Conic Stability in the Geometry of Polynomials

• Applicant: Professor Dr. Thorsten Theobald
• Subject Area: Mathematics
• Term: from 2020 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 438633658

• Final Report Year: 2023

Final Report Abstract

The project dealt with studying the concept of conic stability in the geometry of polynomials. The conic stability captures the property that the imaginary parts of the zeroes of a multivariate, complex polynomial are located outside of a given cone. It generalizes the concept of the stability of polynomials and its geometry is related to the imaginary projection of polynomials. Contributions to the combinatorics of conically stable polynomials, to imaginary projections as well as to the connection of conic stability and positive maps were achieved.

Publications

• Conic stability of polynomials and positive maps. Journal of Pure and Applied Algebra, 225(7), 106610.
  Dey, Papri; Gardoll, Stephan & Theobald, Thorsten
  
• Sublinear circuits and the constrained signomial nonnegativity problem. Mathematical Programming, 198(1), 471-505.
  Murray, Riley; Naumann, Helen & Theobald, Thorsten
  
• Combinatorics and preservation of conically stable polynomials. Journal of Algebraic Combinatorics, 58(3), 811-836.
  Codenotti, Giulia; Gardoll, Stephan & Theobald, Thorsten
  
• Imaginary projections: Complex versus real coefficients. Journal of Pure and Applied Algebra, 227(6), 107308.
  Gardoll, Stephan; Sayyary, Namin Mahsa & Theobald, Thorsten
  
• Properties of conically stable polynomials and imaginary projections. University Library J. C. Senckenberg.
  Gardoll, Stephan