Activities

• IMAG Functional Analysis Seminar
• Title: On some geometric properties of Banach spaces
• By Joanna Markowicz (University of the National Education Commission, Krakow, Poland)
• Abstract: The aim of the talk will be to present some results concerning selected properties of direct sums of Banach spaces and their applications. Among those properties we will study for instance uniform convexity, uniform smoothness, uniform nonsquareness, Opial properties and the García-Falset coefficient. In the results connected to geometric properties of direct sums of Banach spaces there are considered direct sums \(Y=\left(\sum_{i\in I}X_i\right)_E\), where \(\{X_i\}_{i\in I}\) is a family of Banach spaces and the norm in the direct sum comes from the Banach lattice $E$ that is named a substitutional space for the direct sum.

  In addition, we will study Banach lattices and their properties connected to the order such as uniform monotonicity and order uniform smoothness

  The talk will also consider preserving uniform convexity and the Opial property in interpolation spaces constructed with the use of a general abstract discrete \(K\)-method based on a space with an unconditional basis.

📅 martes 18 de noviembre — 13:00

📍 Aula A25, Facultad de Ciencias

👤Conferenciante: Roman Shvydkoy (University of Illinois at Chicago)

📖 Título: On regularity and asymptotics of kinetic alignment models

📄 Resumen: In this talk we discuss wellposedness, regularization, and relaxation for a broad class of Fokker-Planck-Alignment models which appear in collective dynamics and many other applications. The main feature of these results, as opposed to previously known ones, is the lack of regularity or no-vacuum requirements on the initial data. With a particular application to the classical kinetic Cucker-Smale model, we demonstrate that any bounded data with finite high moment, $(1+ |v|^q) f_0 \in L^1$, $f_0 \in L^\infty$,  gives rise to a global instantly smooth solution, satisfying entropy equality and relaxing exponentially fast. The proof is based on hypocoercivity techniques and DiPerna-Lions renormalization.

• Title: Index, nullity and other topics for minimal surface doublings
• By: Nicolaos Kapouleas
• Abstract: I will discuss recent and ongoing work in these directions, including results with J. Zou on index and nullity, and results with P. McGrath on Yau questions.

• IMAG Functional Analysis Seminar
• Title: Bohr's inequalities on a bounded balanced domain
• By Tatsuhiro Honda (Senshu University, Japan)
• Abstract: In 1914, H. Bohr proved that if the power series \(f(\zeta)=\sum_{j=0}^{\infty}a_j\zeta^j\) converges in \(\mathbb{U}\), where (\mathbb{U}\) is the unit disc in \(\mathbb{C}\), and \(|f(\zeta)|<1\) holds for all \(\zeta \in \mathbb{U}\), then the inequality $$\sum_{j=0}^{\infty}|a_j|r^j\leq 1$$ holds for all \(\zeta\) with \(|\zeta|=r\leq 1/6\). The largest \(r\leq 1\) such that the above equality holds is called the Bohr radius for the unit disc case. The fact that the constant \(1/3\) is best possible is showen later. In this talk, we will discuss to generalize some results about Bohr's radii for a holomorphic mapping to higher dimensional complex Banach spaces.This work is partially supported by JSPS KAKENHI Grant Number 23K03136.

• IMAG Functional Analysis Seminar
• Title: Radio grande versus diámetro pequeño
• By Esteban Martínez Vañó (UGR)
• Abstract: En este seminario construiremos un ejemplo de un espacio de Banach donde todos los abiertos débiles de su bola unidad tienen radio uno, el máximo posible, pero en el cuál existen slices de su bola unidad de diámetro arbitrariamente cercano a uno.

• Seminario de Ecuaciones Diferenciales

• Conferencia: 12 horas día 29 de octubre (Sala de Conferencias, IMAG)
• Conferenciante: Dmitriy Kim, Kazakh National University, Kazakhstan
• Título: Ruin probability for a process with switching
• Short bio: Dmitriy Kim received the Bachelor degree in mathematics from Kazakh National University, Kazakhstan, in 2000, the Master's and Doctoral degrees in probability theory and mathematical statistics from Novosibirsk State University, Russia, in 2002 and 2005, respectively. He has been a researcher at a number of Kazakhstani and European universities and since 2017 he has been working at the School of Digital Technologies, Narxoz University, Almaty, Kazakhstan. Dmitriy Kim specializes in the boundary problems for random processes and in application of probabilistic methods for modeling complex systems.
• Abstract: We consider a class of stochastic processes defined by a partition of the real line into two disjoint sets, each associated with its own probability distribution. When the process takes a value in one of these sets, its subsequent increment follows the distribution corresponding to that set. Such processes are referred to as a processes with one level of switching. The ruin probability is studied for a process with one level of switching between two independent Lévy processes, one being spectrally negative and the other a compound Poisson process with drift. Explicit representations for the ruin probability are obtained in terms of ladder height distributions. As a consequence, results are derived for a risk process in which the premium rate and the claim size distribution depend on whether the current reserve lies above or below a specified threshold.

• Ponente: Miguel Ortega Titos
• Título: Experimentando con Gems de Gemini y NotebookLM de Google
• Enlace web: https://wpd.ugr.es/~geometry/seminar/es/home
• Hora: de 12:30 a 13:30
• Lugar: Seminario 1

• IMAG Functional Analysis Seminar
• Title: M-ideals of compact operators
• By Manwook Han (Chungbuk National University, Republic of Korea)
• Abstract: A closed subspace J of a Banach space X is called an M-ideal if and only if X^* = J^* \oplus_1 J^{\perp}. Note that if X = J \oplus_{\infty} J′, for some subspace J′ of X, then J is an M-ideal in X. However, the converse does not hold in general. Indeed, for real numbers p, q satisfying 1 < p ≤ q < ∞, the space K(\ell_p, \ell_q) of compact operators from \ell_p to \ell_q is an M-ideal in the space L(\ell_p, \ell_q) of bounded linear operators from \ell_p to \ell_q. On the other hand, L(\ell_p, \ell_q) cannot be represented as an \ell_{\infty}-sum of K(\ell_p, \ell_q) and any other subspace of L(\ell_p, \ell_q). In this talk, I will introduce several known properties that arise in such cases and present new results that connect this study to the theory of norm-attaining operators.