The problem of determining the homotopy type of a simplicial complex is very much simplified if the complex happens to be shellable. This means that there exists an enumeration of the facets of a particularly favourable type. But when is a simplicial complex shellable? In general, there is no...
Exponential families are a particular class of statistical manifolds which are important in statistical inference, and which appear very frequently in statistics. For example, the set of normal distributions, with mean $\mu$ and deviation $\sigma$ forms a 2-dimensional exponential family.
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Gromov width of a symplectic manifold M is a supremum of capacities of balls that can be symplectically embedded into M. The definition was motivated by the Gromov's Non-Squeezing Theorem which says that maps preserving symplectic structure form a proper subset of volume preserving maps.
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The Monopole (Bogomolnyi) equations are Geometric PDE in 3 dimensions that admit generalizations to Higher dimensional manifolds with special structures on them. Calabi Yau and G_2 manifolds are the main candidates for interesting solutions to these equations. There are several conjectural...
We show that the Reeb flow of every contact form on the tight three-sphere has at least two geometrically distinct periodic orbits. This result was obtained recently by Cristofaro-Gardiner and Hutchings using embedded contact homology but our approach instead is based on cylindrical contact...
Rigidity of Lagrangian intersections play a fundamental role in symplectic geometry and topology. In this talk, after a general introduction, I will address a natural Lagrangian intersection problem in the context of toric symplectic manifolds: displaceability of torus orbits. The emphasis will...
Sala M031. Será servido café depois da palestra (15h30-16h00).
Uma equação diferencial complexa é localmente dada por um campo de vectores da forma F(x,y)d/dx+G(x,y)d/dy, x,y∈C. Alternativamente essa equação pode ser pensada como uma folheação holomorfa singular definida localmente pela 1-forma F(x,y)dy−G(x,y)dx. Nesta palestra consideraremos o...
A conjecture of Victor Ivrii (1980) says that in every billiard with smooth boundary the set of periodic orbits has measure zero. This conjecture is closely related to a conjecture of Hermann Weyl (1911) from the spectral theory. The particular case of Ivrii’s conjecture for triangular orbits was...
I will present some recent results on symplectic invariants concerning the possibility of embedding a given set in another one, discussing their relevance for conservative dynamics.