The Future of Organic Agriculture: Otopia or Oblivion?

Organic agriculture could feed the world, but will it? A state of Otopia, an organic Utopia of 100% organic food and organic agriculture, is a dream, or is it a pipe-dream? And if a dream, then when might it manifest? Two scenarios are presented, extrapolating from the rate of growth of the organics sector achieved over the past decade. Under a geometric rate of growth, Otopia could be achieved in 39 years, whereas under an arithmetic rate of growth, Otopia would take 544 years to be achieved

Is I-Voting I-Llegal?

The Voting Rights Act was passed to prevent racial discrimination in all voting booths. Does the existence of a racial digital divide make Internet elections for public office merely a computer geek\u27s pipe dream? Or can i-voting withstand scrutiny under the current state of the law? This i-Brief will consider the current state of the law, and whether disproportionate benefits will be enough to stop this extension of technology dead in its tracks

Schubert calculus and shifting of interval positroid varieties

Consider k x n matrices with rank conditions placed on intervals of columns. The ranks that are actually achievable correspond naturally to upper triangular partial permutation matrices, and we call the corresponding subvarieties of Gr(k,n) the _interval positroid varieties_, as this class lies within the class of positroid varieties studied in [Knutson-Lam-Speyer]. It includes Schubert and opposite Schubert varieties, and their intersections, and is Grassmann dual to the projection varieties of [Billey-Coskun]. Vakil's "geometric Littlewood-Richardson rule" [Vakil] uses certain degenerations to positively compute the H^*-classes of Richardson varieties, each summand recorded as a (2+1)-dimensional "checker game". We use his same degenerations to positively compute the K_T-classes of interval positroid varieties, each summand recorded more succinctly as a 2-dimensional "K-IP pipe dream". In Vakil's restricted situation these IP pipe dreams biject very simply to the puzzles of [Knutson-Tao]. We relate Vakil's degenerations to Erd\H os-Ko-Rado shifting, and include results about computing "geometric shifts" of general T-invariant subvarieties of Grassmannians.Comment: 35 pp; this subsumes and obviates the unpublished http://arxiv.org/abs/1008.430

Subword complexes via triangulations of root polytopes

Subword complexes are simplicial complexes introduced by Knutson and Miller to illustrate the combinatorics of Schubert polynomials and determinantal ideals. They proved that any subword complex is homeomorphic to a ball or a sphere and asked about their geometric realizations. We show that a family of subword complexes can be realized geometrically via regular triangulations of root polytopes. This implies that a family of $\beta$-Grothendieck polynomials are special cases of reduced forms in the subdivision algebra of root polytopes. We can also write the volume and Ehrhart series of root polytopes in terms of $\beta$-Grothendieck polynomials.Comment: 17 pages, 15 figure

Is I-Voting I-Llegal?

The Voting Rights Act was passed to prevent racial discrimination in all voting booths. Does the existence of a racial digital divide make Internet elections for public office merely a computer geek\u27s pipe dream? Or can i-voting withstand scrutiny under the current state of the law? This i-Brief will consider the current state of the law, and whether disproportionate benefits will be enough to stop this extension of technology dead in its tracks