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SIMBa: Osculating spaces and Lefschetz properties

SIBMa

El proper dimecres, 14 de novembre, se celebrarà una nova xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Martí Salat Moltó
Universitat: Universitat de Barcelona

Data: Dimecres, 14 de novembre de 2018
Hora: 13:00, cafè; 13:20, xerrada
Lloc: Aula B1 Facultat de Matemàtiques de la Universitat de Barcelona.
Idioma: Castellà

Títol: Osculating spaces and Lefschetz properties
Resum: Let X \in \mathbb{P}^N be an algebraic variety. The sth osculating space of X at a point p \in X is the vector space T_{p}^{(s)}X spanned by all the sth partial derivatives of a local parametrization of X at p. Hence it can be seen as a natural generalization of the well-known notion of tangent space. It is a wide and longstanding problem to study and classify varieties whose osculating space is defective (i.e. it does not reach the maximal dimension).
In the first part of this talk we will recall the notion of osculating space and we will see some examples. In the second part we will explore the connection made by Mezzetti, Ottaviani and Miró-Roig. This connection explains why some varieties have a defective osculating space by means of the –a priori unrelated notion– of the weak Lefschetz property. This result motivates the definition of Togliatti systems. Finally, if the time allows us to do so, we will give an insight to the classification problem of Togliatti systems using combinatorial methods of Toric varieties.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.


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SIMBa: An Introduction to post-quantum cryptography

SIBMa

El proper dimecres, 24 d’octubre, se celebrarà una nova xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Sergi Rovira Cisterna
Universitat: Universitat de Barcelona

Data: Dimecres, 24 d’octubre de 2018
Hora: 12:00, cafè; 12:20, xerrada
Lloc: Aula B1 Facultat de Matemàtiques de la Universitat de Barcelona.
Idioma: Anglès

Títol: An Introduction to post-quantum cryptography
Resum: Quantum Computers exploit quantum mechanical phenomena to solve mathematical problems considered difficult or intractable for conventional computers. Ongoing advances in physics point towards the eventual construction of large-scale quantum computers. If these computers are ever build, this would compromise the confidentiality and integrity of our current digital communications.
Post-Quantum Cryptography studies cryptosystems that can be implemented in a classical computer but for which no efficient cryptanalytic technique using either classical or quantum computers is known.
The goal of this talk is to give a broad overview of the field of Post-Quantum Cryptography and present one cryptosystem believed to be post-quantum. All the necessary notions of classical cryptography will be introduced during the talk.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.


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SIMBa: Invariant Manifolds near L1 and L2 in the Planar Restricted Three-Body Problem

SIBMa

El proper diemcres, 17 d’octubre, se celebrarà una nova xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Gladston Duarte Ferreira
Universitat: Universitat de Barcelona

Data: Dimecres, 17 d’octubre de 2018
Hora: 12:00, cafè; 12:20, xerrada
Lloc: Aula T1 Facultat de Matemàtiques de la Universitat de Barcelona.
Idioma: Castellà

Títol: Invariant Manifolds near L1 and L2 in the Planar Restricted Three-Body Problem
Resum: In this work we investigate the connections between the stable and unstable manifolds of periodic orbits around the points L1 and L2 of the Restricted Three-Body Problem (RTBP). In the Planar Circular RTBP (PCRTBP) we can see, that there is a connection of these manifolds on the phase space of this problem, which means that there is a mechanism of an orbit that goes outside the orbit of one primary (for instance, that describes an orbit close to an ellipse with greater semi-major axis), to go through it and start to describe an orbit inside of it (close to an ellipse with smaller semimajor axis) and/or vice-versa; in other words, this mechanism is a bridge connecting orbits outside with orbits inside. Using some
computer algebra tools we start by computing the normal forms around L1 and L2 to describe periodic orbits around each of these points. After that, with the same tools, we focus on the computation of the stable and unstable manifolds of these orbits and on the searching for connections between them. Time permitting, it will be presented some differences between the PCRTBP and the PERTBP (the E letter standing for ’Elliptic’). Which are the features and the objects in this new problem and what could be used from the PCRTBP what could not.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.


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SIMBa: Lorenz dynamics prevail under compressibility

SIBMa

El proper diemcres, 10 d’octubre, se celebrarà una nova xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Juan Pello García
Universitat: Universitat de Barcelona

Data: Dimecres, 10 d’octubre de 2018
Hora: 12:00, cafè; 12:20, xerrada
Lloc: Aula T1 Facultat de Matemàtiques de la Universitat de Barcelona.
Idioma: Castellà

Títol: Lorenz dynamics prevail under compressibility
Resum: In the present talk we will make the route that goes from the fundamental equations of Fluid Mechanics (continuity equation, Navier-Stokes equations and the conservation of energy law) to the Lorenz equations. Furthermore, knowing the process that led Edward N. Lorenz, in his studies on convection phenomena in the upper layers of the atmosphere, to the discovery in 1963 of the chaotic dynamics of the three-dimensional system it is possible to propose new and consistent problems, on the one hand, in the modi cation of the approximations made, and on the other hand, in the mathematical study of other more complex possibilities, such as the obtaining of new decoupled di erential equation systems, with a larger number of state variables. Hereafter, we set out to reconstruct the process that led to Lorenz system also setting the basis for the development of these other approaches.  Moreover, in relation to the modi cation of the approximations made, we have advanced in the process of obtaining the Lorenz-type equations in the case in which the coecient of isothermal compressibility is not neglected.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.


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SIMBa: Una conjetura clásica sobre teoría de nudos

SIBMa

El proper diemcres, 20 de juny, se celebrarà una nova xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Marithania Silvero Casanova
Universitat: Universitat de Barcelona

Data: Dimecres, 20 de juny de 2018
Hora: 12:00, cofee break; 12:15, xerrada
Lloc: Aula T1 Facultat de Matemàtiques de la Universitat de Barcelona.
Idioma: Castellà

Títol: Una conjetura clásica sobre teoría de nudos
Resum: Los enlaces alternativos son pseudoalternantes. En 1983 Louis Kauffman conjeturó que ambas clases son iguales. Posteriormente, en 1989, se introduce la familia de enlaces homogéneos, probándose que contienen a la familia de enlaces alternativos, y que están contenidos en la de pseudoalternantes. La conjetura de Kauffman es, por tanto, equivalente a la igualdad entre estas tres clases de enlaces. Algunos autores han usado los conceptos anteriores como sinónimos, dando por cierta la conjetura.

En esta charla se refuta la conjetura de Kauffman, presentando dos contraejemplos. Probamos también que, en el caso particular de nudos de género 1, la conjetura es cierta (no siendo posible aumentar el número de componentes del enlace o el género); las técnicas empleadas para ello permiten dar una descripción explícita de la familia de nudos homogéneos de género 1.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.


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SIMBa: La ecuación del calor con ruido fraccionario blanco

SIBMa

El proper divendres, 8 de juny, se celebraran dues xerrades del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Adrián Hinojosa Calleja
Universitat: Universitat de Barcelona

Data: Divendres, 8 de juny de 2018
Hora: 12:15, cofee break; 12:30, xerrada
Lloc: Aula T1 Facultat de Matemàtiques de la Universitat de Barcelona.
Idioma: Castellà

Títol: La ecuación del calor con ruido fraccionario blanco
Resum: The main goal of this talk is to introduce the stochastic heat equation u_{t}-\Delta u=\dot{F} in (0,T)\times \mathbb{R}^{d}, with vanishing initial conditions, driven by a Gaussian fractional-white noise F.

 

We will start with the basics studying first the deterministic heat equation and inspired on it we will analize how is it possible to generalize this idea to construct an stochastic solution.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.


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SIMBa: Topological operators for partial differential equation modeling i Fourier integral operators, wave equation and maximal operators

SIBMa

El proper dimecres, 6 de juny, se celebraran dues xerrades del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Camilo Torres Rey
Universitat: Universitat de Barcelona

Data: Dimecres, 6 de juny de 2018
Hora: 11:15
Lloc: Aula T1 Facultat de Matemàtiques de la Universitat de Barcelona.
Idioma: Castellà

Títol: Topological operators for partial differential equation modeling
Resum: In matters of Computational Simulation, Continuous models seem invariably affected by issues that compromise their quality (accuracy), cost (machinewise), and time-complexity. Currently used methods can attack some of these issues, but fail to provide a rationale to study their nature and entanglements, showcasing an epistemological problem within Computer Sciences, a fracture between mathematics and computation, and a gap between software engineers and scientists. Under the right mindset, algebraic topology provides a solid foundation on which to redefine the notion of differentiability in a natural fashion for computer scientists, shedding a new light over the pervasiveness of the quality-time-cost entanglement.

With this in mind, the Discrete First Approach is an attempt to generalize two non-mainstream simulation techniques for continuous models, where the rigor of classical computer sciences is maintained, while at the same time enriched by the introduction of a formal treatment of some elements of algebraic topology, that promises a restatement of differential constructions in a computational setting, compliant with standards and practices of algorithm design and Software engineering.

Speaker: Ramesh Manna
Universitat: TIFR Centre For Applicable Mathematics

Data: Dimecres, 6 de juny de 2018
Hora: 12:00, coffee break ; 12:15, xerrada
Lloc: Aula T1 Facultat de Matemàtiques de la Universitat de Barcelona.
Idioma: Anglès

Títol: Fourier integral operators, wave equation and maximal operators
Resum: The main goal of this talk is to present several applications in the theory of Fourier integral operators (FIOS). The theory of FIOS was developed by H ̈ormander (1971).

It will be given an overview of the local smoothing results which have been proven to date. Finally, it will be discussed the local smoothing of Fourier integral operators with application to the wave equation and spherical maximal operator

 

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.