³ÉÈË´óƬ

Speaker: Kamryn Spinelli

Affiliation: ³ÉÈË´óƬ

Title: The positive closure: algebraic and geometric

Abstract: In this talk, motivated by the intersection condition that we previously deduced for the Chevalley restriction property, we will introduce a new algebraic notion called the positive closure. This construction shares many properties with integral extensions, but differs in several key aspects. One key difference is that the positive closure is generally not a ring, which obstructs many arguments one would like to make regarding the Chevalley restriction property. After discussing this construction from the algebraic viewpoint, we will reinterpret it as a kind of surjectivity condition which sheds light on the relationship between the Chevalley restriction property and the polar restriction theorem of Dadok and Kac.