AnàlisiAsymptotic regularity for mean value properties
Resum: The relation between harmonic functions and the mean value property is one of the most classic results in the analysis of PDEs. In the recent years, similar connections have been found between mean value properties and the solutions of certain elliptic PDEs, as for example the so-called $p$-laplacian.
Seminari de doctorandsSisè Seminari de Teoria de Categories
Resum: Seguim amb els conceptes de dualitat.
Cinquè Seminari de Teoria de Categories
Resum: Es revisaran les seccions 7 i 8 del capítol 1 de "Categories for the Working Mathematician", en concret sobre "Large Categories" i Hom-Sets. Si hi ha temps es començarà amb el concepte de dualitat, ja a la primera secció del capítol 2.
GeometriaMin-max width and volume of Riemannian three-dimensional spheres
Resum: By the work of Simon and Smith, every Riemannian three-dimensional sphere contains an embedded minimal two-dimensional sphere. Their method of construction is a min-max method for the area functional and the area of this minimal sphere is bounded from above by a number depending only on the ambient geometry, known as the width. In this talk, we will discuss upper bounds for the width among certain classes of metrics with the same volume. This is joint work with Rafael Montezuma (UMass-Amhrest).
Entropia de volum i longituds de corbas homotòpicament independents
Resum: Presentaré una desigualtat per les varietats riemannianes tancades que impliqua l'entropía del volum i el conjunt de longituds de qualsevol família de corbes homotòpicament independents basats en un mateix punt. Aquesta desigualitat implica un teorema del collaret universal, és a dir sense restricció de curvatura. És un treball en col.laboració amb el Louis Merlin.
Sistemes DinàmicsNew lower bounds for the local Hilbert number for cubics systems and piecewise systems
Resum: Let $\mathcal{P}_n$ the class of polynomial differential systems of degree $n.$ In this class, we are interested in the isolated periodic orbits, the so called limit cycles, surrounding only one equilibrium point of monodromic type. For the unperturbed system, the origin is always an equilibrium point of nondegenerate center-focus type. We define $M(n)$ as the maximum number of small limit cycles bifurcating from the origin via a degenerate Hopf bifurcation. We will prove that $M(5)\geq 33$. We will also consider this problem in the class of piecewise polynomial systems defined in two zones. Here, we are interested in the small crossing limit cycles surrounding only one equilibrium point or an sliding segment. When the separation curve is a straight line, we provide a piecewise cubic system exhibiting at least $26$ small crossing limit cycles. All of them nested surrounding only one equilibrium point, in fact an sliding segment. The computations use a parallelization algorithm.
The theory of the weak centers
Resum:
Teoria d'AnellsCuntz-Pimsner algebras associated to C*-correspondences over commutative C*-algebras
Resum: In this talk, structural properties of Cuntz-Pimsner algebras arising by full, minimal, non-periodic, and finitely generated C*-correspondences over commutative C*-algebras will be discussed. A broad class of examples is provided considering the continuous sections $\Gamma(V,\varphi)$ of a complex locally trivial vector bundle $V$ on a compact metric space $X$ twisted by a minimal homeomorphism $\varphi: X\to X$.
Teoria de NombresLa conjectura del zero excepcional de Teitelbaum sobre cossos de funcions IV
TopologiaThe universal property of bispans
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