Heterodimensionality of skew-products with concave fiber maps.

Event Date: Oct 28, 2020 in Dynamical Systems, Seminars

  ABSTRACT: I will discuss examples of skew-products with concave interval fiber maps over a certain subshift. Here the subshift occurs as the projection of those orbits that stay in a given neighborhood and gives rise to a new type of symbolic space which is (essentially) coded. The fiber maps have expanding and contracting regions. As a consequence, the skew-product dynamics has pairs of horseshoes of different types of hyperbolicity. In some cases, they dynamically interact due to the superimposed effects of the (fiber) contraction and expansion, leading to nonhyperbolic dynamics...

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Modified scattering for the nonlinear Schrödinger equation in an external field.

Event Date: Oct 27, 2020 in Differential Equations, Seminars

Abstract: In this talk, we consider the cubic nonlinear Schrödinger equation with an external potential. We prove the existence of modified scattering for this model, that is, linear scattering modulated by a phase. Our approach is based on the spectral theorem for the perturbed linear Schrödinger operator and a factorization technique, which allows us to control the resonant nonlinear term. This approach requires a detailed and subtle study of the low-energy properties of the scattering data. Therefore, we study the cases of generic and exceptional potentials separately. The exceptional...

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Strategic and Structural Aspects of Bitcoin Mining.

Event Date: Oct 21, 2020 in ACGO, Seminars

Abstract: Just over a decade ago, Satoshi Nakamoto published a landmark white paper outlining the backbone protocol to Bitcoin, arguably the world’s first mainstream digital currency. Through the Nakamoto protocol and blockchain technology, users can reliably agree upon a common transaction history maintained by miners on the public Bitcoin ledger in a decentralised and anonymous fashion. This is possible in part because agents within the protocol are assumed to be strategic rather than adversarial—a fair assumption when creating a ledger for currency. The Nakamoto protocol is...

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Variational principles and equilibrium states for (semi)group actions.

Event Date: Oct 21, 2020 in Dynamical Systems, Seminars

ABSTRACT: The search for a thermodynamic formalism for dynamical systems aims to prove the existence of invariant probability measures which maximize the topological pressure, besides reporting on their statistical properties. A special feature of the classical thermodynamic formalism for Ruelle expanding maps, which becomes an important tool in many applications including applications to multifractal analysis or large deviations, is the upper-semicontinuity of the Kolmogorov-Sinai entropy map. Simple examples illustrate that this property breaks down in the absence of expansiveness. In this...

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Simulating Microenvironmental effects in tumor progression.

Event Date: Oct 20, 2020 in Differential Equations, Seminars

Abstract. In this presentation, we will see the preliminary numerical exploration of a mathematical approach that captures and explores a wide range of mechanisms and biological variabilities in tumor progression is presented. Precisely, the mathematical model captures cell-cell interactions including micro-environment effects in solid tumor progression. The biological principle consists in to assume that the tumor cells interact with Tumor-Associated Macrophages, and simultaneously with the extracellular matrix. Such two different mechanisms are modeled coupling the parabolic-elliptic...

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Embedding de árboles en grafos expansores.

Event Date: Oct 15, 2020 in Seminario de Grafos, Seminars

Resumen: Vamos hablar sobre el paper “Tree Embeddings”,  de Penny E. Haxell. En este paper, Penny muestra un teorema general para embedding de árboles en grafos expansores, y como aplicación se probará un caso particular de la conjetura de Erdős-Sós, que pregunta si un grafo G con grado promedio a lo menos t-1 contiene todo árbol T con t aristas como subgrafo. Ella muestra que la conjetura es verdad si el grafo G no contiene K_{2,r}.

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