Enumerative geometry meets statistics, combinatorics and topology

TL;DR

This paper explores the deep interconnections between combinatorics, algebraic statistics, topology, and enumerative algebraic geometry, emphasizing the role of Lorentzian polynomials and matrix spaces in unifying these fields.

Contribution

It introduces a novel framework linking diverse mathematical areas through the concept of a linear space of matrices and discrete invariants associated with Lorentzian polynomials.

Findings

Identifies connections between combinatorics and algebraic geometry.

Highlights the role of Lorentzian polynomials in multiple fields.

Proposes a unified perspective on discrete invariants across disciplines.

Abstract

We explain connections among several, a priori unrelated, areas of mathematics: combinatorics, algebraic statistics, topology and enumerative algebraic geometry. Our focus is on discrete invariants, strongly related to the theory of Lorentzian polynomials. The main concept joining the mentioned fields is a linear space of matrices.