Metric Algebraic Geometry
June 22 - June 26, 2026
In the early 19th century, algebraic and differential geometry formed a unified field, with geometers investigating intrinsic properties of curves and surfaces—such as curvature, singularities, arc lengths, and defining equations—often through metric and analytic techniques. Many important varieties were defined via distances and angular relationships. By the 20th century, these disciplines had split and are nowadays developed along distinct lines.
However, the rise of data-driven applications in the 21st century—spanning machine learning, tensor methods, computer vision, and geometric statistics—has sparked a renewed need for integration. This motivates Metric Algebraic Geometry, a new framework that blends ideas and techniques from algebraic, differential, metric, and random geometry.
The goal of this workshop is to explore foundational questions in real and complex algebraic geometry from a metric and probabilistic perspective, motivated by applications.