Bruce Reznick (born February 3, 1953 in New York City) is an American mathematician long on the faculty at the

University of Illinois at Urbana–Champaign The University of Illinois Urbana-Champaign (U of I, Illinois, University of Illinois, or UIUC) is a public land-grant research university in Illinois in the twin cities of Champaign and Urbana. It is the flagship institution of the Unive ...

. He is a prolific researcher noted for his contributions to number theory and the combinatorial-algebraic-analytic investigations of

polynomial In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An ex ...

s.Biographical Sketch of Bruce Reznick
/ref> In July 2019, to mark his 66th birthday, a day long symposium "Bruce Reznick 66 fest: A

mensch ( yi, מענטש, ''mentsh'', from Middle High German , from Old High German ''mennisco''; akin to Old English ''human being'', ''man'') means "a person of integrity and honor". According to Leo Rosten, a is "someone to admire and emulate, so ...

of Combinatorial-Algebraic Mathematics" was held at the

University of Bern The University of Bern (german: Universität Bern, french: Université de Berne, la, Universitas Bernensis) is a university in the Swiss capital of Bern and was founded in 1834. It is regulated and financed by the Canton of Bern. It is a compreh ...

, Switzerland.

Education and career

Reznick got his B.S. in 1973 from the

California Institute of Technology The California Institute of Technology (branded as Caltech or CIT)The university itself only spells its short form as "Caltech"; the institution considers other spellings such a"Cal Tech" and "CalTech" incorrect. The institute is also occasional ...

and his Ph.D. in 1976 from Stanford University under

Per Enflo Per H. Enflo (; born 20 May 1944) is a Swedish mathematician working primarily in functional analysis, a field in which he solved problems that had been considered fundamental. Three of these problems had been open for more than forty years: * Th ...

for the thesi
"Banach Spaces Which Satisfy Linear Identities"
Bruce Arie Reznick
at the Mathematics Genealogy Project He was a

Sloan Fellow The Sloan Fellows program is the world's first mid-career and senior career master's degree in general management and leadership. It was initially supported by a grant from Alfred P. Sloan, the late CEO of General Motors, to his alma mater, MI ...

(1983–1986) and is a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings ...

(AMS). From 1983 to 1985 he was on the Putnam Competition Preparation Committee of the Mathematical Association of America (MAA). As an undergraduate he had been a member of the first place team in the Putnam Competition twice, also being ranked twice in the top ten as an individual Reznick is a frequent author on matters relating to teaching and mentoring, and the overall training of graduate students. He wrote the popular article "Chalking It Up: Advice to a New TA".

Research

Reznick has done a systematic analysis of the representation of real forms of even degree as sums of powers of linear forms. This work was described in his monograph ''Sum of Even Powers of Real Linear Forms'' (Memoirs of the American Mathematical Society, 1992) Reznick specializes in combinatorial methods in

algebra Algebra () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathem ...

analysis Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (3 ...

and

number theory Number theory (or arithmetic or higher arithmetic in older usage) is a branch of pure mathematics devoted primarily to the study of the integers and integer-valued functions. German mathematician Carl Friedrich Gauss (1777–1855) said, "Math ...

, often involving polynomials,

polytope In elementary geometry, a polytope is a geometric object with flat sides ('' faces''). Polytopes are the generalization of three-dimensional polyhedra to any number of dimensions. Polytopes may exist in any general number of dimensions as an ...

s and

integer sequence In mathematics, an integer sequence is a sequence (i.e., an ordered list) of integers. An integer sequence may be specified ''explicitly'' by giving a formula for its ''n''th term, or ''implicitly'' by giving a relationship between its terms. Fo ...

s.
The secret lives of polynomial identities
' Speaker Bruce Reznick, Claremont Center for the Mathematical Sciences, September 21, 2011 He is known for his contributions to the study of sums of squares and positivity of polynomials. In joint work with M.D. Choi and T. Y. Lam, he developed the

Gram matrix In linear algebra, the Gram matrix (or Gramian matrix, Gramian) of a set of vectors v_1,\dots, v_n in an inner product space is the Hermitian matrix of inner products, whose entries are given by the inner product G_ = \left\langle v_i, v_j \right\r ...

method for writing real polynomials as sums of squares; this method has important applications to other areas of mathematics including optimization.

Awards

* 2013 fellow of the

* 2008-2009 Campus Award for Excellence in Undergraduate Teaching in the University of Illinois at Urbana-Champaign * Reznick has an Erdős–Bacon number of 3 which puts him in a tie for the lead with MIT math professor

Daniel Kleitman Daniel J. Kleitman (born October 4, 1934)article availableon Douglas West's web page, University of Illinois at Urbana–Champaign)."Kleitman, Daniel J.," in: ''Who's Who in Frontier Science and Technology'', 1, 1984, p. 396. is an American mathe ...

.''Mulcahy, Colm
Centenary of Mathematician Paul Erdős -- Source of Bacon Number Concept
' Huffpost, December 6, 2017. Accessed November 14, 2022.

Selected publications

* * * * * * * * *

References

External links

*
Bruce Reznick's homepage
{{DEFAULTSORT:Reznick, Bruce 20th-century American mathematicians 21st-century American mathematicians Number theorists Combinatorialists Fellows of the American Mathematical Society Sloan Research Fellows University of Illinois Urbana-Champaign faculty California Institute of Technology alumni Stanford University alumni People from New York City 1953 births Living people