Evolutionary expansion and complexification of the primate cerebral cortex are largely linked to the emergence of the outer subventricular zone (OSVZ), a uniquely structured germinal zone that generates the expanded primate supragranular layers. The primate OSVZ departs from rodent germinal zones in that it includes a higher diversity of precursor types, inter-related in bidirectional non-hiera...

We give a simple interpretation of the adapted complex structure of Lempert-Szőke and Guillemin-Stenzel: it is given by a polar decomposition of the complexified manifold. We then give a twistorial construction of an SO(3)-invariant hypercomplex structure on a neighbourhood of X in TTX, where X is a real-analytic manifold equipped with a linear connection. We show that the Nahm equations arise ...

This is similar to how Cardano’s formula, which expresses the roots of a real cubic polynomial in terms of its coefficients, involves complex numbers and yet the final result may still be real. In the following, unless I specify the dimension of a vector space, any statement about real vector spaces is about real vector spaces of finite or infinite dimension, and any statement about complex vec...

We realize Stasheff’s multiplihedron geometrically as the moduli space of stable quilted disks. This generalizes the geometric realization of the associahedron as the moduli space of stable disks. We also construct an algebraic variety that has the multiplihedron as its non-negative real part, and use it to define a notion of morphism of cohomological field theories.

A bstract Field transformation rules of the standard fermionic T-duality require isometries to anticommute, which leads complexification Killing spinors and results in complex valued dual backgrounds. We generalize field transformations setting with non-anticommuting show that resulting backgrounds are solutions double theory. Explicit examples non-abelian T-dualities produce real given. Some o...

L'article traduit une préoccupation quant à la complexification des situations de travail du XXIesiècle. Prenant appui sur un modèle développement compétences durables inscrit en didactique professionnelle, dix personnes expérimentées soudage-montage ont participé recherche qualitative le processus travail. Une démarche d’analyse contenu a permis décrire les paliers décisionnels et opérationnel...

In this paper, we consider the connected split rank one Lie group of real type F4 which we denote by F4. We first exhibit F4 as a group of operators on the complexification of A. A. Albert's exceptional simple Jordan algebra. This enables us to explicitly realize the symmetric space F4/Spin(9) as the unit ball in R with boundary S . After decomposing the space of spherical harmonics under the a...

(Ivan Arzhantsev) In the talk of Hirokaki Ishida it was proved that a torus manifold with an (S)-invariant complex structure is equivariantly biholomorphic to a toric manifold (a joint work with Yael Karshon). After the talk I asked whether every action of a compact torus T = (S) on a compact complex manifold M of complex dimension n by holomorphic automorphisms may be extended to an action of ...

M. Brion proved a convexity result for the moment map image of an irreducible subvariety of a compact integral Kähler manifold preserved by the complexification of the Hamiltonian group action. V. Guillemin and R. Sjamaar generalized this result to irreducible subvarieties preserved only by a Borel subgroup. In another direction, L. O’Shea and R. Sjamaar proved a convexity result for the moment...

A complex Lie algebroid is a complex vector bundle over a smooth (real) manifold M with a bracket on sections and an anchor to the complexified tangent bundle of M which satisfy the usual Lie algebroid axioms. A proposal is made here to integrate analytic complex Lie algebroids by using analytic continuation to a complexification of M and integration to a holomorphic groupoid. A collection of d...