Some problems at the interface of approximation theory and algebraic geometry

TL;DR

This paper presents a collection of unresolved problems at the intersection of approximation theory and algebraic geometry discussed during a 2022 conference, highlighting open research challenges in these interconnected fields.

Contribution

It compiles and summarizes unresolved problems from a recent conference, fostering future research directions at the interface of approximation theory and algebraic geometry.

Findings

Identified key open problems in approximation theory and algebraic geometry.

Highlighted the need for new approaches to longstanding mathematical questions.

Encouraged collaboration between researchers in both fields.

Abstract

We sketch an assortment of problems that were posed -- and not yet solved -- during problem sessions at the conference ``Approximation Theory and Numerical Analysis meet Algebra, Geometry, and Topology'', which was held at the Palazzone Cortona 5--9 September 2022.