Victoria Powers
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Victoria Ann Powers (1958 – February 2, 2025) was an American mathematician specializing in
algebraic geometry Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometry, geometrical problems. Classically, it studies zero of a function, zeros of multivariate polynomials; th ...
and known for her work on
positive polynomial In mathematics, a positive polynomial (respectively non-negative polynomial) on a particular set is a polynomial whose values are positive (respectively non-negative) on that set. Precisely, Let p be a polynomial in n variables with real coefficie ...
s and on the mathematics of
electoral system An electoral or voting system is a set of rules used to determine the results of an election. Electoral systems are used in politics to elect governments, while non-political elections may take place in business, nonprofit organizations and inf ...
s. She was a professor in the department of mathematics at
Emory University Emory University is a private university, private research university in Atlanta, Georgia, United States. It was founded in 1836 as Emory College by the Methodist Episcopal Church and named in honor of Methodist bishop John Emory. Its main campu ...
, where she worked starting in 1987. Powers was the author of the book ''Certificates of Positivity for Real Polynomials—Theory, Practice, and Applications'' (Springer, 2021). A review on
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 ...
said that "In the reviewer's opinion this is a very nice and concise presentation of the most important pillars of real algebra up to the present time".


Life and career

Powers graduated from the
University of Chicago The University of Chicago (UChicago, Chicago, or UChi) is a Private university, private research university in Chicago, Illinois, United States. Its main campus is in the Hyde Park, Chicago, Hyde Park neighborhood on Chicago's South Side, Chic ...
in 1980, with a bachelor's degree in mathematics. She completed her Ph.D. in 1985 at
Cornell University Cornell University is a Private university, private Ivy League research university based in Ithaca, New York, United States. The university was co-founded by American philanthropist Ezra Cornell and historian and educator Andrew Dickson W ...
. Her dissertation, ''Finite Constructable Spaces of Signatures'', was supervised by
Alex F. T. W. Rosenberg Alex F. T. W. Rosenberg (1926–2007) was a German-American mathematician who served as the editor of the ''Proceedings of the American Mathematical Society'' from 1960 to 1965, and of the ''American Mathematical Monthly'' from 1974 to 1976.. H ...
. After completing her doctorate, she joined the faculty at the
University of Hawaiʻi The University of Hawaiʻi System is a public college and university system in Hawaii. The system confers associate, bachelor's, master's, and doctoral degrees through three universities, seven community colleges, an employment training center, ...
, but moved to Emory University only two years later, in 1987. She was on leave from Emory as a Humboldt Fellow and Alexander von Humboldt research professor at the
University of Regensburg The University of Regensburg () is a public research university located in the city of Regensburg, Germany. The university was founded on 18 July 1962 by the Landtag of Bavaria as the fourth full-fledged university in Bavaria. Following groundbr ...
in 1991–1992, as a visiting professor at the
Complutense University of Madrid The Complutense University of Madrid (, UCM; ) is a public research university located in Madrid. Founded in Alcalá in 1293 (before relocating to Madrid in 1836), it is one of the oldest operating universities in the world, and one of Spain's ...
in 2002–2003, and as a program officer at the
National Science Foundation The U.S. National Science Foundation (NSF) is an Independent agencies of the United States government#Examples of independent agencies, independent agency of the Federal government of the United States, United States federal government that su ...
in 2013–2015. From 2012 to 2014, Powers served as a Council Member at Large for 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, ...
. Powers' work moved from abstract
real algebraic geometry In mathematics, real algebraic geometry is the sub-branch of algebraic geometry studying real algebraic sets, i.e. real-number solutions to algebraic equations with real-number coefficients, and mappings between them (in particular real polynomi ...
to more concrete questions related to positive polynomials in one and several variables and
voting theory Social choice theory is a branch of welfare economics that extends the theory of rational choice to collective decision-making. Social choice studies the behavior of different mathematical procedures ( social welfare functions) used to combine i ...
. Her collaborators included Bruce Reznick,
Eberhard Becker Eberhard Becker (born July 23, 1943 in Stavenhagen) is a German mathematician whose career was spent at the University of Dortmund. A very active researcher in algebra, he later became rector of the university there. During his term as rector, ...
, Mari Castle, Claus Scheiderer and Thorsten Wormann. Powers was married to
Colm Mulcahy Colm Mulcahy (born September 1958) is an Irish mathematician, academic, columnist, book author, public outreach speaker, amateur magician and Professor Emeritus at Spelman College. In addition to algebra, number theory, and geometry, his interes ...
, an Irish mathematician who had the same doctoral advisor. On February 2, 2025, she died at home from complications of
ALS Amyotrophic lateral sclerosis (ALS), also known as motor neuron disease (MND) or—in the United States—Lou Gehrig's disease (LGD), is a rare, terminal neurodegenerative disorder that results in the progressive loss of both upper and low ...
.


Selected papers

* 1988 "Higher level reduced Witt rings of
skew field In algebra, a division ring, also called a skew field (or, occasionally, a sfield), is a nontrivial ring in which division by nonzero elements is defined. Specifically, it is a nontrivial ring in which every nonzero element has a multiplicative ...
s", Math Z., vol. 198, no.4, 545–554. * 1991 "Holomorphy rings and higher level orders on skew fields", J. Algebra, vol. 136, no.1, 51-59. * 1996 (with
Eberhard Becker Eberhard Becker (born July 23, 1943 in Stavenhagen) is a German mathematician whose career was spent at the University of Dortmund. A very active researcher in algebra, he later became rector of the university there. During his term as rector, ...
) "Sums of powers in rings and the real holomorphy ring", J. Reine Angew. Math., vol 480, 71-103. * 1996 " Hilbert's 17th problem and the champagne problem", Amer. Math. Monthly, vol. 103, no.10, 879-887. * 1998 (with Thorsten Wormann) "An algorithm for sums of squares of
real polynomial In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer ...
s", J. Pure Appl. Algebra, vol. 127, no.1, 99-104. * 2000 (with Bruce Reznick) "Polynomials that are positive on an interval", Trans. Amer. Math. Soc., vol. 352, no. 10, 4677-4692. * 2000 (with Bruce Reznick) "Notes towards a constructive proof of Hilbert's theorem on
ternary quartic In mathematics, a ternary quartic form is a degree 4 homogeneous polynomial in three variables. Hilbert's theorem showed that a positive semi-definite ternary quartic form over the reals can be written as a sum of three squares of quadratic form ...
s",
Quadratic form In mathematics, a quadratic form is a polynomial with terms all of degree two (" form" is another name for a homogeneous polynomial). For example, 4x^2 + 2xy - 3y^2 is a quadratic form in the variables and . The coefficients usually belong t ...
s and their applications (Dublin 1999), Contemp. Math. vol. 272, 209-227. * 2001 (with Claus Scheiderer) "The moment problem for non-compact semialgebraic sets.", Adv. Geom, vol.1, 71-88 * 2001 (with Bruce Reznick) "A new bound for Polya's theorem with applications to polynomials positive on polyhedra", J. Pure Appl. Algebra, vol.164, no. 1-2, 221-229. * 2004 (with Bruce Reznick, Claus Scheiderer, and Frank Sottile) "A new approach to Hilbert's theorem on ternary quartics", C. R. Acad. Sci. Paris, vol. 339, no.9, 617-620. * 2007 (with James Demmel and Jiawang Nie) "Representations of
positive polynomial In mathematics, a positive polynomial (respectively non-negative polynomial) on a particular set is a polynomial whose values are positive (respectively non-negative) on that set. Precisely, Let p be a polynomial in n variables with real coefficie ...
s on
noncompact In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space. The idea is that a compact space has no "punctures" or "missing endpoints", i.e., it ...
semialgebraic set In mathematics, a basic semialgebraic set is a set defined by polynomial equalities and polynomial inequalities, and a semialgebraic set is a finite union of basic semialgebraic sets. A semialgebraic function is a function with a semialgebraic gr ...
s via KKT ideals." J. Pure Appl. Algebra, vol. 209, no.1, 189-200. * 2017 "Positive polynomials and sums of squares: theory and practice"
Real algebraic geometry In mathematics, real algebraic geometry is the sub-branch of algebraic geometry studying real algebraic sets, i.e. real-number solutions to algebraic equations with real-number coefficients, and mappings between them (in particular real polynomi ...
, Panor. Syntheses, vol. 51, 155-180. * 2019 "Power index rankings in bicameral legislatures and the US legislative system., Soc. Choice, Welf. vol. 53, no. 2, 179-196. * 2024 Chapter "Who's Got the Power? Measuring Power in the US Legislative System" in book ''Teaching Mathematics through Cross-Curricular Projects'', MAA Press, 2024


Awards

In May 2024, Powers was the recipient of Emory University's George P. Cuttino Award for mentoring.Vicki Powers named Cuttino Award recipient for outstanding mentorship
By Senta Scarborough May 10, 2024, Emory University New Center


References


External links


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{{DEFAULTSORT:Powers, Victoria 1958 births 2025 deaths 20th-century American mathematicians 21st-century American mathematicians Algebraic geometers University of Chicago alumni Cornell University alumni University of Hawaiʻi faculty Emory University faculty 20th-century American women mathematicians 21st-century American women mathematicians Deaths from motor neuron disease in the United States