# Trevor Wooley named the Andris A. Zoltners Distinguished Professor of Mathematics at Purdue University

**12-10-2019**

The Purdue University Board of Trustees on Friday, December 6, approved the appointments of Trevor Wooley as the Andris A. Zoltners Distinguished Professor of Mathematics.

Prior to joining Purdue University in August 2019, Professor Wooley was Professor of Mathematics at the University of Bristol, UK, where he served as Head of Pure Mathematics from 2015-16. Prior to that he was Professor of Mathematics at the University of Michigan, where he served as Department Chair from 2002 to 2005. In addition to these positions, he has held visiting positions at Princeton, Harvard, Cambridge, the Max Planck Institute in Bonn, and the Institute for Advanced Study in Princeton, among others.

Wooley has made fundamental contributions on a variety of topics related to number theory, most notably related to the Hardy-Littlewood circle method and Waring’s problem. Waring’s problem is a particular example of a Diophantine equation, which is a polynomial equation to be solved using only integers. Such equations influence the development of codes and cryptosystems for use in DVDs, in mobile phones, and in banking security. Key to their practical utility is the illusion of randomness; although deterministic in nature, the solutions of these equations in integers should appear randomly distributed to an outsider. One therefore seeks to provide assurance that hidden patterns underlying these solution sets do not unravel their usefulness. A significant portion of Wooley’s work has focused on the study of Diophantine equations using seemingly unrelated methods from Fourier analysis to make deep connections between harmonic analysis and number theory.

In one major direction of research, Wooley greatly improved the bounds on the number of summands required in Waring’s problem, which is concerned with the ways in which a positive integer can be written as the sum of the fewest possible number of *k*th powers of positive integers. Wooley developed a method called efficient differencing that reduced by a factor of two the relevant bound. This was the first significant progress in 30 years on this well-studied problem; this method led to further advances in related problems by many researchers. Some of the recognition he received for this research includes a 45-minute invited address at the 2002 International Congress of Mathematicians, election to the Fellowship of the Royal Society (the UK version of the National Academy of Sciences), the Salem Prize, and the Junior Berwick Prize of the London Mathematical Society.

In another direction, Wooley developed a method called efficient congruencing that provides bounds on certain sums of exponential functions. Special cases of such sums occur in Waring’s problem and in the analysis of the zero-free region of the Riemann zeta function. Wooley’s approach led eventually to a complete understanding of Vinogradov’s mean value theorem, settling conjectures originating in 1935. This theorem relates sums of fixed powers of integers to mean values of an associated sum of exponential functions. Wooley developed his method of proof over a period of years and received substantial recognition for his contributions in this area, including a second 45-minute invited lecture at the 2014 International Congress of Mathematicians, the Fröhlich Prize of the London Mathematical Society, and a 5-year European Research Council Advanced Grant of 1.9 million euros.

Wooley’s research accomplishments have been recognized in the US and abroad throughout his career. In addition to the distinctions indicated above, he has been supported by a Sloan Fellowship and a Packard Fellowship (given at that time to 20 scientists and engineers across the US, with roughly one per year to a mathematician), a Royal Society Wolfson Merit Award, and several NSF grants in the US. He has more than 140 publications in excellent journals and has a remarkably high profile in the mathematics community as indicated by his lectures at top universities and conferences throughout the world.

About the donor: The position of the Andris A. Zoltners Professorship is made possible in part by Andris A. Zoltners, Founder of ZS Associates, who is Frederic Esser Nemmers Distinguished Professor Emeritus of Marketing at the Kellogg School of Management at Northwestern University, where he served as a faculty member for more than 30 years. In 1983, Professor Zoltners and former Kellogg colleague, Prabha Sinha, founded ZS Associates, a consulting firm with over 1,000 people, across 17 offices, who work closely with sales and marketing organizations, typically Global 500 companies and their affiliates around the world, to develop optimal strategies and to implement them. The success of ZS was recognized by induction of the founders into the Chicago Entrepreneurship Hall of Fame in 2005.

Professor Zoltners' areas of expertise are sales force strategy; sales force size, structure and deployment; sales force compensation; and sales force effectiveness. He has personally consulted for over 100 companies in over 20 countries. In addition to his consulting, he has spoken at numerous conferences and has taught sales force topics to several thousand Executive, M.B.A. and Ph.D. students. He has published more than 40 academic articles, edited two books on Marketing Models and has co-authored a series of books on sales force management.

Prior to joining the faculty at Kellogg, Professor Zoltners was a member of the Business School Faculty at the University of Massachusetts. He received his Ph.D. from Carnegie-Mellon University and an M.S. in Mathematics from Purdue University.