MSGSS
Inverse PDE problems in Geometry
When studying differential equations, a very natural question to ask is whether a given system of equations has a unique solution. A different question that we can ask is: Given a polynomial F, what are the partial differential equations that have F as a solution? It turns out that specific cases of questions like this can be understood using techniques from Commutative Algebra and have applications to several areas of Mathematics, including Combinatorics, Geometry, Topology and Representation Theory. In this talk, we will focus on some problems in (algebraic and differential) Geometry that can be studied from this perspective. If there is enough time, we will also talk about how graph theory can help us in this setting.