Hem convidat la comunitat investigadora a mostrar resultats de recerca no inclosos en les ponències i sessions programades, en format pòster. Donem així un valor afegit a les pauses, afavorint l’intercanvi d’idees i les discussions matemàtiques. En especial, pels joves, és una oportunitat per mostrar la seva recerca.
Llistat de pòsters acceptats
- L²-boundedness of the n-th Calderón commutator on Lipschitz graphs
Joan Hernández García (Universitat Autònoma de Barcelona) - A conic optimization framework for shape-constrained functional regression analysis
Cristina Molero-Río (Universidad de Sevilla) - Balanced subtournaments of a random tournament
Xavier Povill (Universitat Politècnica de Catalunya) - Decorated groupoids on marked bordered surface
Benedetta Facciotti (Universitat Politècnica de Catalunya) - Dynamics in the center manifold around a fixed point of a map
Leonor Domingo (Universitat de Barcelona) - Eccentricity sequences of quasitrees and unicycle graphs
Nacho (Ignacio) López Lorenzo (Universitat de Lleida) - Gender inequality in care work using direct responses and NSUM estimates
Belén Pulido (Universidad Nacional de Educación a Distancia) - Jordan type of Perazzo algebras
Josep Pérez Díez (Universitat de Barcelona) - Maximum likelihood threshold bounds for colored Gaussian models
Danai Deligeorgaki (Universitat de Barcelona) - Morphisms of Theta Lifts and families of Relative Trace Formulae
Ron Erez (Tel Aviv University) - Nonlocal Inverse Problems and Long-Range Propagation on Cellular Graphs
Salvish Goomanee and Grégoire Malandain (Université de la Côte d’Azur, INRIA) - Simplification of Non-Orientable Maps
Lingxuan Wu (Universitat Politècnica de Catalunya, Central South University) - Square-Free Parts of Tate–Shafarevich Groups
Alexandros Konstantinou (Max Planck Institute for Mathematics) - Tracing the Emergence of Nonsmooth Bifurcations in Piecewise-Linear Quasiperiodically Forced Continuous Models
Rafael Martinez Vergara (Universitat de Barcelona) - Unified theory for regularity persistence of vortex patch boundaries
Marc Magaña Centelles (Universitat Autònoma de Barcelona) - Where Fractals Just Touch: A Four-Dimensional Connectedness Atlas for Planar Binary Self-Similar Sets
Bernat Espigulé (Universitat de Girona)
Llistat de resums
- L²-boundedness of the n-th Calderón commutator on Lipschitz graphsAbstract: Our work investigates the asymptotic behavior of the norm, as a bounded operator in L²(R), of the n-th Calderón commutator T_{A,n} on the graph of a Lipschitz function A. We prove the estimate |T_{A,n}|_{L²–> L²} \leq Cn |A’|_\infty^n, thus formalizing a claim by Mateu and Verdera via a symmetrization strategy and the T1 theorem. We also show that additional regularity on A yields sublinear growth in n. Specifically, for A supported in [0,1], the bound improves to a behavior of the form n^(1/2)|A’|_\infty^n under a Dini condition on A’, or if A’ belongs to the logarithmic Besov space B^{1,0}_{1,1}(R). This space contains all compactly supported functions in the Sobolev spaces H^s(R) for 0<s<1, as well as functions of bounded variation. These refined estimates are established through an alternative framework based on Hörmander-type conditions and interpolation, bypassing the standard T1 approach. Counterexamples are provided to demonstrate that the Dini and Sobolev fractional regularity conditions are incomparable.
- A conic optimization framework for shape-constrained functional regression analysis
Cristina Molero-Río (Universidad de Sevilla)
Abstract:
- Balanced subtournaments of a random tournament
Xavier Povill (Universitat Politècnica de Catalunya)
Abstract: We study the size of the largest balanced subtournament in a random tournament on n vertices. A tournament is balanced if all vertices have equal indegree and outdegree. We show that, with high probability, the largest balanced subtournament has size O(n^{2/3}). Moreover, for every k = o(n^{2/3}), with high probability the random tournament on n vertices contains a balanced subtournament of size k. Our proof combines enumeration results for tournaments with prescribed degree sequences, due to McKay and Wang, with probabilistic arguments of Krivelevich, Sudakov and Wormald.
- Decorated groupoids on marked bordered surface
Benedetta Facciotti (Universitat Politècnica de Catalunya)
Abstract: Building on the classical equivalence of groupoids among linear local systems on compact orientable surfaces, linear representations of the fundamental groupoid, linear representations of the action groupoid for the conjugation action of G on the space of G-representations for G=GLn(C), we extend this result to the case of surfaces with marked points on the boundaries, which carry additional data on such special points.
- Dynamics in the center manifold around a fixed point of a map
Leonor Domingo (Universitat de Barcelona)
Abstract: In this work, we study the asymptotic behavior in the neighborhood of a fixed point of a map. To describe the dynamics near this point, we consider the reduction to the center manifold for a map. Our approach relies on the use of the graph transform method where the invariant center manifold of a fixed point is locally represented as a graph. We numerically compute the parametrization of the center-stable and center-unstable manifolds by using power series expansions around the fixed point. We propose to consider the jet transport technique to obtain an accurate approximation in the expansion of the center manifold through automatic differentiation on the map. The method is considered for an application to celestial mechanics. We are interested in the dynamics near the vicinity of the L3 point of the Earth-Moon system. The model for studying the dynamics of the problem is the Sun-Earth-Moon Bicircular Problem (BCP). To remove the dependence on time in the BCP model, in particular we consider a stroboscopic map defined at time of the perturbation. In this BCP model, the linear dynamics of the periodic orbit that replaces the L3-equilibrium point of the Restricted Three-Body Problem is described by a hyperbolic direction and two elliptical directions. To describe the different types of orbits in the neighborhood of L3, we uncouple the instability behavior caused by the hyperbolic direction from the other elliptical directions. This can be accomplished by performing the reduction to the center manifold around the dynamical substitute of L3. We numerically compute the high order approximation of the center-stable and center-unstable manifolds around this fixed point. As a result, we can then analyze the bounded motion described by the center manifold near the fixed point and visualize the phase space behavior in the original coordinate system.
- Eccentricity sequences of quasitrees and unicycle graphs
Nacho (Ignacio) López Lorenzo (Universitat de Lleida)
Abstract: The eccentricity of a vertex in a connected graph is the maximum distance from this vertex. The eccentricity sequence of a graph is the list of eccentricities of its vertices given in nondecreasing order. A sequence of positive integers is a graphical eccentric sequence if it is the eccentricity sequence of some graph. The study of graphical eccentric sequences takes back to the 70’s of the past century where some results focus on the characterization of these sequences, specially for the family of trees. However, the general problem remains open. In this work we present some necessary and sufficient conditions for a sequence to be a graphical eccentric sequence of some families of graphs related to quasitrees and unicyclic graphs.
- Gender inequality in care work using direct responses and NSUM estimates
Belén Pulido (Universidad Nacional de Educación a Distancia)
Abstract: This study draws on data from CuidaNSUM, an interdisciplinary project examining perceptions of the distribution of care work and time use within Spanish households. The survey targets different gender, cohabiting couples with at least one child under 16 and combines sociodemographic information with direct and indirect questions on household tasks, childcare, employment adjustments, support networks, gender attitudes, and wellbeing.
- Jordan type of Perazzo algebras
Josep Pérez Díez (Universitat de Barcelona)
Abstract: Perazzo algebras constitute a familly of standard graded Artinian Gorenstein algebras over a field K. We show that the Hilbert function does not determine the weak Lefschetz property for Perazzo algebras in general. This motivates the study of finer invariants, focusing in a new family of Perazzo algebras which we call full-like Perazzo algebras.
The first of these invariants is the Jordan type of a linear form, as it encodes not only the dimensions of the graded components but also the behaviour of the induced multiplication maps. We start by computing the Jordan type of any linear form in a full Perazzo algebra, and deduce the generic linear Jordan type. This allows us to compute the generic linear Jordan type of any full-like Perazzo algebra, leading to the characterization of those algebras satisfying the weak Lefschetz property.
- Maximum likelihood threshold bounds for colored Gaussian models
Danai Deligeorgaki (Universitat de Barcelona)
Abstract: Colored Gaussian graphical models are a widely-used class of models which address the issue of statistical inference with limited samples by imposing linear conditions on the concentration matrix of the model. In this article, we apply and extend known methods for bounding maximum likelihood thresholds (MLTs) for uncolored Gaussian graphical models to the colored case.
- Morphisms of Theta Lifts and families of Relative Trace Formulae
Ron Erez (Tel Aviv University)
Abstract: The theta correspondence relates automorphic representations of orthogonal and metaplectic groups and is a fundamental ingredient of the Siegel–Weil formula and Kudla’s program. We study when theta lifts of two nontrivial automorphic characters of orthogonal groups are isomorphic. We determine necessary local matching conditions for such morphisms in terms of central characters and Jacquet modules of the associated local representations. We further propose that these morphisms should induce relative trace identities. This philosophy is motivated by a striking resemblance between our local conditions and those arising in the work of Mao and Rallis on families of relative trace formulae, where analogous conditions are formulated using coinvariants of induced representations. Our goal is to better understand the relationship between morphisms of theta lifts and families of relative trace formulae.
- Nonlocal Inverse Problems and Long-Range Propagation on Cellular Graphs
Salvish Goomanee and Grégoire Malandain (Université de la Côte d’Azur, INRIA)
Abstract: We develop a mathematical framework for studying long-range interactions in cellular tissues from partial observations. Cells are represented as nodes of a weighted graph, with nonlocal interactions encoded by a kernel defining a graph operator. The central inverse problem is to determine whether the hidden interaction structure can be recovered from the response of only a subset of observed cells to controlled perturbations. Under a connectedness assumption on the interaction graph, we establish a unique-continuation property for eigenmodes and show that the source-to-solution response contains sufficient spectral information to identify the hidden interaction kernel. We further obtain stability results in the simple-eigenvalue regime, with spectral projectors providing the natural formulation when eigenvalues are repeated. Numerical experiments on synthetic cellular graphs support these theoretical predictions, demonstrating recovery from partial observations across different graph geometries. Finally, we investigate how the spectral gap links tissue connectivity and nonlocal interactions to the characteristic timescale of perturbation propagation. Together, these results provide a spectral perspective on tissue-scale dynamics: long-range cellular interactions leave a recoverable spectral fingerprint that connects hidden interaction structure to the propagation of mechanical signals.
- Simplification of Non-Orientable Maps
Lingxuan Wu (Universitat Politècnica de Catalunya, Central South University)
Abstract: This poster discusses an ongoing attempt to extend the ordinary/fully simple correspondence from orientable maps to non-orientable maps. In the orientable setting, ordinary maps allow boundary faces to meet each other or to self-touch at vertices, while fully simple maps forbid these boundary contacts. This correspondence is related to moment-free cumulant relations in free probability and to the x-y duality in topological recursion. Our starting point is the orthogonally invariant real symmetric matrix model. Using orthogonal Weingarten calculus, we derive transformation formulae between ordinary correlators and their fully simple analogues. The aim is to explain these formulae combinatorially in terms of maps on locally orientable surfaces, where twisted and untwisted edge gluings are both allowed, and to interpret the transformation as a non-orientable boundary simplification procedure. This may also give some hints towards real free probability and refined topological recursion.
- Square-Free Parts of Tate–Shafarevich Groups
Alexandros Konstantinou (Max Planck Institute for Mathematics)
Abstract: The Tate–Shafarevich group is a central yet mysterious object in the study of rational points on abelian varieties. It measures the obstruction to determining generators for the Mordell–Weil group and plays a crucial role in the Birch and Swinnerton-Dyer conjecture. Yet it is notoriously difficult to compute or even prove finite. For elliptic curves, it is known to have square order when finite. In higher dimensions, this can fail, a fact long overlooked and often misstated in the literature. We show that every square-free integer arises as the square-free part of the order of the Tate–Shafarevich group of some abelian variety over the rationals.
- Tracing the Emergence of Nonsmooth Bifurcations in Piecewise-Linear Quasiperiodically Forced Continuous Models
Rafael Martinez Vergara (Universitat de Barcelona)
Abstract: We introduce a two-parameter family of quasiperiodically forced piecewise-linear maps. We identify a curve $b^*(a)$ where a nonsmooth period-doubling bifurcation occurs. The study analyzes fractalization through the growth of the Lipschitz constant of the attractor. This research builds upon and extends previous investigations into quasiperiodically forced systems.
- Unified theory for regularity persistence of vortex patch boundaries
Marc Magaña Centelles (Universitat Autònoma de Barcelona)
Abstract: We establish a unified local theory for the persistence of Sobolev regularity of vortex patch boundaries in a family of two-dimensional active scalar equations with radial convolution kernels K(|x-y|). The class includes the 2D Euler equation, the generalized SQG equation in the locally integrable range 0<\beta<1, and the quasi-geostrophic shallow water equation. Under natural assumptions on K (smoothness, integrability near the origin, monotonicity, and polynomial growth), we prove that if the initial boundary belongs to H^3(\mathbb T) and satisfies the arc-chord condition, then the contour dynamics equation admits a unique local solution in C([0,T];H^3(\mathbb T)). Under a stronger integrability condition on the kernel, we also obtain local existence of H^2 solutions. The proof combines Sobolev energy estimates for the contour equation with quantitative control of the arc-chord quantity.
- Where Fractals Just Touch: A Four-Dimensional Connectedness Atlas for Planar Binary Self-Similar Sets
Bernat Espigulé (Universitat de Girona)
Abstract: Start with two shrunken copies of the complex plane, place them at -1 and +1, and iterate forever. Some parameter choices produce a connected planar self-similar set; others break apart into dust. This poster studies the frontier where the two symbolic halves just touch. After normalization, relabelling, and conformal or anti-conformal affine conjugacy, every non-degenerate planar binary similarity system belongs to one of three orientation-parity normal forms: direct–direct, direct–opposite, or opposite–opposite. These are controlled by four real parameters: branch angle α, relative phase γ, magnitude ρ, and scale weight w. The resulting parameter space forms a four-dimensional connectedness atlas. Its boundary can be explored as a geometric shell, coloured by finite symbolic address data and organized by watershed cracks where the local address structure changes. The accompanying interactive explorer makes this object visible and navigable. Classical examples such as the twindragon, Lévy dragon, Heighway dragon, tent-tiles, triangle tile, and H-tree tile appear as landmarks in the same atlas, while the near-H-tree regime reveals exact dyadic branch phenomena.