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ALGEBRAIC STRUCTURES ON THE TOPOLOGY OF MODULI SPACES OF CURVES AND MAPS
MODULI SPACES CURVES AND MAPS
2015/7/14
We discuss selected topics on the topology of moduli spaces
of curves and maps, emphasizing their relationwith GromovWitten theory and integrable systems
In the theory of schemes, faithfully
at descent is a very powerful tool. One wants a descent theory
not only for quasi-coherent sheaves and morphisms of schemes (which is rather elementary), but al...
Andr´es Navas asked us if there is a fixed point theorem for all isometries of L1 that preserve a given bounded set. Unlike many known cases where a geometric argument applies, there is a fundam...
Strichartz estimates on asymptotically de Sitter spaces
Strichartz estimates Sitter spaces
2010/11/24
In this article we obtain two families of weighted Strichartz estimates with derivative loss for the Klein-Gordon equation on asymptotically de Sitter spaces, one for nonnegative $\lambda$ and a stro...
Classifying spaces of degenerating mixed Hodge structures, III: Spaces of nilpotent orbits
mixed Hodge structures Spaces of nilpotent orbits
2010/11/23
We construct toroidal partial compactifications of the moduli spaces of mixed Hodge structures with polarized graded quotients. They are moduli spaces of log mixed Hodge structures with polarized grad...
Stratified spaces constitute a Fraïssé catego
Stratified spaces constitute Fraï ssé catego
2010/11/23
We prove that stratified spaces and stratified pseudomanifolds satisfy categorical Fra\"{\i}ss\'e properties. This result was presented for the First Meeting of Logic and Algebra in Bogot\'a, on Sept...
Stability of symmetric spaces of noncompact type under Ricci flow
symmetric spaces noncompact type under Ricci flow
2010/11/23
In this paper we establish stability results for symmetric spaces of noncompact type under Ricci flow, i.e. we will show that any small perturbation of the symmetric metric is flown back to the origin...
An algorithm for the Cartan-Dieudonné theorem on generalized scalar product spaces
the Cartan-Dieudonné theorem scalar product
2010/11/9
We present an algorithmic proof of the Cartan-Dieudonn\'e theorem on generalized real scalar product spaces with arbitrary signature. We use Clifford algebras to compute the factorization of a given ...
Polynomial estimates for c-functions on reductive symmetric spaces
Polynomial c-functions reductive symmetric spaces
2010/11/8
The c-functions, related to a reductive symmetric space G/H and a fixed representation of a maximal compact subgroup K of G, are shown to satisfy polynomial bounds in imaginary directions.
Local properties of Hilbert spaces of Dirichlet series
Local properties Hilbert spaces Dirichlet series
2010/11/19
We show that the asymptotic behavior of the partial sums of a sequence of positive numbers determine the local behavior of the Hilbert space of Dirichlet series defined using these as weights. This ex...
Polynomial Approximation in Sobolev Spaces on the Unit Sphere and the Unit Ball
Polynomial Sobolev Spaces Unit Sphere Unit Ball
2010/11/18
This work is a continuation of the recent study by the authors on approximation theory over the sphere and the ball. The main results define new Sobolev spaces on these domains and study polynomial ap...
Decompositions of looped co-H-spaces and applications
Decompositions of looped co-H-spaces and applications
2010/11/11
We prove two homotopy decomposition theorems for the loops on co-H-spaces, including a generalization of the Hilton-Milnor Theorem. These are applied to problems arising in algebra, representation the...
Let $(X,\mathcal{O}_X(1))$ be a polarized smooth projective variety over the complex numbers. Fix $\mathcal{D}\in \mathrm{coh}(X)$ and a nonnegative rational polynomial $\delta$. Using GIT we contruct...
Geometry of the Banach spaces C(beta mathbb N times K, l_p) for compact metric spaces K
Geometry of the Banach spaces C compact metric spaces K
2010/11/19
In this paper we provide the complete isomorphic classification of the spaces C(beta mathbb N times K, l_p) of all continuous l_p-valued functions, 1 <= p < infinity, defined on the topological produ...
In 1962, H. de Vries proved a duality theorem for the category {\bf HC} of compact Hausdorff spaces and continuous maps. The composition of the morphisms of the dual category obtained by him differs ...