Department of

April 2015 May 2015 June 2015 Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 2 3 4 1 2 1 2 3 4 5 6 5 6 7 8 9 10 11 3 4 5 6 7 8 9 7 8 9 10 11 12 13 12 13 14 15 16 17 18 10 11 12 13 14 15 16 14 15 16 17 18 19 20 19 20 21 22 23 24 25 17 18 19 20 21 22 23 21 22 23 24 25 26 27 26 27 28 29 30 24 25 26 27 28 29 30 28 29 30 31

Wednesday, May 6, 2015

**Abstract:** The $K$-length of a form $f$ of degree $d$, $K \subseteq \mathbb{C}$, is the smallest number of $d$-th powers of linear forms of which $f$ is a $K$-linear combination. If $\mathbb{R}$-length of $f$ is d, then we say that $f$ has full length over $\mathbb{R}$. In this talk, we will show that a real binary quintic form $f$ has full length over $\mathbb{R}$ if and only if $f$ splits over $\mathbb{R}$. We will also give examples of binary forms with 3 different lengths over the subfields of $\mathbb{C}$.