Robert Wolfe Brooks (Washington, D.C., September 16, 1952 – Montreal, September 5, 2002) was a

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

known for his work in

spectral geometry Spectral geometry is a field in mathematics which concerns relationships between geometric structures of manifolds and spectra of canonically defined differential operators. The case of the Laplace–Beltrami operator on a closed Riemannian manifo ...

Riemann surfaces In mathematics, particularly in complex analysis, a Riemann surface is a connected one-dimensional complex manifold. These surfaces were first studied by and are named after Bernhard Riemann. Riemann surfaces can be thought of as deformed vers ...

circle packing In geometry, circle packing is the study of the arrangement of circles (of equal or varying sizes) on a given surface such that no overlapping occurs and so that no circle can be enlarged without creating an overlap. The associated ''packing den ...

s, and

differential geometry Differential geometry is a Mathematics, mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of Calculus, single variable calculus, vector calculus, lin ...

Biography

Brooks was born in 1952 in

Washington, D.C. Washington, D.C., formally the District of Columbia and commonly known as Washington or D.C., is the capital city and federal district of the United States. The city is on the Potomac River, across from Virginia, and shares land borders with ...

and grew up in

Bethesda, Maryland Bethesda () is an unincorporated, census-designated place in southern Montgomery County, Maryland, United States. Located just northwest of Washington, D.C., it is a major business and government center of the Washington metropolitan region ...

, where he graduated in 1970 from Walt Whitman High School. In 1974 he completed his Masters thesis from

Harvard University Harvard University is a Private university, private Ivy League research university in Cambridge, Massachusetts, United States. Founded in 1636 and named for its first benefactor, the History of the Puritans in North America, Puritan clergyma ...

; his thesis "

Russell Russell may refer to: People * Russell (given name) * Russell (surname) * Lady Russell (disambiguation) * Lord Russell (disambiguation) ** Bertrand Russell *Justice Russell (disambiguation) Places *Russell Island (disambiguation) *Mount Russel ...

Poincaré Poincaré is a French surname. Notable people with the surname include: * Henri Poincaré Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, Theoretical physics, theoretical physicist, engineer, and philos ...

, and the foundations of geometry" won him the

Bowdoin Prize The Bowdoin Prizes are prestigious awards given annually to Harvard University undergraduate and graduate students. From the income of the bequest of Governor James Bowdoin, AB 1745, prizes are offered to students at the university in graduate an ...

for Essays in the Natural Sciences in 1975. He received his

Ph.D. A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...

from Harvard University in 1977; his thesis, ''The smooth cohomology of groups of diffeomorphisms'', was written under the supervision of

Raoul Bott Raoul Bott (September 24, 1923 – December 20, 2005) was a Hungarian-American mathematician known for numerous foundational contributions to geometry in its broad sense. He is best known for his Bott periodicity theorem, the Morse–Bott function ...

. He then undertook postdoctoral studies with J. Peter Matelski at the

State University of New York at Stony Brook Stony Brook University (SBU), officially the State University of New York at Stony Brook, is a public university, public research university in Stony Brook, New York, United States, on Long Island. Along with the University at Buffalo, it is on ...

, where they created pictures of fractals, leading to

Benoit Mandelbrot Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of phy ...

's creation of the

Mandelbrot set The Mandelbrot set () is a two-dimensional set (mathematics), set that is defined in the complex plane as the complex numbers c for which the function f_c(z)=z^2+c does not Stability theory, diverge to infinity when Iteration, iterated starting ...

in 1980. He worked at the

University of Maryland The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public land-grant research university in College Park, Maryland, United States. Founded in 1856, UMD is the flagship institution of the Univ ...

(1979–1984), then at the

University of Southern California The University of Southern California (USC, SC, or Southern Cal) is a Private university, private research university in Los Angeles, California, United States. Founded in 1880 by Robert M. Widney, it is the oldest private research university in ...

, and then, from 1995, at the Technion in

Haifa Haifa ( ; , ; ) is the List of cities in Israel, third-largest city in Israel—after Jerusalem and Tel Aviv—with a population of in . The city of Haifa forms part of the Haifa metropolitan area, the third-most populous metropolitan area i ...

. Brooks died from

heart attack A myocardial infarction (MI), commonly known as a heart attack, occurs when Ischemia, blood flow decreases or stops in one of the coronary arteries of the heart, causing infarction (tissue death) to the heart muscle. The most common symptom ...

during a visit to

Montreal, Canada Montreal is the largest city in the province of Quebec, the second-largest in Canada, and the ninth-largest in North America. It was founded in 1642 as '' Ville-Marie'', or "City of Mary", and is now named after Mount Royal, the triple-pe ...

and was buried in Sde Yehoshua cemetery in Haifa. He was survived by his parents David and Harriet Brooks, his wife Sharon and four children. His eldest son Shimon Brooks is a mathematics professor at

Bar-Ilan University Bar-Ilan University (BIU, , ''Universitat Bar-Ilan'') is a public research university in the Tel Aviv District city of Ramat Gan, Israel. Established in 1955, Bar Ilan is Israel's second-largest academic university institution. It has 20,000 ...

Work

In an influential paper , Brooks proved that the bounded cohomology of a

topological space In mathematics, a topological space is, roughly speaking, a Geometry, geometrical space in which Closeness (mathematics), closeness is defined but cannot necessarily be measured by a numeric Distance (mathematics), distance. More specifically, a to ...

isomorphic In mathematics, an isomorphism is a structure-preserving mapping or morphism between two structures of the same type that can be reversed by an inverse mapping. Two mathematical structures are isomorphic if an isomorphism exists between the ...

to the bounded cohomology of its

fundamental group In the mathematics, mathematical field of algebraic topology, the fundamental group of a topological space is the group (mathematics), group of the equivalence classes under homotopy of the Loop (topology), loops contained in the space. It record ...

Honors

for Essays in the Natural Sciences, 1975 *

Alfred P. Sloan Alfred Pritchard Sloan Jr. ( ; May 23, 1875February 17, 1966) was an American business executive in the automotive industry. He was a longtime president, chairman and CEO of General Motors Corporation. First as a senior executive and later as ...

fellowship * Guastella fellowship

Selected publications

* * * * ::Reviewer Maung Min-Oo for

MathSciNet MathSciNet is a searchable online bibliographic database created by the American Mathematical Society in 1996. It contains all of the contents of the journal ''Mathematical Reviews'' (MR) since 1940 along with an extensive author database, links ...

wrote: "This is a well written survey article on the construction of isospectral manifolds which are not isometric with emphasis on hyperbolic Riemann surfaces of constant negative curvature." *Brooks, Robert, "Form in Topology", The Magicians of Form, ed. by Robert M. Weiss. Laurelhurst Publications, 2003.

References

External links

Memorial page (Technion)
* {{DEFAULTSORT:Brooks, Robert W. 1952 births 2002 deaths 20th-century American Jews 20th-century American mathematicians 21st-century American Jews 21st-century American mathematicians Academic staff of Technion – Israel Institute of Technology American emigrants to Israel American topologists Citizens of Israel through Law of Return Differential geometers Harvard Graduate School of Arts and Sciences alumni Israeli Jews Israeli mathematicians Mathematicians from Washington, D.C. Sloan Research Fellows University of Southern California faculty