Alex Dunbar

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math.AG2024

Pythagoras Numbers for Ternary Forms

Grigoriy Blekherman, Alex Dunbar, Rainer Sinn

We study the Pythagoras numbers $p y (3, 2 d)$ of real ternary forms, defined for each degree $2 d$ as the minimal number $r$ such that every degree $2 d$ ternary form which is a sum of…

math.AG2024

A Topological Approach to Simple Descriptions of Convex Hulls of Sets Defined by Three Quadrics

Grigoriy Blekherman, Alex Dunbar

We study the convex hull of a set $S \subset R^{n}$ defined by three quadratic inequalities. A simple way of generating inequalities valid on $S$ is to take nonnegative linea…