Title: Macroscopic limits of active matter systems .
Abstract:
Active matter systems consist of large collections of self-propelled particles and arise in a wide range of biological and physical contexts, including bird flocks, fish schools, and bacterial suspensions. Unlike passive systems, such particles can exhibit phase separation even in the absence of attractive interactions.
In this talk, the speaker will introduce stochastic particle models for active matter, focusing on systems of interacting active Brownian particles subject to purely repulsive forces. Then, the speaker will discuss several approaches to derive macroscopic descriptions as partial differential equations. Finally, the speaker will present results on the stability and analytical properties of one such macroscopic model.
Speaker: Professor Nikolaos Limnios (Université de Technologie de Compiègne, Sorbonne University Alliance)
Title: Normal deviation of Gamma Processes in Semi-Markov Random Media.
Abstract:
Gamma processes are a special case of subordinators (increasing Lévy processes). Their increasing nature makes them particularly well-suited for modeling risk insurance problems of cumulative claims (see, for example, Risk Theory with the Gamma Process (177–192)), monotonic degradation (see, for example, Survival in Dynamic Environments (86–103)), and so on. In the latter reference, the authors use the gamma process to model cumulative claims in risk processes. They also tabulated the probabilities of ruin for the standardized gamma process.
This presentation follows on from article Diffusion Approximation of Gamma Processes in Semi-Markov Random Media. We consider gamma processes in random media (environment) represented by semi-Markovian processes. We approximate these gamma processes using diffusion processes. We first obtain an average result, which will serve as an equilibrium, and then the diffusion approximation. This is a diffusion approximation with equilibrium or normal deviation of the gamma process in semi-Markovian random media. The tools used here differ from those employed in the case of Markov (see a previous article by the first author [Normal Deviation of Gamma Processes in Random Environment With Applications]) because we do not have semigroups. Applications are also discussed.
Title: On existence and concentration phenomena for Kirchhoff type problems.
Abstract:
This talk focuses on the existence, asymptotic behaviour and local uniqueness of solutions for Kirchhoff type equations and constrained minimizers of Kirchhoff type energy functionals. Four main results are presented.
First, the existence of multi-peak solutions for a singularly perturbed Kirchhoff equation is established via variational method. Second, for a Kirchhoff equation with a radially symmetric potential in the whole space, the existence of infinitely many non-radial solutions is proved by means of finite dimensional reduction method. Third, the concentration behavior and local uniqueness of constrained minimizers for a Kirchhoff energy functional are investigated. Fourth, the existence and asymptotic behaviour of constrained minimizers are studied for a Kirchhoff energy functional with a degenerate potential. These results characterize the solution structure and concentration phenomena for Kirchhoff elliptic problems under nonlocal effects. These are joint works with Lu Lu, Wei Shuai and Chun-Lei Tang.
Title: The nonlinear Shrödinger equation on products of R^N and compact metric graphs .
Abstract:
The study of the nonlinear Shrödinger equation on non-smooth structures has attracted increasing interest in recent years. In this talk, I will present existence results for mass-constrained minimizers of the nonlinear Shrödinger energy on the product of R^N with a compact metric graph. In particular, I will introduce the variational framework, including partial rearrangements and Gagliardo-Nirenberg inequalities. Moreover, I will describe the phenomenon of dimensional reduction, namely, when the minimizers do not depend on the graph variable. This is a joint research with Nicola Soave and Gianmaria Verzini.
Speaker: Yexuan Li, North University of China (China).
Title: The relative Auslander-Reiten theory over an infinite-dimensional coalgebra.
Abstract:
In this talk we discuss three aspects. Firstly, we focus on the higher-dimensional Auslander-Reiten theory for infinite-dimensional coalgebras. We introduce the n-transpose of finitely n-copresented comodules and establish the n-Auslander-Reiten formula on n-cluster-tilting subcategories of comodule categories. Secondly, we introduce the Gorenstein transpose via a minimal Gorenstein injective copresentation of a quasi-finite comodule, compare it with the classical transpose, and construct the almost split sequences in terms of the Gorenstein transpose. Finally, we further generalize the classical transpose to the T-transpose via a semidualizing bicomodule T, discuss its homological properties, establish a Foxby equivalence, and characterize T-reflexive comodules.
Title: Elliptic Helicoidal Translators in Minkowski 3-space.
Abstract:
In this talk, we study elliptic helicoidal translating solitons of the mean curvature flow in three-dimensional Minkowski space, that is, helicoidal translators whose axis is timelike. By expressing the generating curve in terms of its Frenet frame, we reformulate the translator equation in terms of curvature and support functions, obtaining a planar system of ordinary differential equations. We then employ techniques from the qualitative theory of dynamical systems, together with an inversion that transforms the dynamics at infinity into a bounded region, to investigate the equilibrium points and the global behavior of the phase portrait. A bifurcation occurs at the critical pitch value $h=2$, where the number of equilibrium points increases from two to six. This analysis leads to a complete classification of the corresponding translating solitons and a description of their causal characters. Our results illustrate how dynamical systems techniques provide an effective framework for understanding the geometry and global structure of helicoidal translators in Lorentzian settings.
Speaker: Misael E. Marriaga (Universidad Rey Juan Carlos, Madrid, Spain).
Title: Generalized symmetric classical orthogonal polynomials in two variables.
Abstract:
In this talk I will discuss bivariate symmetric orthogonal polynomials governed by reflection-type interaction weights. In several variables, the geometry of the domain and the symmetry of the weight determine not only the orthogonal basis, but also the natural differential operators acting on it. I will focus on weights with singular interaction factors along reflection walls and on the corresponding orthogonality problems on fundamental chambers.
The main theme is an operator-theoretic construction of these systems. For product domains associated with the classical Hermite, Laguerre and Jacobi weights, for the unit disk through generalized Zernike polynomials, and for the unit triangle with Jacobi-type weights, the symmetric orthogonal families arise as eigenfunctions of self-adjoint second-order differential operators.
I will explain how lowering and raising operators shift degrees and parameters, and how their compositions produce additional commuting operators. The passage to elementary symmetric variables plays a central role: apparent rational singularities disappear and the operators acquire polynomial coefficients. This leads to explicit descriptions of the differential-operator algebras for which the transformed polynomials form a joint eigenbasis, revealing a common Koornwinder-type structure behind these bivariate models with interaction terms.
Joint work with Miguel A. Piñar and Gema Alhama (Universidad de Granada, Granada, Spain).
Second talk
Time: 18:30h.
Speaker: Cristina Rodríguez Perales (Universidad de Almería, Spain).
Title: Nevai-Sobolev orthogonal polynomials: zeros, local asymptotics and differential properties.
Abstract:
In this talk, we consider the orthogonal polynomials \(\{q_n\}_{n\geq 0}\) with respect to a Sobolev inner product involving the Freud weight \(\exp(-x^4)\). This weight is a particular case of the Freud weights and, due to its historical relevance, we will refer to it as Nevai weight. So that, we consider the inner product
Our first objective is to study the local asymptotics known as Mehler--Heine asymptotics for this family of polynomials. Moreover, this result together with the well-known Hurwitz's Theorem allows us to establish the asymptotic behavior of the zeros of these polynomials. Motivated by this consequence, we also address the problem of computing the zeros of the polynomials \(\{q_n\}_{n\geq 0}\). With that purpose, we construct a generalized eigenvalue problem from the five-term recurrence relation satisfied by these polynomials, so that the computation of the zeros is equivalent to computing the generalized eigenvalues. We also present numerical experiments illustrating the computation of the zeros for different values of \(\lambda\). Finally, if we have time we will deduce the fourth-order differential equation satisfied by these polynomials.
Joint work with Juan F. Mañas-Mañas and Juan J. Moreno-Balcázar.
A. Cachafeiro, F. Marcellán, J. J. Moreno--Balcázar (2003).
On asymptotic properties of Freud--Sobolev orthogonal polynomials, J. Approx. Theory 125, 26--41.
J. F. Mañas-Mañas, J. J. Moreno-Balcázar, C. Rodríguez-Perales (2026).
Nevai--Sobolev orthogonal polynomials, Mediterr. J. Math. 23, 21.
J. F. Mañas-Mañas, J. J. Moreno-Balcázar, C. Rodríguez-Perales (2026).
Zeros of Nevai--Sobolev orthogonal polynomials, Notebook Archive.
https://notebookarchive.org/2026-07-0gvs3pi
P. Nevai (1983).
Orthogonal polynomials associated with \(\exp(-x^4)\), Proc. Canad. Math. Soc. 3, 263--285.
Funding:
Work financed by the PPIT-UAL grant, by MICIU/AEI/10.13039/501100011033 grant PID2025-170285NB-I00; and Research Group FQM--0229 of the University of Almería.
Title: Transnational Meeting – Math4U Supports Teachers and Students.
Abstract: The meeting will bring together the partners of the Math4U Supports Teachers and Students project to discuss the progress of the project, review the work carried out within the different work packages, and plan the activities for the coming months. The meeting will also address project management, dissemination of results, and the preparation of future scientific publications.
Speaker: Jyotshana Prajapat (University of Mumbai).
Title: Symmetry results for H-type groups.
Abstract: For H-type groups, which includes the Iwasawa N groups, I will discuss the symmetry and classification of solutions to PDEs with application of moving plane method in these settings.
Speaker: Jyotshana Prajapat (University of Mumbai).
Title: The Moving plane method in the Heisenberg group.
Abstract: I will present the adaptation of the moving plane method in the Heisenberg for proving symmetry and classification of solutions of PDEs in the Heisenberg group. I will also discuss its application for solving overdetermined problems in Heisenberg group and H-type groups.
