Geometry of the theta divisor of a compactified jacobian

We study the theta divisor of the compactified jacobian of a nodal, possibly reducible, curve. We compute its irreducible components and give it a geometric interpretation consistent with the classical Brill-Noether theory of smooth curves. Some applications on hyperelliptic stable curves are appended.Comment: 36 pages. Final version, to appear in JEM

Maximum entropy generation in open systems: the Fourth Law?

This paper develops an analytical and rigorous formulation of the maximum entropy generation principle. The result is suggested as the Fourth Law of Thermodynamics

Algebraic and tropical curves: comparing their moduli spaces

We construct the moduli space for equivalence classes of n-pointed tropical curves of genus g, together with its compactification given by weighted tropical curves, and establish some of its basic topological properties. We compare it to the moduli spaces of smooth and stable algebraic curves, from the combinatorial, the topological, and the Teichm\"uller point of view. The paper is written in an expository style, and it generalizes some results contained in sections 4-6 of arXiv:1001.2815v3.Comment: Changes in numbering to match the published versio

Sign conjugacy classes of the symmetric groups

A conjugacy class $C$ of a finite group $G$ is a sign conjugacy class if every irreducible character of $G$ takes value 0, 1 or -1 on $C$. In this paper we classify the sign conjugacy classes of the symmetric groups and thereby verify a conjecture of Olsson