Theory of cones

Cones in Homotopy Probability Theory

This note defines cones in homotopy probability theory and demonstrates that a cone over a space is a reasonable replacement for the space. The homotopy Gaussian distribution in one variable is revisited as a cone on the ordinary Gaussian.

K-theory of Cones of Smooth Varieties

Let R be the homogeneous coordinate ring of a smooth projective variety X over a field k of characteristic 0. We calculate the K-theory of R in terms of the geometry of the projective embedding of X. In particular, if X is a curve then we calculate K0(R) and K1(R), and prove that K−1(R) = ⊕H(C,O(n)). The formula for K0(R) involves the Zariski cohomology of twisted Kähler differentials on the va...

Turing cones and set theory of the reals

Mesonic chiral rings in Calabi-Yau cones from field theory

We study the half-BPS mesonic chiral ring of the N = 1 superconformal quiver theories arising from N D3-branes stacked at Y pq and Labc Calabi-Yau conical singularities. We map each gauge invariant operator represented on the quiver as an irreducible loop adjoint at some node, to an invariant monomial, modulo relations, in the gauged linear sigma model describing the corresponding bulk geometry...

Duality Theory for Maximizations with Respect to Cones

Generalizations of Pareto optimality have been studied by a number of authors. In finite dimensions such work is exemplified by Corley [ 5 ], DaCunha and Polak [10], Goeffrion [131, Hartley [151, Lin [171, Tanino and Sawaragi [211, Wendell and Lee [221, and Yu [231. The optimization of functions into possibly infinite dimensions has been considered by Borwein [21, Cesari and Suryanarayana [31, ...