturer and fellow of Wolfson College, 1986-93; University of Georgia, Athens, visiting associate professor, 1993-94, professor, 1994-2000, distinguished research professor, 2000-05; University of Aberdeen, Aberdeen, Scotland, Sixth Century Chair of pure mathematics, 2005—. Visiting professorships, including the University of Minnesota, Minneapolis, 1991; Bernoulli Centre, Lausanne, Switzerland, 2005; and Paderborn University, Germany, 2005-08. Also Arhus Universitet, Denmark Royal Society exchange fellow, 1981-82.

## AWARDS, HONORS:

Yeats Mathematics Essay Prize, Trinity College, Cambridge, 1977; Raleigh Prize, Trinity College, Cambridge, 1980; Junior Whitehead Prize, London Mathematical Society, 1993; Creative Research Medal, University of Georgia, 1998; Sandy Beaver Teaching Award, University of Georgia, 2003; Creative Research Award, University of Georgia, 2004; Humboldt Research Award for Senior U.S. Scientists, Germany, 2004; Simons Professorship for the MSRI representation theory program, 2008. Recipient of grants, including grants from the National Science Foundation.

## WRITINGS:

(As D.J. Benson) *Representations and Cohomology,* Volume 1: *Basic Representation Theory of Finite Groups and Associative Algebras,* and Volume 2: *Cohomology of Groups and Modules,* Cambridge University Press (New York, NY), 1991.

(As D.J. Benson, with F.R. Cohen) *Mapping Class Groups of Low Genus and Their Cohomology,* American Mathematical Society (Providence, RI), 1991.

(As D.J. Benson) *Polynomial Invariants of Finite Groups,* Cambridge University Press (New York, NY), 1993.

*Music: A Mathematical Offering,* Cambridge University Press (New York, NY), 2007.

(As David J. Benson, with Stephen D. Smith) *Classifying Spaces of Sporadic Groups,* American Mathematical Society (Providence, RI), 2008.

Contributor to books, including *Lecture Notes in Mathematics 190,* Cambridge University Press, 1993. Contributor to periodicals, including *Memoirs of the American Mathematical Society, Algebra 11, Journal of Algebra, Journal of Pure & Applied Algebra, Pure Math, Bulletin of the London Mathematical Society, Quarterly Journal of Mathematics, Topology, New York Journal of Mathematics, Bulletin of the American Mathematical Society,* and *Algebras and Representation Theory.*

Editor of the book series "London Mathematical Society Student Texts," published by the Cambridge University Press. Member of editorial boards, including the *Electronic Research Announcements of the American Mathematical Society,* 1999-2005; *Advances in Mathematics,* 2001—; *Bulletin of the American**Mathematical Society,* 2005—; *Bulletin of the American Mathematical Society,* 2005—; and *Algebra and Number Theory,* 2006—.

## SIDELIGHTS:

Dave Benson is a mathematician whose primary research interest is the cohomology of finite and compact Lie groups. His other scholarly interests include modular representation theory, algebraic topology, and invariant theory for finite groups. The fact that he is a Sixth Century Professor of mathematics at the University of Aberdeen, Benson notes on his home page, "doesn't mean, as some people seem to think, that I'm six centuries old. It means that the University of Aberdeen recently began its sixth century as an academic institution." Benson has received numerous awards for his work in mathematics, including a Yeats Mathematics Essay Prize from Trinity College at Cambridge University and the Junior Whitehead Prize from the London Mathematical Society.

Benson has written extensively for professional journals and is the author or editor of several books about mathematics. In *Music: A Mathematical Offering,* the author writes about the relationship between music and mathematics, addressing issues such as harmony and number theory as well as musical patterns and group theory. The author begins by discussing waves and music, the anatomy of the human ear, and their relationship to Fourier analysis. "The medium for the transmission of music is sound," Benson writes. "A proper understanding of music entails at least an elementary understanding of the nature of sound and how we perceive it."

The author goes on to discuss issues in physics, psychoacoustics, the history of science, and modern technology that makes digital recordings. His primary emphasis, however, is mathematics and music. The book's third chapter, "A Mathematician's Guide to the Orchestra," focuses on "discussing characteristic instrumental timbres in terms of their harmonic spectra," noted *American Scientist* contributor Peter Pesic. The author begins the chapter by noting: "Ethnomusicologists classify musical instruments into five main categories, which correspond reasonably well to the mathematical description of the sound they produce." He goes on to describe the categories, which are idophones, which produce sound via the vibration of the instruments body; membranophones, which use a stretched membrane to produce sound; chordophones, which use vibrating strings; aerophones, based on a vibrating column of air, and electrophones, which use electronic means to produce music.

In the following chapters, the author discusses consonance and dissonance, scales and temperaments, digital music, and symmetry in music. In the process, he looks at scale construction from the time of the Greeks through to the thirteen-tone Bohlen-Pierce scale developed in 1989, which is a scale that is not based around the interval of an octave. Writing about digital music, the author notes: "The commonest method of digital representation of sound is about as simple minded as you can get. To digitize an analog signal, the signal is sampled by a large number of times a second, and a binary number represents the height of the signal at each sample time. Both of these processes are sometimes referred to as *quantization.*"

Benson also provides guidance on further readings and listening, thus "giving his book an aural dimension that adds greatly to its interest," wrote Pesic. The book includes several appendixes, references, a bibliography, and an index. Noting that the author "has constructed the different sections that flow from his general introduction to be independent, allowing readers to follow their own interests and predilections," Pesic commented that Benson "has assembled a fascinating variety of topics that make his book a uniquely rich source, whether for classroom use, reference or self-study."

Benson is also author with Stephen D. Smith of *Classifying Spaces of Sporadic Groups.* Written for non-experts, the book provides a background in areas such as algebraic topology and local geometries from group theory. The authors then look at aspects of group cohomology and simplicial sets as they pertain to topological space. A *Sci-Tech Book News* contributor noted that the authors are "remarkably accessible at explaining sporadic groups."

## BIOGRAPHICAL AND CRITICAL SOURCES:

### BOOKS

Benson, Dave, *Music: A Mathematical Offering,* Cambridge University Press (New York, NY), 2007.

### PERIODICALS

*American Scientist,* July-August, 2007, Peter Pesic, "Harmonious Relations," review of *Music: A Mathematical Offering.*

*Bulletin of the American Mathematical Society (New Series),* October, 1993, J.E. Humphreys, review of *Representations and Cohomology,* Volume 2: *Cohomology of Groups and Modules,* p. 262.

*Choice,* December, 2007, D.V. Feldman, "Reviews," review of *Music,* p. 665.

*Mathematics,* June, 2007, Paul J. Campbell, "A Mathematical Offering," review of *Music,* p. 238.

*SciTech Book News,* October, 1991, review of *Mapping Class Groups of Low Genus and Their Cohomology,* p. 10; March, 1994, review of *Advanced Computational Methods for Material Modeling: Presented at the 1993 ASME Winter Annual Meeting, New Orleans, Louisiana, November 28-December 3, 1993,* p. 31; June, 2008, review of *Classifying Spaces of Sporadic Groups.*

### ONLINE

*University of Aberdeen Mathematics Department Web site,*http://www.maths.abdn.ac.uk/ (July 11, 2008), faculty profile.

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