In this paper we explain how the cocycle of the momentum map of the action of the affine symplectic group on $\mathbb{R}^{2n}$ gives rise to a coadjoint orbit of the odd real symplectic group with a modulus.
Given a semipositive symplectic manifold, we prove that the pseudocycle genus-zero Gromov-Witten invariants are equal to the polyfold genus-zero Gromov-Witten invariants.
Stefania Della Vecchia, Maria Marchese, Filippo Maria Santorelli
Background: Lafora disease (LD) is a neurodegenerative condition characterized by the accumulation of polyglucosan bodies (PBs) throughout the brain. Alongside metabolic and molecular alterations, neuroinflammation has emerged as another key histopathological feature of LD. Methods: To investigate the role of astrocytes and microglia in LD, we performed a systematic review according to the PRISMA statement. PubMed, Scopus, and Web-of-Science database searches were performed independently by two reviewers. Results: Thirty-five studies analyzing the relationship of astrocytes and microglia with LD and/or the effects of anti-inflammatory treatments in LD animal models were identified and included in the review. Although LD has long been dominated by a neuronocentric view, a growing body of evidence suggests a role of glial cells in the disease, starting with the finding that these cells accumulate PBs. We discuss the potential meaning of glial PB accumulations, the likely factors activating glial cells, and the possible contribution of glial cells to LD neurodegeneration and epilepsy. Conclusions: Given the evidence for the role of neuroinflammation in LD, future studies should consider glial cells as a potential therapeutic target for modifying/delaying LD progression; however, it should be kept in mind that these cells can potentially assume multiple reactive phenotypes, which could influence the therapeutic response.
We study the moduli space of frozen planet orbits in the Helium atom for an interpolation between instantaneous and mean interactions and show that this moduli space is compact.
This re-certifying paper describes the details of the Morse homology of manifolds with boundary, introduced by the author before, in terms of handlebody decompositions.
We provide a short proof that an $L^2_1$ and $J$-holomorphic curve is in fact smooth. As an application, we deduce a removal of singularity theorem for curves of finite energy.
We develop an analytic framework that combines the compactness theory of Gromov for J-holomorphic curves with that of Uhlenbeck for ASD connections. Compactness, regularity and removal of singularity theorems are discussed.
This is an expository account of some applications of string topology to the study of Lagrangian embeddings into symplectic manifolds, originally due to Fukaya, which was written as a contribution to a book on free loop spaces.
In this paper, we prove that the "quantization commutes with reduction" phenomenon of Guillemin-Sternberg applies in the context of the metaplectic correction.