Notions of Positivity and the Geometry of Polynomials

1. Front Matter

   Pages i-xx

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2. Commuting Linear Differential Operators and Hankel Matrices

   • Alexandru Aleman, Andreea Sarafoleanu

   Pages 1-15

3. Variants of the Effective Nullstellensatz and Residue Calculus

   • Mats Andersson, Elizabeth Wulcan

   Pages 17-31

4. An Extension Problem for Convex Functions

   • Bo Berndtsson

   Pages 33-37

5. Subharmonic Configurations and Algebraic Cauchy Transforms of Probability Measures

   • Jan-Erik Björk, Julius Borcea, Rikard Bøgvad

   Pages 39-62

6. Proof of the Monotone Column Permanent Conjecture

   • Petter Brändén, James Haglund, Mirkó Visontai, David G. Wagner

   Pages 63-78

7. Tracial Nullstellensätze

   • Matej Brešar, Igor Klep

   Pages 79-101

8. Iterated Turán Inequalities and a Conjecture of P. Brändén

   • George Csordas

   Pages 103-113

9. Double Scaling Limit for Modified Jacobi-Angelesco Polynomials

   • Klaas Deschout, Arno B. J. Kuijlaars

   Pages 115-161

10. Constrained Approximation via Functional Analysis

    • Peter Duren, Harold S. Shapiro

    Pages 163-166

11. An Elementary Proof of the B. and M. Shapiro Conjecture for Rational Functions

    • Alexandre Eremenko, Andrei Gabrielov

    Pages 167-178

12. The Pressure, Densities and First-order Phase Transitions Associated with Multidimensional SOFT

    • Shmuel Friedland, Uri N. Peled

    Pages 179-220

13. Matrix Weyl Functions and Non-Abelian Coxeter-Toda Lattices

    • Michael Gekhtman, Olena Korovnichenko

    Pages 221-237

14. On the Exponential Transform of Lemniscates

    • Björn Gustafsson, Vladimir Tkachev

    Pages 239-257

15. On a Family of Positive Linear Integral Operators

    • Mourad Ismail, Plamen Simeonov

    Pages 259-274

16. Monomial Inequalities for Newton Coefficients and Determinantal Inequalities for p-Newton Matrices

    • C. R. Johnson, C. Marijuán, M. Pisonero, O. Walch

    Pages 275-282

17. Borcea’s Variance Conjectures on the Critical Points of Polynomials

    • Dmitry Khavinson, Rajesh Pereira, Mihai Putinar, Edward B. Saff, Serguei Shimorin

    Pages 283-309

18. Stability on {0, 1, 2, …}^S: Birth-Death Chains and Particle Systems

    • Thomas M. Liggett, Alexander Vandenberg-Rodes

    Pages 311-329

19. The Convex Hull of a Variety

    • Kristian Ranestad, Bernd Sturmfels

    Pages 331-344

20. Blenders

    • Bruce Reznick

    Pages 345-373

The book consists of solicited articles from a select group of mathematicians and physicists working at the interface between positivity and the geometry, combinatorics or analysis of polynomials of one or several variables. It is dedicated to the memory of Julius Borcea (1968-2009), a distinguished mathematician, Professor at the University of Stockholm. With his extremely original contributions and broad vision, his impact on the topics of the planned volume cannot be underestimated. All contributors knew or have exchanged ideas with Dr. Borcea, and their articles reflect, at least partially, his heritage.

• multivariate polynomials
• positivity

• , Department of Mathematics, Royal Institute of Technology, Stockholm, Sweden

  Petter Brändén

• , Mathematical Department, Stockholm University, Stockholm, Sweden

  Mikael Passare

• , Department of Mathematics, University of California, Santa Barbara, USA

  Mihai Putinar

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