Quantum ring of singularity Xp + XYq

QUANTUM RING OF SINGULARITY Xp + XYq

In this paper, we will prove that the quantum ring of the quasi-homogeneous polynomial X p + XYq(p ≥ 2, q > 1) with some admissible symmetry group G defined by Fan-Jarvis-Ruan-Witten theory is isomorphic to the Milnor ring of its mirror dual polynomial X pY + Yq. We will construct an concrete isomorphism between them. The construction is a little bit different in case (p − 1, q) = 1 and case (p...

Quantum evaporation of a naked singularity.

We investigate here quantum effects in gravitational collapse of a scalar field model which classically leads to a naked singularity. We show that nonperturbative semiclassical modifications near the singularity, based on loop quantum gravity, give rise to a strong outward flux of energy. This leads to the dissolution of the collapsing cloud before the singularity can form. Quantum gravitationa...

The Nil Hecke Ring and Singularity of Schubert Varieties

Let G be a semi-simple simply-connected complex algebraic group and T ⊂ B a maximal torus and a Borel subgroup respectively. Let h = Lie T be the Cartan subalgebra of the Lie algebra Lie G, and W := N(T )/T the Weyl group associated to the pair (G, T ), where N(T ) is the normalizer of T in G. We can view any element w = w mod T ∈ W as the element (denoted by the corresponding German character)...

Singularity resolution from polymer quantum matter

Time, Incompleteness and Singularity in Quantum Cosmology

In this paper we extend our 2007 paper, “Comparative Quantum Cosmology: Causality, Singularity, and Boundary Conditions”, http://arxiv.org/ ftp/arxiv/papers/0710/0710.5046.pdf, to include consideration of universal expansion, various implications of extendibility and incompleteness in spacetime metrics and, absent the treatment of Feynman diagrams, the use of Penning trap dynamics to describe t...