Matthew Brassil

collaborators

3 papers

math.AG2020

On the number of symmetric presentations of a determinantal hypersurface

Matthew Brassil, Zinovy Reichstein

A hypersurface $H$ in $P^{r}$ of degree $n$ is called determinantal if it is the zero locus of a polynomial of the form $det (x_{0} A_{0} + \dots + x_{r} A_{r})$ for…

math.RA2020

A graph-theoretic approach to a conjecture of Dixon and Pressman

Matthew Brassil, Zinovy Reichstein

Given $n \times n$ matrices, $A_{1}, \dots, A_{k}$ , consider the linear operator $L (A_{1}, \dots, A_{k}) : M_{n} \to M_{n}$ given by \[ L(A_1,\dots,A_k)(…

math.GR2018

Hermite's theorem via Galois cohomology

Matthew Brassil, Zinovy Reichstein

An 1861 theorem of Hermite asserts that for every field extension $E / F$ of degree $5$ there exists an element of $E$ whose minimal polynomial over $F$ is of the form $f(x) = x^5 +…