Seminar Day - UB-UPC DSG
📅 When: 16:00, July 15th
📍 Where: Aula S002, FME-UPC.
🧑 Who:: Álvaro Fernández-Mora (Monash University)
📔Title: Computer-assisted approach for the Infinitesimal Hilbert 16th problem
Abstract:
The infinitesimal Hilbert's 16th problem asks for a uniform upper bound on the number of limit cycles in polynomial Hamiltonian vector fields under polynomial perturbations. Let Z(n) denote this maximum number of limit cycles, where n is the degree of the perturbation and n+1 is the degree of the Hamiltonian. Upper bounds for Z(n) remain largely unknown even for low degrees. In this work, we present novel computer-assisted techniques to approach this classical problem. We apply our framework to construct an alternative proof of the celebrated result Z(2)=2. While the quadratic case is one of the few cases that has been fuly solved, our primary objective is to build a scalable toolkit capable of overcoming the algebraic complexity that currently limits the study of Z(n) for large n.
As of yesterday, June 9th, 2026, the asteroid 1996 PX8 has been officially named after our colleague and friend, Angel Jorba.
Angel was a mentor, a brilliant colleague, and a dear friend to most of us. This is a small tribute to honor his memory and his lasting legacy. 🌌✨
🔗 Find more information about the asteroid here: https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html#/?sstr=angeljorba
#Astronomy #Asteroids #AppliedMathematics #DynamicalSystems #Tribute #InMemoriam
Seminar Day - UB-UPC DSG
📅 When: 16:00, May 27th
📍 Where: Aula 004, FME-UPC.
🧑 Who:: Pablo Roldan (UPC)
📔Title: Efficient shadowing of pseudo-orbits generated by the transition map
Abstract: In a recent paper [DGR26], we considered the spatial R3BP around the equilibrium point \(L_1\), and constructed diffusion pseudo-orbits with optimal diffusion time. The pseudo-orbits are obtained by iterating the so-called transition map on a suitable NHIM. They are chains of (finite-time) heteroclinic orbit segments, so they are not true orbits of the R3BP system.
In this talk, we will explain how to construct true diffusion orbits that shadow the pseudo-orbits. We will use:
- the transition map;
- the Birkhoff normal form around \( L_1 \); and
- a (numerical) multiple shooting scheme.
Seminar Day - UB-UPC DSG
📅 When: 16:00, february 11th
📍 Where: Aula 004, FME-UPC.
🧑 Who:: Alejandro Cabrera (UPC)
📔Title: Relating dynamical systems and certain singular spaces
Abstract: The aim of this talk is to give an overview of joint work with M. del Hoyo and E. Pujals (2020) in which we relate the study of (discrete) dynamical systems to that of its -typically singular- space of orbits, seen as a so-called differentiable stack. In the first part, I will motivate this observation and give a brief introduction to differentiable stacks. I will then explain the main results stating that, for simply connected manifolds, the stack of orbits allows one to recover a dynamics up to conjugation and inversion. I finally discuss some applications, including a geometric version of a celebrated result of M.Rieffel in the context of C* algebras for distinguishing irrational rotations of the circle.
Seminar Day - UB-UPC DSG
📅 When: 16:00, December 17th
📍 Where: Aula T2 (2n pis), Facultat de Matemàtiques i Informàtica, UB.
🧑 Who:: Domènec Ruiz i Balet (UB)
📔Title: Connections between dynamical systems, deep learning and large language models
Abstract: This introductory talk aims to introduce some of the most relevant machine learning architectures and understand them as dynamical systems. We will navegate through formulations, different problems and perspective and some of the current results.
Seminar Day - UB-UPC DSG
📅 When: 16:00, December 10th
📍 Where: Aula T2 (2n pis), Facultat de Matemàtiques i Informàtica, UB.
🧑 Who: Illya Koval (IST Austria)
📔Title: Fractal-like meanders appear in KAM theory
Abstract:
In KAM theory, a certain nondegeneracy of the Hessian of the unperturbed Hamiltonian is crucial to show the existence of invariant tori.
These invariant tori have to be the graphs of Lipschitz functions. However, when such a type of nondegeneracy is violated, very little is known. Inspired by the works of Simó, we will show the existence of non-graph meandering invariant tori and that they are generic. We discuss meanders of the first order, second order, and even fractal-like meanders. This is a joint work in progress with Vadim Kaloshin and Yi Pan.
Seminar Day - UB-UPC DSG
📅 When: 16:00, December 3
📍 Where: Aula T2 (2n pis), Facultat de Matemàtiques i Informàtica, UB.
🧑 Who: Frank Trujillo (CRM)
📔Title: Hausdorff Dimension of Invariant Measures of AIETs
Abstract:
In this talk, we will discuss the Hausdorff dimension of invariant measures of affine interval exchange transformations (AIETs). AIETs are piecewise affine bijections of a bounded interval with a finite number of discontinuities. In general, these maps are uniquely ergodic, and their unique invariant probability measure is singular with respect to Lebesgue measure.
We will provide explicit values for the Hausdorff dimension of this unique invariant probability measure for a particular class of AIETs, called self-similar AIETs.
This is joint work with P. Berk, K. Frączek, and Ł. Kotlewski.