Isometry-Invariant and Subdivision-Invariant Representations of Embedded Simplicial Complexes

Abstract: Geometric objects such as meshes and graphs are commonly used in various applications, but analyzing them can be challenging due to their complex structures. Traditional approaches may not be robust to transformations like subdivision or isometry, leading to inconsistent results. Here is a novel approach to address these limitations by using only topological and geometric data to analyze simplicial complexes in a subdivision-invariant and isometry-invariant way. This approach involves using a graph neural network to create an $O(3)$-equivariant operator and the Euler curve transform to generate sufficient statistics that describe the properties of the object.

machine learningmathematical physicscommutative algebraalgebraic geometryalgebraic topologycombinatoricsdifferential geometrynumber theoryrepresentation theory

Audience: researchers in the topic

Machine Learning Seminar

Series comments: Online machine learning in pure mathematics seminar, typically held on Wednesday. This seminar takes place online via Zoom.

For recordings of past talks and copies of the speaker's slides, please visit the seminar homepage at: kasprzyk.work/seminars/ml.html