Colloquium – Talk by Dr. Christine Berkesch: January 29th, 2026
January 29, 2026 (Thursday), 4:10-5:15 PM
Dr. Christine Berkesch, University of Minnesota
Geometry and Multigraded Polynomials
In a graded polynomial, all terms have the same degree. For instance, $x^3+x^2y+z^3$ is graded of degree 3. There is a long and rich history tying the geometry of projective varieties and the algebra of graded polynomials and modules. Multigraded polynomials have even more structure. For instance, $x_0^2y_0^3 + x_1^2y_1^3$ is bigraded of degree (2,3): it is graded of degree 2 with respect to the x-variables and degree 3 with respect to the y-variables. Recent work has led to new frameworks for leveraging geometry (including toric geometry and symplectic geometry) to understand multigraded algebra. I will give a survey of the history and recent progress.