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. He is a prolific researcher[1] noted for his contributions to number theory and the combinatorial-algebraic-analytic investigations of polynomials.[2] In July 2019, to mark his 66th birthday, a day long symposium "Bruce Reznick 66 fest: A mensch of Combinatorial-Algebraic Mathematics" was held at the University of Bern, Switzerland.[3]
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".[5]
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)[6]
Reznick specializes in combinatorial methods in algebra, analysis and number theory, often involving polynomials, polytopes and integer sequences.[7] 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 method for writing real polynomials as sums of squares; this method has important applications to other areas of mathematics including optimization.[8]
Reznick, Bruce (1978). "Extremal PSD forms with few terms". Duke Mathematical Journal. 45 (2). doi:10.1215/S0012-7094-78-04519-2.
"The Pythagoras number of some affine algebras and local algebras". Journal für die reine und angewandte Mathematik (Crelle's Journal). 1982 (336): 45–82. 1982. doi:10.1515/crll.1982.336.45. MR0671321. S2CID116098763.
