AnàlisiSolving inverse spectral problems with Schur's algorithm for bounded analytic functions
Resum: The half-line Dirac operators with $L^2$-potentials can be characterized by their spectral data. It is known that the spectral correspondence is a homeomorphism: close potentials give rise to close spectral data and vice versa. We prove the first explicit two-sided uniform estimate related to this continuity in the general $L^2$-case. The proof is based on an exact solution of the inverse spectral problem for Dirac operators with $\delta$-interactions on a half-lattice in terms of the Schur's algorithm for analytic functions. Joint work with Pavel Gubkin (St. Petersburg).
Models Estocàstics i DeterministesWell-posedness of some dissipative semilinear SPDEs
Resum: I shall report on some recent results on existence and uniqueness of mild solutions to a class of semilinear stochastic evolution equations with additive noise. The linear part of the drift term is the generator of a compact semigroup of contractions, while the nonlinear part is only assumed to be the superposition operator associated to a decreasing function. Generalizations to the case where the semigroup of contractions is not compact will also be discussed.
Teoria d'Anells The Cuntz semigroup of rings with stable rank one
Resum: The Cuntz semigroup of a C*-algebra A with stable rank one enjoys a key structural property due to Coward, Elliott and Ivanescu: the order relation in Cu(A) among countably generated Hilbert A-modules is simply the order of isometric embeddings: $[X] \leq [Y]$ if and only if $X$ is isomorphic to a submodule of $Y$, and $[X] = [Y]$ iff $X$ is isomorphic to $Y$.
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