Mini-workshop on Algebraic geometry and its Applications
"Expressing a polynomial of degree kd as sum of k-th powers"
SPEAKER | Giorgio Ottaviani
INSTITUTE | Universit? di Firenze
DATE | February 21(Fri), 2014
TIME | 10:00
PLACE | Room 403, Center for Mathematical Challenges(CMC)
ABSTRACT | : Any homogeneous polynomial of degree kd can be expressed as a sum of k-th powers of homogeneous polynomials of degree d. A natural question is to compute the minimal number of summands which are needed to express in this way a general polynomial. In the case d=1 the answer has been given by a celebrated theorem by Alexander and Hirschowitz, in 1995. The case k=1 being trivial, the case k=2 leads to interesting questions for polynomials which can be written as sum of squares. We exhibit a upper bound on the number of needed summands, which is asymptotically sharp for any fixed k and d going to infinity, obtained in collaboration with R. Froberg and B. Shapiro.