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The Plücker matrix B L (n , E) of the Lagrangian Grassmannian L (n , E) , is determined by the linear envelope 〈 L (n , E) 〉 of the Lagrangian Grassmannian. The linear envelope 〈 L (n , E) 〉 is the intersection of linear relations of Plücker of Lagrangian Grassmannian, defined here. The Plücker matrix B L (n , E) is a direct sum of the incidence matrix of the configuration of subsets. These matrices determine the isotropy index r n and r n -atlas which are invariants associated with the symplectic vector space E. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present an algebraic theoretical basis for the study of ω -Hamiltonian vector fields defined on a symplectic vector space (V , ω) with respect to coordinates that are not necessarily symplectic. We introduce the concepts of ω -symplectic and ω -semisymplectic groups, and describe some of their properties that may not coincide with the classical context. We show that the Lie algebra of such groups is a useful tool in the recognition and construction of ω -Hamiltonian vector fields. [ABSTRACT FROM AUTHOR]

We derive Heisenberg uncertainty principles for pairs of Linear Canonical Transforms of a given function, by resorting to the fact that these transforms are just metaplectic operators associated with free symplectic matrices. The results obtained synthesize and generalize previous results found in the literature, because they apply to all signals, in arbitrary dimension and any metaplectic operator (which includes Linear Canonical Transforms as particular cases). Moreover, we also obtain a generalization of the Robertson-Schrödinger uncertainty principle for Linear Canonical Transforms. We also propose a new quadratic phase-space distribution, which represents a signal along two intermediate directions in the time-frequency plane. The marginal distributions are always non-negative and permit a simple interpretation in terms of the Radon transform. We also give a geometric interpretation of this quadratic phase-space representation as a Wigner distribution obtained upon Weyl quantization on a non-standard symplectic vector space. Finally, we derive the multidimensional version of the Hardy uncertainty principle for metaplectic operators and the Paley-Wiener theorem for Linear Canonical Transforms. [ABSTRACT FROM AUTHOR]

This article is an interview with mathematician Elisabetta Strickland, who has been actively involved in promoting women in mathematics. The interview covers her family background, her passion for mathematics, and her career in the field. Strickland discusses her preference for abstract proofs and her work in algebraic geometry, particularly in studying special varieties with a lot of structure. She also mentions her interest in groups and her work in invariant theory. The conversation explores various topics including mathematics, career experiences, women in mathematics, and personal interests. It highlights the importance of collaboration, the challenges faced by women in mathematics, the role of travel and conferences in the field, and the value of face-to-face interactions. The interview also reveals Strickland's interests in literature, writing, sailing, photography, and interior decorating. [Extracted from the article]