Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of
algebraic topology and discrete mathematics. This volume is the first comprehensive …

The tropical variety defined by linear equations with constant coefficients is the Bergman fan
of the corresponding matroid. Building on a self-contained introduction to matroid polytopes …

We study a graded algebra D=D(L,G) over ℤ defined by a finite lattice ℒ and a subset G in ℒ,
a so-called building set. This algebra is a generalization of the cohomology algebras of …

Generalized permutahedra are a family of polytopes with a rich combinatorial structure and
strong connections to optimization. We prove that they are the universal family of polyhedra …

We present new definitions for and give a comprehensive treatment of the canonical
compactification of configuration spaces due to Fulton–MacPherson and Axelrod–Singer in …

Tropical geometry is used to develop a new approach to the theory of discriminants and
resultants in the sense of Gel $'$ fand, Kapranov and Zelevinsky. The tropical $ A …

Chow rings of matroids were instrumental in the resolution of the Heron–Rota–Welsh
Conjecture by Adiprasito, Huh, and Katz and in the resolution of the Top-Heavy Conjecture …

We introduce the Bergman fan of a polymatroid and prove that the Chow ring of the
Bergman fan is isomorphic to the Chow ring of the polymatroid. Using the Bergman fan, we …

This note which can be viewed as a complement to Alex Postnikov's paper math.
CO/0507163, presents a self-contained overview of basic properties of nested complexes …

We present two models for the space of knots which have endpoints at fixed boundary points
in a manifold with boundary, one model defined as an inverse limit of spaces of maps …