Matrix Invariants of Spectral Categories

Spectral Enrichments of Model Categories

We prove that every stable, combinatorial model category can be enriched in a natural way over symmetric spectra. As a consequence of the general theory, every object in such a model category has an associated homotopy endomorphism ring spectrum. Basic properties of these invariants are established.

Spherical 2-categories and 4-manifold Invariants

Cluj Matrix Invariants

The problem of distances in a graph, G, is one of the most studied questions, both from theoretical point of view and applications (the reader can consult two recent reviews ). It is connected to the Wiener number, W, or "the path number" as denominated by its initiator. In acyclic structures, Wiener number and its extension, hyper-Wiener number, can be defined as edge/path contributions, Ie/p ...

Computing with Matrix Invariants

This is an improved version of the talk of the author given at the Antalya Algebra Days VII on May 21, 2005. We present an introduction to the theory of the invariants under the action of GLn(C) by simultaneous conjugation of d matrices of size n × n. Then we survey some results, old or recent, obtained by a dozen of mathematicians, on minimal sets of generators, the defining relations of the a...

Invariants of isospectral deformations and spectral rigidity

We introduce a notion of weak isospectrality for continuous deformations. Let us consider the Laplace-Beltrami operator on a compact Riemannian manifold with boundary with Robin boundary conditions. Given a Kronecker invariant torus Λ of the billiard ball map with a Diophantine vector of rotation we prove that certain integrals on Λ involving the function in the Robin boundary conditions remain...