Contact Isotropic Realisations of Jacobi Manifolds via Spencer Operators

Motivated by the importance of symplectic isotropic realisations in the study of Poisson manifolds, this paper investigates the local and global theory of contact isotropic realisations of Jacobi manifolds, which are those of minimal dimension. These arise naturally when considering multiplicity-free actions in contact geometry, as shown in this paper. The main results concern a classification of these realisations up to a suitable notion of isomorphism, as well as establishing a relation between the existence of symplectic and contact isotropic realisations for Poisson manifolds. The main tool is the classical Spencer operator which is related to Jacobi structures via their associated Lie algebroid, which allows to generalise previous results as well as providing more conceptual proofs for existing ones

The Rise and Fall of Venezuela’s Pacted Democracy: A Story of Coups, Oil Riches, and Political Pacts

Senior Project submitted to The Division of Social Studies of Bard College

Role of evolutionary conserved MAP kinase C-terminal regions in transcriptional activation in Arabidopsis thaliana

Mitogen-activated protein kinase (MAPK) cascades are central signaling components among eukaryotes that mediate intracellular signaling in numerous physiological processes. MAPKs cascades consist of three kinases, MAPKKKs, MAPKKs, and MAPKs whose activity is regulated through phosphorylation. The Arabidopsis thaliana MAPKs AtMPK3 and AtMPK6 modulate the function of substrates through phosphorylation and are positive immune regulators. However, AtMPK3 and AtMPK6 substrates are not fully understood, especially for transcription factors (TFs) that control immune transcriptional reprogramming. Only a few TFs (e.g., AtWRKY33, AtVIP1, AtERF6, AtERF104, and AtMYB44) are known to be phospho-targets of AtMPK3/6 during plant immunity. Here I identified 12 novel TFs interactors of AtMPK3 and or AtMPK6 through a large-scale yeast two-hybrid (Y2H) screening with a library composed of ̴ 1500 Arabidopsis TFs. Moreover, I found that when fused to a DNA binding protein, AtMPK3/6 activated transcription of reporter genes in yeast and that the C-terminus region of AtMPK3/6 was necessary and sufficient for this activation. Notably, this novel MAPK function was preserved in two transient expression systems of Arabidopsis. This MAPK C-terminus-mediated transcriptional activation was sequence-specific. Furthermore, consistently with the highly conserved amino acid sequences of MAPK C-terminal regions across kingdoms, all tested C-terminal domains of MAPKs from Arabidopsis thaliana, the early-diverged bryophyte Marchantia polymorpha, mammals, and yeast exhibited the ability for transcriptional enhancement. These results imply that MAPKs can activate transcription via the evolutionary conserved MAPK C-terminal domains when close to DNA. Taken together, this study broadens the knowledge of MAPKs immune signaling networks by identifiying 12 TFs interactors of AtMPK3 and or AtMPK6 and revealing a novel kinase-independent MAPK function, which may be conserved across eukaryotes