6 papers
Reinforcement Learning the Chromatic Symmetric Function
Gergely Bérczi, Jonas Klüver
We propose a conjectural counting formula for the coefficients of the chromatic symmetric function of unit interval graphs using reinforcement learning. The formula counts specific…
Complete collineations for maximum likelihood estimation
Gergely Bérczi, Eloise Hamilton, Philipp Reichenbach +1
We import the algebro-geometric notion of a complete collineation into the study of maximum likelihood estimation in directed Gaussian graphical models. A complete collineation pro…
An ML approach to resolution of singularities
Gergely Bérczi, Honglu Fan, Mingcong Zeng
The solution set of a system of polynomial equations typically contains ill-behaved, singular points. Resolution is a fundamental process in geometry in which we replace singular p…
Fixed point distribution on Hilbert scheme of points
Gergely Bérczi, Jonas M. Svendsen
Let be a closed field of characteristic zero. We prove that all monomial ideals sit in the curvilinear component of the Hilbert scheme of points of the affine space $\…
Tautological integrals on Hilbert scheme of points II: Geometric subsets
Gergely Bérczi
We develop a formula for tautological integrals over geometric subsets of the Hilbert scheme of points on complex manifolds. As an illustration of the theory, we derive a new itera…
Tautological integrals on Hilbert scheme of points I
Gergely Bérczi
We develop a new method to study intersection theory of the main component of the Hilbert scheme of points on complex manifolds. The main result is an iterated residue formula for…