Building on the theory of parity sheaves due to Juteau–Mautner– Williamson, we develop a formalism of “mixed modular perverse sheaves” for varieties equipped with a stratification by affine spaces. We then give two applications: (1) a “Koszul-type” derived equivalence relating a given flag variety to the Langlands dual flag variety, and (2) a formality theorem for the modular derived category o...

The amyloid-β precursor protein (APP), a type I transmembrane protein genetically associated with Alzheimer's disease, has a complex biology that includes proteolytic processing into potentially toxic fragments, extensive trafficking and multiple, yet poorly-defined functions. We recently proposed that a significant fraction of APP is proteolytically cleaved in the neuronal soma into N- and C-t...

relationship between grain yield and its component traits can improve the efficiency of breeding programs by determining appropriate selection criteria. an investigation was carried out on barnyard millet (echinochloa spp.) global germplasm collection to investigate the association among yield components and their direct and indirect effects on the grain yield of barnyard millet. the experiment...

In this paper, we study the (small) quantum cohomology ring of the partial flag manifold. We give proofs of the presentation of the ring and of the quantum Giambelli formula for Schubert varieties. These are known results, but our proofs are more natural and direct than the previous ones. One of our goals is to give evidence of a relationship between universal Schubert polynomials, which give t...

The global surge in obesity with its attendant increase in diabetes mellitus, dyslipidemia, hypertension, and cardiovascular disease is provoking alarm. Fortunately, the surge in obesity has been paralleled by a revolution in understanding the biological regulation of appetite, metabolism, and adiposity.1,2 Mushrooming discoveries are identifying new pathways regulating appetite and metabolism....

We classify the invariant prime ideals of a quantum partial flag variety under the action of the related maximal torus. As a result we construct a bijection between them and the torus orbits of symplectic leaves of the standard Poisson structure on the corresponding flag variety. It was previously shown by K. Goodearl and the author that the latter are precisely the Lusztig strata of the partia...

1.1. Flag Manifolds. One of the best understood examples of algebraic varieties is the flag manifold. One is first interested in flag varieties as they are well-defined examples for many basic concepts. Besides this, however, one can find that they deserve individual attention, for they naturally arise in many circumstances, e.g. in the theory of characteristic classes of vector bundles, mirror...