Implications of Lee-Yang Theorem In Quantum Gravity

The contributions of this note are twofold: First, it gives a generic recipe to apply Lee-Yang Theorem to solutions of Einstein field equations. Secondly, this existence of the applicability of Lee-Yang Theorem on a partition function of spacetime manifolds might also shed some light on the connection between the number theory, gravity, and gauge field theory. The connection to the Riemann Zeta function is quite interesting when one is also studying the distribution of non-trivial zeroes of the Riemann Zeta function\cite{BRiemann}, or its generic form (Dirichlet L-function)

Solid-state production of complex organic molecules: H-atom addition versus UV irradiation

Complex organic molecules (COMs) have been observed in comets, hot cores and cold dense regions of the interstellar medium. It is generally accepted that these COMs form on icy dust grain through the recombination reaction of radicals triggered by either energetic UV- photon or non-energetic H-atom addition processing. In this work, we present for the first time laboratory studies that allow for quantitative comparison of hydrogenation and UV-induced reactions as well as their cumulative effect in astronomically relevant CO:CH3OH=4:1 ice analogues. The formation of glycolaldehyde (GA) and ethylene glycol (EG) is confirmed in pure hydrogenation experiments at 14 K, except methyl formate (MF), which is only clearly observed in photolysis. The fractions for MF:GA:EG are 0 : (0.2-0.4) : (0.8-0.6) for pure hydrogenation, and 0.2 : 0.3 : 0.5 for UV involving experiments and can offer a diagnostic tool to derive the chemical origin of these species. The GA/EG ratios in the laboratory (0.3-1.5) compare well with observations toward different objects.Comment: Astrochemistry VII Through the Cosmos from Galaxies to Planets Proceedings IAU Symposium No. 332, 2017. arXiv admin note: This version has been removed because it is in violation of arXiv's copyright polic

Symmetric groups, wreath products, Morita equivalences, and Broue's abelian defect group conjecture

It is shown that for any prime p, and any non-negative integer w less than p, there exist p-blocks of symmetric groups of defect w, which are Morita equivalent to the principal p-block of the group Sp [rmoust ] Sw. Combined with work of J. Rickard, this proves that Broué's abelian defect group conjecture holds for p-blocks of symmetric groups of defect at most 5

Derived equivalences for symmetric groups and sl2- categorification

We define and study sl2-categorifications on abelian categories. We show in particular that there is a self-derived (even homotopy) equivalence categorifying the adjoint action of the simple reflection. We construct categorifications for blocks of symmetric groups and deduce that two blocks are splendidly Rickard equivalent whenever they have isomorphic defect groups and we show that this implies Brou´e’s abelian defect group conjecture for symmetric groups. We give similar results for general linear groups over finite fields. The constructions extend to cyclotomic Hecke algebras. We also construct categorifications for category O of gln(C) and for rational representations of general linear groups over ¯Fp, where we deduce that two blocks corresponding to weights with the same stabilizer under the dot action of the affine Weyl group have equivalent derived (and homotopy) categories, as conjectured by Rickard