seminar

GEOMETRY SEMINAR

Speaker: Changhwa Woo (Pukyong National University)

Abstract: In this talk, we investigate a pseudo-Ricci-Bourguignon soliton on real hypersurfaces in the complex two-plane Grassmannian \(G_2({\mathbb C}^{m+2})\). By using pseudo-anti commuting Ricci tensor, we give a complete classification of Hopf pseudo-Ricci-Bourguignon soliton real hypersurfaces in \(G_2({\mathbb C}^{m+2})\) . Moreover, we have proved that there exists a non-trivial classification of gradient pseudo-Ricci-Bourguignon soliton \((M, {\xi}, {\eta}, {\Omega}, {\theta}, {\gamma}, g)\) on real hypersurfaces with isometric Reeb flow in the complex two-plane Grassmannian \(G_2({\mathbb C}^{m+2})\). In the class of contact hypersurface in \(G_2({\mathbb C}^{m+2})\), we prove that there does not exist a gradient pseudo-Ricci-Bourguignon soliton in \(G_2({\mathbb C}^{m+2})\)

GEOMETRY SEMINAR

Speaker: Young Jin Suh (Kyungpook National University)

Abstract: In this talk, we give a complete classification of Yamabe soliton, Ricci-Bourguignon soliton on real hypersurfaces in complex hyperbolic quadric \({Q^m}^*\) and complex hyperbolic space \(CH^m\). Next as applications, we also give a complete classification of gradient Yamabe soliton and gradient Ricci-Bourguignon soliton on real hypersurfaces in complex hyperbolic quadric \({Q^m}^*\) and complex hyperbolic space \(CH^m\). Related to this topics, finally we want to mention soliton problems and Fisher-Marsden conjecture in other Hermitian symmetric spaces like complex two-plane Grassmannians, complex hyperbolic two-plane Grassmannians, complex quadric or etc.

SEMINARIO DE JÓVENES INVESTIGADORES

Conferenciante: Jose Manuel Muñoz Fuentes (UGR)

Abstract: The theory on error-correcting block codes focuses on how to identify and, if possible, fix errors that might be inserted into fixed-length messages while being sent or stored. Rank codes, which have notable applications on network coding, are known to provide a convenient way to do so. Our approach generalizes the classical family of maximum-rank-distance Gabidulin codes into a larger one, which is endowed with a Hartmann-Tzeng-like lower bound on their rank (and Hamming) distance. For these codes, we develop a syndrome-based error correction algorithm up to the known Hartmann-Tzeng-like bound by decomposing the error-correcting problem into solvable solvable linear algebra ones, including the skew-feedback shift-register synthesis problem. This approach also generalizes previous work on error correction algorithms over skew Reed-Solomon codes (that is, skew-cyclic codes with a Reed-Solomon-like defining set), as those are a subset of the ones studied through our approach.

GEOMETRY SEMINAR

Conferenciante: João Paulo dos Santos (Universidade de Brasilia)

Abstract: A smooth function \(f\) on a Riemannian manifold \(\widetilde{M}\) is isoparametric if \(|\nabla f|\) and \(\Delta f\) are constant on the level sets of \(f\). A hypersurface \(M \subset \widetilde{M}\) is an isoparametric hypersurface if it is a regular level set of an isoparametric function defined on \(\widetilde{M}\). When the ambient space is a space form \(\mathbb{Q}^{n}_c\), the definition of isoparametric hypersurface is equivalent to saying that the hypersurface has constant principal curvatures. However, in arbitrary ambient spaces of nonconstant sectional curvature, the equivalence between isoparametric hypersurfaces and hypersurfaces with constant principal curvatures may no longer be true. In this talk, it will be presented characterization and classification results on isoparametric hypersurfaces with constant principal curvatures in the product spaces \(\mathbb{Q}_{c_{1}}^2 \times \mathbb{Q}_{c_{2}}^2\), for \(c_{i} \in \{-1,0,1\}\) and \(c_1 \neq c_2\). The talk is based on a joint work with João Batista Marques dos Santos.

SEMINARIO DE ÁLGEBRA

Conferenciante: Amela Muratović-Ribić

Abstract: In cryptology and coding theory, strings are viewed as elements of vector space \(\mathbb{Z}_2^n\). Given is definition of Boolean function and its directional derivative. It is important for cryptology as it is a basis for so called differential cryptoanalysis. If function is as far as possible from the lieanr function it is called perfect nonliner and it is equivalent with bent functions. In Bollean case equvivalent is almost perfect nonlinear function. In cryptology these are used for a construction of S-boxes and in coding theory for construction of the codes with a spefific minimal distance. We will give introductionary lecture on bent functions and vectorial bent abd the most important of its constructions.

SEMINARIO DE ÁLGEBRA

Conferenciante: Amela Muratović-Ribić

Abstract: We will show a lot of pictures of Bosnia and Herzegovina and Sarajevo, with a short overview of University of Sarajevo. We will introduce Latin squares, orthogonal Latin squares and Knut Vic designs with applications, over finite groups and later over finite fields. We will define a complete mapping which is used for construction of the orthogonal Latin squares and we will give many constructions of strong complete mappings used for construction of Knut Vic designs.

CICLO DE CONFERENCIAS ESTADÍSTICA Y CIENCIA DE DATOS PATRICIA ROMÁN

Conferenciante: Christian Leonardo Urbano León (Departamento de Estadística e Investigación Operativa, UGR)

Resumen: El Análisis de Datos Funcionales engloba una gran variedad de métodos estadísticos en los que los datos proporcionan información sobre curvas, superficies o cualquier otra función que varía de forma continua. En la Universidad de Granada, el grupo Modelización y Predicción con Datos Funcionales (FQM 307) de la Junta de Andalucía, dirigido por el Profesor M.J. Valderrama, lleva más de 20 años aportando metodologías en este campo en el Dpto. de Estadística e Investigación Operativa. Durante todo este tiempo, se han realizado aportaciones en este campo proporcionando así, métodos de estimación del Análisis en Componentes Principales Funcional (FPCA) (Ocaña-Lara et al., 1999), proponiendo modelos lineales de predicción en componentes principales (PCP) para estimar un proceso estocástico a partir de otro correlacionado (Aguilera et al., 1999), introduciendo los modelos de regresión logística funcional en componentes principales para predecir una variable de respuesta binaria a partir de un predictor funcional (Escabias et al., 2004), proponiendo distintas formas de suavizado con splines penalizados (P-splines) de la regresión PLS funcional con respuesta escalar (Aguilera-Morillo et al., 2013), o extendiendo métodos de ANOVA funcional para el caso de medidas repetidas (Acal y Aguilera, 2022).

Siguiendo con la línea del grupo, en esta conferencia se pretende mostrar los últimos resultados obtenidos con el objetivo de proponer solución al modelo funcional de respuesta binaria cuando las variables funcionales no se consideran independientes, lo que se conoce como modelos con medidas repetidas.

SEMINARIO DE JÓVENES INVESTIGADORES

Conferenciante: Niccolò Tassi (Universidad de Granada)

Absract: We present a nonlocal Fokker-Planck equation in which we can estimate the speed of convergence to equilibrium independent of the non-locality of the equation. This uniform estimate cannot be easily obtained with standard inequalities or entropy methods, but can be obtained through the use of Harris’s theorem, a tool coming from porbability. We point out some interesting links to quantitative versions of the central limit theorem in probability. We also carry out a study of the properties of the stationary states of the problem, especially the behavior of its tails using various techniques.

FUNCTIONAL ANALISYS SEMINAR

Conferenciante: Prof. Matej Bresar

Abstract: ConferenceBresar2023

SEMINARIO DE GEOMETRÍA

Conferenciante: Maria Andrade (Universidade Federal de Sergipe)

Abstract: One of the most extensively studied topics in Differential Geometry is minimal surfaces. This subject has connections with a wide range of mathematics areas, such as complex analysis, partial differential equations and topology. A classic problem in this context is the Plateau problem and recently much attention has been given to problems with the free boundary condition. In this talk, we will present some results about classification for constant mean curvature (CMC) surfaces with the free boundary condition in certain spaces. This is a joint work with Ezequiel Barbosa (UFMG) and Edno Pereira (UFSJ).