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.
Date: Friday September 18th and Friday September 25th.
Time: 09:00h.
Place: Seminario del Departamento de Análisis Matemático, Facultad de Ciencias.
Area: Functional Analysis Seminar.
Speaker: Vladimir Kadets (Holon Institute of Technology, Israel).
Title: B-convex spaces - From classical results to some modern applications.
Abstract: I am going to start with a short survey about B-convex spaces (i.e. those Banach spaces that have the strong law of large numbers) with brief explanation of basic results. After that there will be a collection of applications to various differently looking geometric properties of Banach spaces that happen to be equivalent to B-convexity.
Title: Some classifications for steady incompressible Euler system and their applications.
Abstract: When two-dimensional steady flows are away from stagnation which corresponds to the critical points of the stream functions, the associated Euler equations can be locally reduced to a semilinear equation. On the other hand, stagnation of flows is not only an interesting phenomenon in fluid mechanics, but also plays a significant role in understanding many important properties of fluid equations. It also induces many challenging problems in analysis. First, we discuss the scenario when the Euler equations can be reduced to a single semilinear equation in terms of stream function, where the analysis for the topology of critical point sets and the overdetermined elliptic problems plays a crucial role. Second, we give a classification of incompressible Euler flows via the set of flow angles, where a counterpart of Picard's little theorem for steady Euler equations is established. Finally, the selection for the solutions of Euler equations via vanishing viscosity limit will be addressed.
Conferenciante: Ruymán Cruz-Barroso, Universidad de La Laguna
Título: Integración numérica en la circunferencia unidad basada en la interpolación y regresión
Abstract:
Las conocidas fórmulas de cuadratura de Szegő representan en la circunferencia unidad las reglas de integración numérica análogas a las clásicas fórmulas de cuadratura Gaussianas para la estimación de integrales con respecto a medidas soportadas en subconjuntos de la recta real.
Las fórmulas de Szegő son de naturaleza interpolatoria, siendo la función F en (1) una función Riemann-Stieltjes integrable con respecto a µ, y toman como nodos los ceros de polinomios para-ortogonales con respecto a µ, que se encuentran en la circunferencia unidad.
En numerosos contextos científicos ocurre que la función F no se conoce de manera explícita, sino que proviene de valores obtenidos por dispositivos, o medidas experimentales de diversos tipos. Por esta razón se han introducido recientemente nuevas técnicas de integración numérica con respecto a medidas soportadas en el eje real, aprovechando la información discreta disponible del integrando y llevando a cabo una técnica mixta entre interpolación y regresión.
This talk presents a novel latent Markov model with Plackett-Luce emission distributions for the analysis of longitudinal ranking data. The proposed framework models preference dynamics through a finite number of latent preference regimes, allowing for abrupt changes in individual ranking behavior rather than assuming smooth temporal evolution. Individuals transition between latent states over time according to a first-order Markov process, capturing unobserved heterogeneity in preference trajectories. Model parameters are estimated by maximum likelihood via an Expectation-Maximization (EM) algorithm. An application to experimental task scheduling data illustrates the ability of the proposed model to identify distinct behavioral profiles, characterize temporal heterogeneity, and detect individual transitions between latent preference regimes.
This talk presents the Fairness Uncertainty-Aware Classification Tree (FUNACT), a novel in-processing framework that extends the classical CART algorithm to jointly optimize predictive accuracy and algorithmic fairness. The proposed approach explicitly accounts for the statistical uncertainty associated with fairness estimation by constructing confidence intervals for group fairness metrics, such as statistical parity, at each candidate split. Splits exhibiting statistically significant fairness violations, identified when the corresponding confidence interval excludes zero, are penalized through a graduated adjustment of the Information Gain criterion. A tunable regularization parameter allows us to flexibly balance predictive performance and fairness according to the application context. Experimental results on both synthetic and benchmark datasets show that FUNACT effectively mitigates algorithmic bias while preserving the transparency, interpretability, and computational efficiency of decision trees.
Abstract: In this talk we investigate the long time dynamics of interacting particle systems subject to singular interactions. We consider a microscopic system of N interacting point particles, where the time evolution of the joint distribution fN(t) is governed by the Liouville equation. Our primary objective is to analyze the system's behavior over extended time intervals, focusing on the stability, the potential chaotic dynamics and the impact of singularities. In particular, we aim to derive reduced models in the regime N >> 1, exploring both the mean-field approximation and configurations far from chaos, where the mean-field approximation no longer holds. These reduced models do not always emerge but in these cases we prove that itis possible to derive uniform bounds in L2, both over time and with respect to the number of particles, on the marginals (fk,N)1 ≤ k ≤ N, irrespective of the initial state’s chaotic nature. Furthermore, we extend previous results by considering a wide range of singular interaction kernels K ∈ W-2/(d+2), d+2 in dimension d ≥ 2, surpassing the traditional Ld regularity barriers. Finally, we address the highly singular case of K ∈ H-1 under a threshold temperature regime, offering new insights into the behavior of such systems.
Abstract: There has been a dramatic increase in the use of AI within mathematical research recently and it seems very likely that this trend will continue. In this talk, I will share some personal reflections on what we have seen so far and the changes that this will bring to our community and culture moving forward.
A logical model of the intracellular signaling network in CD8+ T cells was developed, formalized as a Boolean dynamical system, to investigate the influence of interleukin-2 (IL-2) and its engineered muteins on cell fate decisions. The model was implemented via continuous-time stochastic simulation using a Markov chain framework, explicitly representing the three IL-2 receptor subunits and antigen-presenting cell (APC) signaling inputs. Systematic attractor analysis identified eleven stable steady states — null, memory, and effector phenotypes — and differentiation probabilities were computed across distinct input configurations. The system exhibits multistability: bistability under IL-2+APC stimulation, monostability toward the effector attractor under NASB+APC, and monostability toward the memory attractor under NA+APC. Sensitivity analysis over the network topology identified CD28, FOXO, AMPK, and SATB1 as critical nodes governing attractor selection and cell fate determination.
