Notions of Positivity and the Geometry of Polynomials

Front Matter....Pages i-xx
Commuting Linear Differential Operators and Hankel Matrices....Pages 1-15
Variants of the Effective Nullstellensatz and Residue Calculus....Pages 17-31
An Extension Problem for Convex Functions....Pages 33-37
Subharmonic Configurations and Algebraic Cauchy Transforms of Probability Measures....Pages 39-62
Proof of the Monotone Column Permanent Conjecture....Pages 63-78
Tracial Nullstellensätze....Pages 79-101
Iterated Turán Inequalities and a Conjecture of P. Brändén....Pages 103-113
Double Scaling Limit for Modified Jacobi-Angelesco Polynomials....Pages 115-161
Constrained Approximation via Functional Analysis....Pages 163-166
An Elementary Proof of the B. and M. Shapiro Conjecture for Rational Functions....Pages 167-178
The Pressure, Densities and First-order Phase Transitions Associated with Multidimensional SOFT....Pages 179-220
Matrix Weyl Functions and Non-Abelian Coxeter-Toda Lattices....Pages 221-237
On the Exponential Transform of Lemniscates....Pages 239-257
On a Family of Positive Linear Integral Operators....Pages 259-274
Monomial Inequalities for Newton Coefficients and Determinantal Inequalities for p-Newton Matrices....Pages 275-282
Borcea’s Variance Conjectures on the Critical Points of Polynomials....Pages 283-309
Stability on {0, 1, 2, …} S : Birth-Death Chains and Particle Systems....Pages 311-329
The Convex Hull of a Variety....Pages 331-344
Blenders....Pages 345-373
Random Complex Fewnomials, I....Pages 375-400
Finite-order Invariants for ( n , 2)-Torus Knots and the Curve $${Y^2}={X^3}+{X^2}$$ ....Pages 401-403