The construction of joins and secant varieties is studied in the combinatorial context of monomial ideals. For ideals generated by quadratic monomials, the generators of the secant ideals are obstructions to graph colorings, and this leads to a commutative algebra version of the Strong Perfect Graph Theorem. Given any projective variety and any term order, we explore whether the initial ideal o...

Different realizations of the Hubbard operators in different Hilbert spaces give rise to various microscopic lattice electron models driven by strong correlations. In terms Gutzwiller projected operators, most familiar examples are t-J and BCS-Hubbard at coupling. We focus on spin-dopon representation operators. this case no double occupancy constraint (NDO) can be reexpressed as a Kondo intera...

We discuss the domain-theoretic and topological content of the operator calculus used in the Irish School of the Vienna Development Method (VDM♣) of formal systems development. Thus, we examine the Scott continuity, or otherwise, of the basic operators used in this calculus when viewed as operators on the domain (X → Y ) of partial functions mapping X into Y . It turns out that the override, on...

In flat bands, superconductivity can lead to surprising transport effects. The superfluid "mobility", in the form of weight $D_s$, does not draw from curvature band but has a purely band-geometric origin. mean-field description, non-zero Chern number or fragile topology sets lower bound for which, via Berezinskii-Kosterlitz-Thouless mechanism, might explain relatively high superconducting trans...