Titlebook: Extended Abstracts GEOMVAP 2019; Geometry, Topology, Maria Alberich-Carramiñana,Guillem Blanco,Eva Mira Conference proceedings 2021 The Ed

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Ivan A. Veliky,Robert J. C. McLeanThe classification of Legendrian knots is one of the basic questions in 3-dimensional contact topology. In this note, the classification results for Legendrian knots are discussed. The first classification result for exceptional non-trivial knot types is studied and several open problems related to Legendrian knots are listed.

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Immobilized Enzymes in Milk Systems,Less rigid than phylogenetic trees, phylogenetic networks allow the description of a wider range of evolutionary events. In this note, we explain how to extend the rank invariants from phylogenetic trees to phylogenetic networks evolving under the general Markov model and the equivariant models.

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https://doi.org/10.1007/978-1-349-04439-9In this extended abstract we will describe a method to study the dimension of the cohomology of an arithmetic group. We will mainly use the Borel-Serre compactification, the theory of cuspidal and Eisenstein cohomology and the Euler characteristic.

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Some Important Modes of Life in Insects,In this note we discuss an approach to prove existence of infinitely many periodic Reeb orbits in overtwisted contact manifolds. The result is a combination of a plug-like construction and an adaptation of Hofer’s .-holomorphic curve techniques in the case to .-contact manifold.

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,Up-to-Homotopy Algebras with Strict Units,We prove the existence of Sullivan minimal models for operads with non trivial arity zero. So up-to-homotopy algebras with strict units are just operad algebras over these minimal models. As an application we give another proof of the formality of the . .-little disks operad over the rationals.