# Anàlisi

Asymptotic regularity for mean value properties
Ángel Arroyo (Università degli Studi di Genova)
Dia: 20 / 1 / 2020
Hora: 15:00
Lloc: CRM, Aula petita (C1/028)

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.
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In a broad sense, a function $u_\varepsilon$ satisfies the mean value property if the value of $u_\varepsilon$ at a point $x$ agrees with an averaged value of $u_\varepsilon$ over the ball $B_\varepsilon(x)$. In this talk we review some regularity estimates for the solutions $u_\varepsilon$ that include an error term depending on $\varepsilon$ vanishing when $\varepsilon\to 0$ and read as
$$|u_\varepsilon(x)-u_\varepsilon(y)| \leq C\big(|x-y|^\alpha+\varepsilon^\alpha\big),$$
where $C>0$ and $\alpha\in(0,1)$ do not depend on $\varepsilon$. Moreover, by letting $\varepsilon\to 0$, this provides a H\"older estimate for the limit function, which turns out to be a viscosity solution to an elliptic PDE.
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# Seminari de doctorands

Sisè Seminari de Teoria de Categories
Guillermo Carrión Santiago (UAB)
Dia: 22 / 1 / 2020
Hora: 16:30
Lloc: Dpt Matematiques, Seminari Planta -1 (C1/-128)     qG

Resum: Seguim amb els conceptes de dualitat.

Cinquè Seminari de Teoria de Categories
Eduard Vilalta i Vila (uab)
Dia: 15 / 1 / 2020
Hora: 16:30
Lloc: Dpt Matematiques, Seminari Planta -1 (C1/-128)     qG

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.

# Geometria

Min-max width and volume of Riemannian three-dimensional spheres
Lucas Ambrozio (Warwick)
Dia: 30 / 1 / 2020
Hora: 12:00
Lloc: CRM, Aula A1 (C3b/-102)

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

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
Florent Balacheff (UAB)
Dia: 16 / 1 / 2020
Hora: 12:00
Lloc: CRM, Aula A1 (C3b/-102)

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

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 Dinàmics

New lower bounds for the local Hilbert number for cubics systems and piecewise systems
Luiz F. S. Gouveia (Universitat Autònoma de Barcelona)
Dia: 27 / 1 / 2020
Hora: 15:30
Lloc: Dpt Matematiques, Aula C1/-128

Web: Grup de Sistemes Dinàmics de la UAB

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.

This is a joint work with Joan Torregrosa.

This seminar will be presented in Spanish.

The theory of the weak centers
Valentí Ramírez (Universitat Autònoma de Barcelona)
Dia: 20 / 1 / 2020
Hora: 15:30
Lloc: Dpt Matematiques, Aula C1/-128

Web: Grup de Sistemes Dinàmics de la UAB

Resum:
This talk is dedicated to study the subclass of linear type centers which we call the it weak centers. We say that the linear type center is a weak center if the Poincare-Liapunov first integral can be written as $H=(x^2 +y^2)/2(1+h.o.t.).$

We have characterized the expression of an analytic (polynomial) differential systems having a weak center. We prove that the uniform and holomorphic centers are weak centers. Moreover we give the conjecture that the all weak centers are quasi Darboux integrable. Finally we established the relations between a particular case of weak centers and reversibility.

# Teoria d'Anells

Cuntz-Pimsner algebras associated to C*-correspondences over commutative C*-algebras
Maria Stella Adamo(University of Rome "Tor Vergata)
Dia: 23 / 1 / 2020
Hora: 11:00
Lloc: Dpt Matematiques, Seminari C3B (C3B/158)

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

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 $\varphi: X\to X$.
In this case, we identify a "large enough" C*-subalgebra that captures the fundamental properties of the containing Cuntz-Pimsner algebra. Lastly, we will examine conditions when these C*-algebras can be classified using the Elliott invariant.

This is joint work in progress with Archey, Forough, Georgescu, Jeong, Strung, Viola.

# Teoria de Nombres

La conjectura del zero excepcional de Teitelbaum sobre cossos de funcions IV
Francesc Bars (UAB)
Dia: 16 / 1 / 2020
Hora: 11:00
Lloc: Dpt Matematiques, Aula C1/366

# Topologia

The universal property of bispans
Rune Haugseng (Trondheim)
Dia: 10 / 1 / 2020
Hora: 12:00
Lloc: Dpt Matematiques, Seminari C3B (C3B/158)

Web: Grup de Topologia Algebràica