School of Mathematical Sciences

Positivity of some multivariate formal power series arising from fractional powers of determinants menu

Positivity of some multivariate formal power series arising from fractional powers of determinants

Speaker: 
Alan Sokal (NYU and UCL)
Date/Time: 
Fri, 17/03/2017 - 16:00
Room: 
Queen's building W316
Seminar series: 

We prove the coefficientwise positivity for a class of multivariate formal power series that arise as fractional powers of determinants. More precisely, we show that the formal power series $1 - \det(I_n - tA_n)^{1/n}$ is coefficientwise nonnegative when $A_n$ is an $n \times n$ matrix built in a suitable way out of $n^2$ independent indeterminates.

This is joint work with Alex Scott.