Bruce Reznick

Professor
"The John and Harriet J. Absentminded Professor of Mathematics"
Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street
Urbana, Illinois 61801-2975

Office: 327 Altgeld Hall
Office Tel: (217)333-4284
Dept. FAX: (217) 333-9576
e-mail:reznick@math.uiuc.edu

Fall 2014 teaching

  • Math 347 honors
  • CV-type links

  • Biographical Sketch
  • List of Research Publications
  • List of Other Publications
  • 2014 SIAM Conference on Optimization

  • Real psd ternary forms with many zeros, May 21, 2014

    Joint Mathematics Meetings, Baltimore

  • Beamer pages Material related to the talk "Every math major should know this crazy theorem."

    NUS-IMS Program on Inverse Moment Problem, Beamer talks, Singapore

  • From Banach spaces to moments to positive polynomials, December 2, 2103
  • Public lecture: A walk down the algebraic-geometric mean streets of mathematics, December 17, 2103, eventual link to video will be here
  • Ternary forms with lots of zeros (not a complete beamer talk, mostly equations and pictures), December 19, 2013.

    Eastern Illinois University, October 4, 2013

  • The secret lives of polynomial identities (slightly corrected)

    SIAM-AG13, August 2, 2013

  • On elliptesque and hyperbolesque curves (slightly corrected, twice)
  • Forms as sums of powers of lower degree forms (slightly corrected, with a bonus new last page!)

    REGS minicourse home page

  • Summer 2013

    Math 499 Beamer Talk, March 29, 2013

  • The secret lives of polynomial identities

    SIAM 2012, July 13, 2012 (New!!)

  • Klein's idea and identities for powers of polynomials Both beamer slides and a recording of the talk with moving slides!

    Seattle Beamer Talk, May 18, 2012

  • The secret lives of polynomial identities My 5/18/12 talk, with a few corrections.

    Chicago Beamer Talk, December 8, 2011

  • An updated version of the "steampunk canonical forms'' talk.

    Banff Beamer Talk, November 17, 2011

  • A shorter version of the seminar talks, with some new stuff

    Seminars on November 1, 2011

  • Longer abstract of my two seminar talks in number theory and geometry/AGC on November 1, 2011.
  • Linearly dependent powers of quadratic forms A combination of the beamer slides for the two seminars.

    Algecom5 Beamer Talk, October 29, 2011

  • Steampunk canonical forms 10/29/11 talk, an evolution of the talks of 3/19/11 and 10/7/11.

    Raleigh and Steampunk Canonical Form Material

  • Material relevant to my presentation at the SIAM Conference on Applied Algebraic Geometry, 10/7/11.

    Claremont Beamer Talk

  • The secret lives of polynomial identities My 9/21/11 talk.

    Konstanz Beamer Talk

  • The secret lives of polynomial identities My 6/30/11 talk, with a few corrections.

    Iowa Beamer Talk

  • Material relevant to my presentation at the Iowa City Sectional Meeting, 3/19/11

    Math 499 (2010-2011) Talk

  • The secret lives of polynomial identities

    Presentation at the Memorial to Jerry Uhl, held on 11/6/10:

  • Adaptation of retirement talk given on 5/4/08

    Presentation at the Gathering for Gardner, held on 10/21/10:

  • Thanks from an appreciative reader

    Presentation at the Departmental Memorial, held on 10/23/13:

  • On Paul and Felice Bateman

    Notices of the AMS Book review

  • "From Zero To Infinity, 50th Anniversary Edition" by Constance Reid

    When it comes to advice, I'm full of it

  • "Teaching Philosophy"
  • "Chalking It Up: Advice to a new TA"
  • "Resources for research"
  • "One introduction to mathematical research", or "You've proved a theorem, now what?"
  • "Some thoughts on writing for the Putnam"


  • Areas of Specialization

    Combinatorial methods in algebra, analysis and number theory, usually involving polynomials or polytopes.

    .pdf files of recent papers (most recent at top)

  • Preprint Some new canonical forms for polynomials, Revised version
  • Preprint Congruence properties of binary partition functions (with Katherine Anders, Melissa Dennison and Jennifer Weber Lansing), Revised version
  • Preprint On the sums of two cubes (with Jeremy Rouse), Revised version
  • Preprint Blenders, Revised version
  • Preprint On the length of binary forms, Final Revised version
  • Preprint Polya's theorem with zeros (with Vicki Powers and Mari Castle)
  • Preprint Laws of inertia in higher degree binary forms
  • Preprint On Hilbert's construction of positive polynomials
  • Preprint Regularity properties of the Stern enumeration of the rationals
  • Preprint A quantitative Polya's theorem with zeros (with Vicki Powers and Mari Castle)
  • Preprint Clean lattice tetrahedra
  • Preprint A quantitative Polya's theorem with corner zeros (with Vicki Powers)
  • Preprint Almost alternating sums (with Kevin O'Bryant and Monika Serbinowska)
  • Preprint Polynomials positive on unbounded rectangles (with Vicki Powers)
  • Preprint On the absence of uniform denominators in Hilbert's 17th problem
  • Preprint A new approach to Hilbert's theorem on ternary quartics (with Vicki Powers, Claus Scheiderer and Frank Sottile)
  • Preprint On the Diophantine equation xy = ymx (with Michael Bennett)
  • Preprint Patterns of dependence among powers of polynomials
  • Preprint Lattice polytopes with distinct pair-sums (with M. D. Choi and T. Y. Lam)
  • Preprint A new bound for Polya's Theorem with applications to polynomials positive on polyhedra (with Vicki Powers)
  • Preprint Notes towards a constructive proof of Hilbert's Theorem on ternary quartics (with Vicki Powers)
  • Preprint Polynomials that are positive on an interval (with Vicki Powers)
  • Reprint Some Concrete Aspects of Hilbert's 17th Problem
  • Preprint On the non-monotonicity of (|Im(zn)|)
  • Preprint The maximum angular gap among rectangular grid points (with Zoltan Furedi)
  • Reprint Homogeneous polynomial solutions to constant coefficient PDE's over fields
  • Reprint Uniform denominators in Hilbert's Seventeenth Problem
  • Preprint Sums of even powers of real linear forms, chapter by chapter.
  • Reprint An inequality for products of polynomials
  • Seminar Notes

  • Notes Equal sums of higher powers of quadratic forms
  • Ph.D. Students

    Prof. Julie Simon (Ph.D. 1989)
    Prof. William Harris (Ph.D. 1992)
    Ms. Colleen Kilker (1977-2002)
    Prof. Ricardo Rojas (Ph.D. 2008)
    Prof. Han Duong (Ph.D. 2008)
    Prof. Supawadee Prugsapitak (Ph.D. 2009)
    Prof. Melissa Dennison (Ph.D. 2010)
    Dr. Milos Curcic (Ph.D. 2013)
    Dr. Jennifer Weber Lansing (Ph.D. 2014)
    Prof. Katie Anders (Ph.D. 2014)
    Prof. Wipawee Tangjai (Ph.D. 2014)

    Podcast!


    Strongly Connected Components

    Updated September 3, 2014