Análisis

Subcritical uncertainty principles for the Fourier transform
Miquel Saucedo
Día: 22/02/2024
Hora: 15:00
Lugar: CRM

Web: Grup d'Análisi matemàtica i Harmònica

Resum: The uncertainty principle forbids a non-zero function $f$ and its Fourier transform $\hat{f}$ from being "too" (or critically) localized. In this talk I will discuss a result about the pointwise decay of subcritically localized functions. This result is closely related to the well-known Hardy and Cowling-Price uncertainty principles. Joint work with Sergey Tikhonov.

On the analyticity of the trajectories of the particles in the patch problem for some active scalar equations
Josep Maria Burgués
Día: 08/02/2024
Hora: 15:00
Lugar: CRM

Web: Grup d'Análisi matemàtica i Harmònica

Resum: Let $\Omega$ be a bounded domain in $\mathbb R^n$ whose boundary is $\mathcal{C}^{1,\,\gamma}$ for $\gamma\in(0,\,1)$. Consider $2D$ Euler equation for the vorticity or the $nD$ aggregation equation in the case of the initial condition being a positive multiple of the characteristic function of $\Omega$. In this paper we prove global in time analyticity of the flow generated by the velocity field which propagates the vorticity or density solution respectively.

These results are obtained from a detailed study of the Beurling or Riesz transform, that represents derivatives of the velocity field. The precise estimates obtained for the solutions of an equation satisfied by the Lagrangian flow, are a key point in the development.

Estadística

El iceberg de la violència de gènere: Una aproximació des de la modelització estadística
David Moriña (Universitat de Barcelona)
Día: 21/03/2024
Hora: 12:00
Lugar: Fac. de Ciències, Sala de Graus     qG 

Resum: Una de cada tres dones a tot el món pateix violència física o sexual en algun moment a les seves vides, en la majoria dels casos
per part de la parella. Tot i el gran nombre de denúncies, se sospita que només representen una petita part dels casos que es produeixen, ja
que, per motius molt diversos, les víctimes decideixen sovint no denunciar les agressions que pateixen. En aquest treball s'analitza el
nombre de diagnòstics setmanals relacionats amb la violència de gènere registrats al sistema d'Atenció Primària d'una de les àrees més
extenses de Catalunya, estimant la magnitud de casos no reportats considerant el comportament diferent del fenomen com a conseqüència de
les mesures de mitigació contra la Covid-19 impulsades pel govern espanyol i avaluant l'impacte d'una activitat formativa per
sensibilitzar els facultatius realitzada a finals de 2019 a l'àrea considerada.

Modelització forestal i optimització espacial per co-dissenyar paisatges agroforestals resilient a Catalunya
Núria Aquilué
Día: 22/02/2024
Hora: 12:00
Lugar: CRM, Auditori (C1/034)     qG 

Resum: Un dels objectius estratègics principals que conformen l’eix vertebrador de l'Estratègia de Bioeconomia Catalana 2030 és promoure i impulsar l’establiment de paisatges agroforestals resilients i la provisió sostenible de serveis ecosistèmics (SE) en base a eines avançades i coneixement expert. Utilitzant un municipi del Pirineu occidental de Catalunya com a estudi pilot, aquest projecte té per objectiu elaborar un pla de gestió a nivell de paisatge en base a premisses globals de resiliència i incloent el criteri expert. Així, investigadors i responsables de la presa de decisions van acordar prioritzar quatre objectius relacionats amb la resiliència dels paisatges agroforestals Mediterranis, mentre que experts i tècnics del territori van especificar zones estratègiques per garantir o afavorir aquestes prioritzacions. S’ha establer un marc de suport a la presa de decisions que consisteix en la caracterització inicial del paisatge i les masses forestals (detallades a partir de dades LiDAR i d'inventari forestal), un model de dinàmica i gestió forestal, un model de canvis d’usos del sòl, un sistema d’estimació de SE i una mètode d’optimització espacial heurístic. Es van aplicar els models per simular cinc tractaments silvícoles diferents i els possibles canvis de cobertura del sòl entre boscos, arbustos, terres agrícoles i praderies, i es va estimar la provisió de SE de 2021 a 2050 per a totes les alternatives. Amb l’eina d’optimització es van prioritzar els quatre objectius per a la resiliència (la reducció del risc d’incendis forestals, la conservació de la biodiversitat, la producció d’aigua blava i potenciar l’activitat agroramadera), es van tenir en compte les indicacions dels experts i es van incloure els acords en les àrees de superposició d’interessos per acabar donant lloc a un pla de paisatge agroforestal resilient.

Geometría

Pre-foliations of co-degree one on $\mathbb C P^2$ with a flat Legendre transform
Samir Bedrouni (Université des Sciences et de la Technologie Houari Boumediene, Alger)
Día: 19/02/2024
Hora: 12:00
Lugar: Dpt Matematiques, Seminari C3B (C3B/158)

Web: Laboratori d'Interaccions entre Geometria, Àlgebra i Topologia

Resum: A holomorphic pre-foliation of co-degree $1$ and degree $d$ on $\mathbb C P^2$ is the data of a line $L$ of $\mathbb C P^2$ and a holomorphic foliation $F$ on $\mathbb C P^2$ of degree $d-1$. In this talk, I will present the main results of a recent paper on pre-foliations of co-degree $1$ on $\mathbb C P^2$ with a flat Legendre transform (dual web), cf. arXiv:2309.12837. First, I will explain the outline of the proof of the result which states that the dual web of a reduced convex pre-foliation of co-degree $1$ on $\mathbb C P^2$ is flat. Second, I will give a description of pre-foliations of co-degree $1$ and degree $3$ on $\mathbb C P^2$ whose associated foliation has only non-degenerate singularities and whose dual $3$-web is flat.

Lie algebroid holonomy
Jaime Pedregal Pastor (Utrecht)
Día: 05/02/2024
Hora: 12:00
Lugar: Dpt Matematiques, Seminari C3B (C3B/158)

Web: Laboratori d'Interaccions entre Geometria, Àlgebra i Topologia

Resum: Lie algebroids can be considered as “adapted tangent bundles” for specific geometric situations. As such, it makes sense to consider Lie algebroid connections and Lie algebroid holonomy. In this talk, after a very brief recap of classical holonomy, we will introduce the notion of Lie algebroids, with examples, and give some intuition on their usefulness. We will then, following the “adapted tangent bundle” philosophy, introduce Lie algebroid holonomy. Two remarkable properties distinguish Lie algebroid holonomy from classical holonomy: the Ambrose–Singer theorem must be enlarged beyond curvature and holonomy can jump from leaf to leaf, with not much control over these jumps. Depending on time we will give examples of both features.

Sistemas Dinámicos

Normal forms and versal unfoldings in GLV
Weinian Zhang (Sichuan University, China)
Día: 26/02/2024
Hora: 15:00
Lugar: Sala de Zoom

Web: Grup de Sistemes Dinàmics de la UAB

Resum: In the case of the full zero degeneracy, the classic Poincare-Birhoff normal form theory is not available. In this talk a predator-prey system with such a degeneracy is considered. A new normal form is given for generalized Lotka-Volterra systems (abbreviated by GLV), which is employed to unfold the degenerate predator-prey system in GLV class. The universality of unfolding is proved by verifying the trasversality. Further, all possible bifurcations at the degenerate equilibrium including transcritical bifurcation, Hopf bifurcation and heteroclinic bifurcation are discussed.

The flow map parameterization method for invariant tori of autonomous Hamiltonian systems
Josep Maria Mondelo (UAB)
Día: 19/02/2024
Hora: 15:00
Lugar: Dpt Matematiques, Seminari Planta -1 (C1/-128)

Web: Grup de Sistemes Dinàmics de la UAB

Resum: The goal of this talk is to present a methodology for the computation of lower-dimensional (non-Lagrangian), partially hyperbolic invariant tori of autonomous Hamiltonian systems. It is therefore well suited (but not limited to) models from Celestial Mechanics such as the circular, spatial RTBP, spatial Hill or the gravity field around a uniformly rotating, irregular body. It combines flow map (a.k.a. stroboscopic map) methods, parameterization methods and symplectic geometry. While flow map methods reduce the dimension of the tori to be computed by one, parameterization methods make the computational cost negligible with respect to (the unavoidable) numerical integration. Symplectic geometry is responsible for some cancellations that make the cohomological equations solvable. The method simultaneously computes the tori and their invariant stable and unstable bundles. An application is made to the computation of the Lissajous family of tori around $L_1$ in the Earth-Moon circular, spatial RTBP. In this application, when compared to more classical ("large-matrix") discretization techniques of the invariance equations, the speedup factor of the method is $>10$.

Teoría de Anillos

Fraïssé Theory for Cuntz semigroups
Laurent Cantier
Día: 27/02/2024
Hora: 14:30
Lugar: Dpt Matematiques, Seminari C3B (C3B/158)

Resum: We introduce a (categorical) Fraïssé theory applied to the category of abstract Cuntz semigroups, drawing inspiration from Kubiś’ approach for metric-enriched categories. Throughout the discussion, we will explore metric properties available within the Hom-sets of Cu-morphisms, including concepts like Cauchy sequences and approximate intertwinings. Lastly, we will illustrate instances of Cu-semigroups that naturally emerge as Fraïssé limits.

Foelner type approximations and canonical commutation relations
Fernando Lledó (Univ. Carlos III, Madrid)
Día: 20/02/2024
Hora: 14:30
Lugar: Dpt Matematiques, Seminari C3B (C3B/158)

Resum: The dichotomy amenable/paradoxical was first observed in the context of groups by von Neumann in 1929. Since then it has pervaded many areas of mathematics, including, for example, metric spaces, pure algebra or operator theory in Hilbert spaces.
Motivated by the importance of the quantum mechanical canonical commutation relations, I will present new ideas concerning Foelner type (finite-dimensional) approximations in the context of unbounded operators in Hilbert spaces.
These approximations correspond to an operator theoretic version of amenability.

Iterated power intersections of ideals in universal enveloping algebras
Pavel Příhoda
Día: 13/02/2024
Hora: 14:30
Lugar: Dpt Matematiques, Seminari C3B (C3B/158)

Resum: If I is an ideal of a ring R, I(1) denotes the intersection of all powers of I. If m is a positive integer we inductively define I(m) as (I(m-1))(1).
Puninski noticed that if R is noetherian, and for every proper ideal I of R there exists a positive integer m such that I(m)=0, then every projective R-module is either finitely generated or free.
In the talk I will explain an elementary method showing that this property holds if R is a universal enveloping algebra of a completely solvable Lie algebra of finite dimension.

Finite free resolutions (part 2)
Dolors Herbera
Día: 05/02/2024
Hora: 16:00
Lugar: Dpt Matematiques, Seminari C3B (C3B/158)

Resum: Let R be a ring. Given a bounded complex of finitely generated free right R-modules we want to determine for which left R-modules L, C⊗L is exact except for one term. In particular, if C is the free resolution of a module M, we are interested in determining all left modules L such that TorRi(M,L)=0, for all i>0.
For general rings this is a very difficult question but for commutative rings there is a very nice answer.
In this talk we will explain how to use an old theorem due to McCoy (1948) for maps between finitely generated free modules over commutative rings to solve the problem in that case. McCoy's result was extended by Buchsbaum and Eisenbud (1973) to general bounded complexes of finitely generated free modules over commutative noetherian rings and, finally, Northcott (1976) proved it for general commutative rings. These results allow us to give an answer to the initial question for general commutative rings.
As a consequence, we can give some new light to the classification of tilting classes over commutative rings done by Hrbek and Stovicek (2019).

This is work in progress with Giovanna LeGros.

Topología

Quillen's conjecture: first steps into the solvable case
Wolfgang Pitsch (UAB)
Día: 23/02/2024
Hora: 12:00
Lugar: Dpt Matematiques, Seminari C3B (C3B/158)

Web: Grup de Topologia Algebràica

Resum: In this talk we will explain the Cohen-Macaulay properties of the poset $\mathcal{A}_p(G)$ for some extensions of a $p$-solvable group by uniquely $p$-divisible groups. This is the key result to prove Quillen's conjecture for finite solvable groups.

Quillen’s conjecture via finite topological spaces
Gabriel Martínez de Cestafe Pumares (UAB)
Día: 09/02/2024
Hora: 12:15
Lugar: Dpt Matematiques, Seminari C3B (C3B/158)

Web: Grup de Topologia Algebràica

Resum: Given a finite group $G$ and a prime $p$, Quillen studied the poset $S_p(G)$ of non-trivial $p$-subgroups of $G$ from an homotopical point of view. For this, he considered the geometric realization of the order complex of $S_p(G)$ and conjectured that it is contractible if and only if $G$ has a non-trivial normal $p$-subgroup. In this talk, we will follow an alternative approach, which exploits the close relation between the notions of finite poset and finite $T_0$ topological space. This will allow us to view $S_p(G)$ itself as a topological space and to reformulate Quillen’s conjecture in a purely homotopical language.