Activities

• IMAG Functional Analysis Seminar
• Title: Points of continuity in Lipschitz-free spaces
• By Yoël Perreau (University of Tartu, Estonia)
• Abstract: In this talk, I will present some recent results about points of (weak-to-norm) continuity in Lipschitz-free spaces. After recalling some general facts about this notion in Banach spaces, I will give some necessary conditions that an elementary molecule has to satisfy in order to be a point of continuity in a given free space. Then I will provide a complete characterization for these elements in Lipschitz-free spaces over purely 1-unrectifiable (p1u) metric spaces. If time permits, I will also discuss some examples of point of continuity in non p1u compact metric spaces.Based on a work in progress with E. Basset, T. Prochazka and T. Veeorg.

Author: Tjaša Vrhovnik


Location: Seminar Room 2 IMAG


Abstract: Given an open Riemann surface

$M$

, we prove that every nonflat conformal minimal immersion

$M\to {\mathbb{R}}^n$

(

$n\ge 3$

) is homotopic through nonflat conformal minimal immersions

$M\to {\mathbb{R}}^n$

to a proper one. If

$n\ge 5$

, it may be chosen in addition injective, hence a proper conformal minimal embedding. Prescribing its flux, as a consequence, every nonflat conformal minimal immersion

$M\to {\mathbb{R}}^n$

is homotopic to the real part of a proper holomorphic null embedding

$M\to {\mathbb{C}}^n$

. We also obtain a result for a more general family of holomorphic immersions from an open Riemann surface into

${\mathbb{C}}^n$

directed by Oka cones in

${\mathbb{C}}^n$

.

Author : Hector Garcia de Marina (Universidad de Granada)

Title : Spatial awareness within robot swarms: dispersion formation control.

Abstract : In control engineering, formation control scales by focusing on local geometric constraints with neighboring-agent interactions, while natural systems (e.g., insect swarms) seem not to care much about precise geometry but rather prioritize global spatial distributions, forming flexible shapes with dynamic agent densities. Traditional formation control prioritizes precise local relationships; however, this strategy introduces fragility, as a single agent failure can trigger a significant snowball effect. In contrast, biological systems appear more resilient to individual failures and achieve flexibility through loosely defined global patterns.

In this talk, we introduce dispersion formation control—a strategy that shifts focus from controlling local variables to regulating the eigenvalues of the multi-agent spatial covariance matrix. By targeting global dispersion metrics (e.g., variance) rather than enforcing rigid local geometries, individual agent impacts are diluted across the swarm. This swarm-like approach enhances resilience, as agent failures perturb global statistics minimally, unlike traditional multi-robot systems where local errors can cascade. The strategy balances adaptability with robustness, aligning more closely with biological collectives.

Location: Aula A24, Facultad de Ciencias

Author : Jean Mawhin (Université Catholique de Louvain)

Title : Some identities of Jacobi on Jacobians: old and new

Abstract : You can check it here.

• IMAG Functional Analysis Seminar
• Title: Dándole una vuelta a las rotaciones de Mazur
• By Javier Cabello (Universidad de Extremadura)
• Abstract: Let $H$ be a Hilbert space. It is quite clear that its sphere, say $S\subset H$, fulfills that for each $x,y\in S$ there exists a (linear, onto) isometry $T_{x,y}:H\to H$ such that $T_{x,y}(x)=y$. The Banach spaces that fulfil this are called {\em transitive}. It stands to reason that the only separable, transitive Banach space is the Hilbert space $\ell_2$ (needless to say, unique up to isometries). Well, the famous Mazur rotations Problem is to determine whether this is true or not. Among the several properties related to transitivity, today we will focus on the uniform semi-micro transitivity and how this leads to the study ofconvex bodies in finite dimensional spaces.

Conferenciantes:
Simone Ciani (University of Bologna)
Fabio De Regibus (University of Granada)
Umberto Guarnotta (Polytechnic University of Marche)
Francisco J. Reyes-Sánchez (University of Granada)

Horario:
09:45--10:30 Umberto Guarnotta
10:30--11:00 Coffee break
11:00--11:45 Fabio De Regibus
11:45--12:30 Francisco J. Reyes-Sánchez
12:30--13:15 Simone Ciani

Organizadores:
Laura Baldelli
Rafael López Soriano

Libro de resúmenes: Consultar aquí

Póster:
Póster de Young PDEs meeting in Granada

• IMAG Functional Analysis Seminar
• Title: Group-equivariant versions of the Radon-Nikodym property
• By Michal Doucha (Institute of Mathematics of the Czech Academy of Sciences)
• Abstract: I will present several variants of closely related Banach space notions such as the Radon-Nikodym property, the Bishop-Phelps property, dentability, etc., defined in the presence of a continuous action of a topological group on a given Banach space by linear isometries. While in the classical case these notions are equivalent, in the presence of a group action it depends on the group. This is work in progress jointly with Sheldon Dantas, Mingu Jung and Tomáš Raunig.

FIRST TALK: 11:30h

Author : Juan Antonio Villegas

Title : Zonal Function Networks: Super-Resolution approach

Abstract : You can check it here.

SECOND TALK: 12:30h

Author : Plamen Iliev.

Title : Bivariate Bernstein-Szego polynomials.

Resumen : The Bernstein-Szeg˝o measures and polynomials on the real line play an important role in probability, numerical analysis and approximation theory. In this talk, I will define bivariate extensions of these measures and associated spaces of polynomials, and discuss their spectral and characteristic properties. Based on joint work with J. Geronimo.

Location: Seminario 1 IMAG and online in this link.

Título: Mountain Pass solutions for an entire semipositone problem involving the Grushin operator.

Conferenciante: Paolo Malanchini (Università degli Studi di Milano-Bicocca).

Resumen:

For \(N\ge 3\) we study the following semipositone problem$$ -\Delta_\gamma u = g(z) (f(u)- a) \quad \hbox{in $\mathbb{R}^N$}, $$ where \(\Delta_\gamma\) is the Grushin operator $$ \Delta_ \gamma u(z) = \Delta_x u(z) + |x|^{2\gamma} \Delta_y u (z) \quad (\gamma\ge 0), $$ \(g\in L^1(\mathbb{R}^N)\cap L^\infty(\mathbb{R}^N)\) is a positive function, \(a>0\) is a parameter and \(f\) is a continuous function with subcritical and Ambrosetti-Rabinowitz type growth and which satisfies \(f(0) = 0\). Depending on the range of \(a\), we obtain the existence of mountain pass solutions in a suitable Sobolev space associated to the Grushin operator. Finally we study the positivity of the solutions in the degeneracy set.

Toda la información puede encontrarse en:
Seminario de Ecuaciones Diferenciales.

• IMAG Functional Analysis Seminar
• Title: Álgebras de Lie reales simples y sus ideales internos
• By Antonio Fernández López (Universidad de Málaga)
• Abstract: Sea L un álgebra de Lie sobre los complejos del tipo A_l, B_l, C_l, o D_l. En esta charla clasificamos las formas reales de L y sus ideales internos, adoptando un punto de vista distinto del habitual. Derivamos la clasificación de las formas reales, g, de L de dos teoremas de Herstein traducidos a un lenguaje geométrico, lo que nos permite describir los ideales internos en términos algebraicos y geométricos.