The monic rank and instances of Shapiro's Conjecture

  • Arthur Bik (Universität Bern, Bern, Switzerland)
E1 05 (Leibniz-Saal)


Shapiro's Conjecture states that every homogeneous polynomial in C[x,y] of degree de is the sum of at most d d-th powers of homogeneous polynomials of degree e. In this talk, we prove a few instances of this conjecture. We do this by introducing the monic rank. For a polynomial, the monic rank is the minimal k for which we can write (an appropriately scaled version of) the polynomial as a sum of k d-th powers of monic polynomials. We prove that the maximal monic rank of polynomials of degree de is at most d when e=1, d=1,2 or (d,e)=(3,2),(3,3),(3,4),(4,2). This is joint work with Jan Draisma, Alessandro Oneto and Emanuele Ventura.


Saskia Gutzschebauch

Max-Planck-Institut für Mathematik in den Naturwissenschaften Contact via Mail

Tim Seynnaeve

Max Planck Institute for Mathematics in the Sciences, Leipzig

Rodica Dinu

University of Bucharest

Giulia Codenotti

Freie Universität Berlin

Frank Röttger

Otto-von-Guericke-Universität, Magdeburg