# Blog de la Biblioteca de Matemàtiques i Informàtica

## SIMBa: Identities in prime rings

El proper dimecres, 10 de febrer, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: José  Brox
Universitat: Centre for Mathematics of the University of Coimbra (CMUC).

Data: Wednesday, February 10th, 2021.
Hora: 12:00,virtual coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website).
Idioma: English.

Títol: Identities in prime rings.
Resum: Given a ring, a generalized polynomial identity (GPI) is a polynomialidentity in which the coefficients can be taken from the ring. Primerings are a class of rings very well suited to manage problems related toidentities, as for example those coming from Herstein’s theory, which isthe study of nonassociative objects and structures arising from associa-tive rings. After a motivating introduction to prime rings, with someexamples from Herstein’s theory, I will show the usefulness of Martin-dale’s lemma, the key tool for solving GPIs in one variable in primerings, and I will explain a new promising approach to solve them basedon elementary algebraic geometry which avoids some shortcomings ofthe lemma, allowing to find the optimal solutions.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.

## SIMBa: Persistent homology and barcode distance

El proper dimecres, 27 de gener, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Marco Praderio Bova
Universitat: Lancaster University.

Data: Wednesday, January 27th, 2021.
Hora: 12:00,virtual coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website).
Idioma: English.

Títol: Persistent homology and barcode distance.
Resum: Persistent homology is an algebraic topology tool that has gained alot of relevance in topological data analysis during the past few years.During this lecture we will introduce this concept from a categoricalpoint of view and use category theory techniques in order to provewhat is known as stability theorem.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.

## SIMBa: Time-dependent branching processes: a model of oscillating neuronalavalanches

El proper dimecres, 13 de gener, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Rosalba García Millán
Universitat: Imperial College London.

Data: Wednesday, January 13th, 2021.
Hora: 12:00,virtual coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website).
Idioma: English.

Títol: Time-dependent branching processes: a model of oscillating neuronalavalanches.
Resum: Recently, neuronal avalanches have been observed to display oscilla-tions, a phenomenon regarded as the co-existence of a scale-free be-haviour (the avalanches close to criticality) and scale-dependent dy-namics (the oscillations). Ordinary continuous-time branching pro-cesses with constant extinction and branching rates are commonly usedas models of neuronal activity, yet they lack any such time-dependence.In my talk, I will show how we extended a basic branching process byallowing the extinction rate to oscillate in time as a new model to de-scribe cortical dynamics. I will discuss about some observables, suchas the avalanche shape, that we calculated in closed form by meansof a perturbative field theory, and compared to available experimentalresults.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.

## SIMBa: Strand diagrams and generalised braided Thompson’s groups

El proper dimecres, 16 de desembre, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: María Cumplido Cabello

Data: Wednesday, December 16th, 2020.
Hora: 12:00,virtual coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website).
Idioma: Spanish.

Títol: Strand diagrams and generalised braided Thompson’s groups.
Resum: This is a joint work with Julio Aroca. There is a generalisation of Thompson’s groups constructed from the Thompson’s group $V$ and Artin’s braid group. The braided Thompson’s group $B V_{2}$ was independently introduced by Patrick Dehornoy and Matthew G. Brin in 2006. In this talk we will explain how two extend this concept to a much bigger family of groups by using infinite braids: Infinitely braided Thompson’s groups $B V_{n}(H)$ where $H$ is a subgroup of the braid group on $n$ strands. We will prove that they are indeed groups by using braided diagrams and rewriting systems. We will also see that they are finitely generated if $H$ is finitely generated and give an explicit set of generators for $B V_{n}(H)$ and some other cases. Slides will be in English and the talk will be given in Spanish.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.

## SIMBa: Relationship between victorian eugenecists and slot machine free-game- Branching Processes

El proper dimecres, 9 de desembre, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Àngel Joaniquet Tukiainen
Universitat: Zitro.

Data: Wednesday, December 9th, 2020.
Hora: 12:00,virtual coffee break; 12:20, talk.
Lloc: Zoom (L’enllaç apareixerà al web del SIMBA el mateix dia de cada xerrada.)
Idioma: English

Títol: Relationship between victorian eugenecists and slot machine free-game- Branching Processes.
Resum: Originaly, the first branching processes where studied to ensure thes urvival of surnames on Victorian Era aristocrat familes. These use is actually futile as insuficient data, changing laws or simply name changes (ask Victoria’s grandson, Edward) make this idealization irrelevant. Since then, branching processes have found uses beyond surnames, like studing general reproduction, or neutron counts on nuclear reactions. In this talk we will present multi-type branching proceses and how they can be used to model and control populations of germs (or how to know if a slot machine is good).

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.

## SIMBa: Geometric analysis under integral curvature conditions

El proper dimecres, 18 de novembre, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Xavier Ramos Olivé.
Universitat: Worcester Polytechnic Institute.

Data: Wednesday, November 18th, 2020.
Hora: 12:00,virtual coffee break; 12:20, talk.
Lloc: Zoom (L’enllaç apareixerà al web del SIMBA el mateix dia de cada xerrada.)
Idioma: English

Títol: Geometric analysis under integral curvature conditions.
Resum: Curvature is a local property. However, assumptions on curvature have implications on global quantities, like the diameter, the eigenvalues of the Laplacian or topological invariants. An $n$-manifold with Ricci curvature larger than $(n-1)K$ can not have a diameter larger than the one of the $n$-sphere with constant sectional curvature $K$. Similarly, the first non-zero eigenvalue of such a manifold can not be smaller than the one of the sphere. In recent years there has been an increasing interest in weakening the curvature assumptions from pointwise lower bounds to integral conditions. Integral conditions are much more general, they are more stable under perturbations of the metric, and can be more suitable for the study of geometric flows. We will discuss some classical and recent results in the fields of geometric analysis and comparison geometry with integral curvature conditions.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.

## SIMBa: A walk through the Birch and Swinnerton-Dyer conjecture

El proper dimecres, 4 de novembre, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Óscar Rivero Salgado.
Universitat: Universitat Politècnica de Catalunya.

Data: Wednesday, November 4th, 2020.
Hora: 2:00,virtual coffee break; 12:20, talk.
Lloc: Zoom (L’enllaç apareixerà al web del SIMBA el mateix dia de cada xerrada.)
Idioma: English

Títol: A walk through the Birch and Swinnerton-Dyer conjecture.
Resum: The Birch and Swinnerton-Dyer conjecture is one of the seven millennium problems posed by the Clay Mathematics Institute. There have been many different approaches along the last decades, but it still remains open. The conjecture relates the rank of an elliptic curve with the order of vanishing of a complex $L$-function, and it has been proved when the latter is at most one. At this point, there is a natural question posed by Mazur, Tate and Teitelbaum during the eighties: why dowe look at the complex $L$-function? What about the $L$-functions attached to other non-archimedian completions of the rational numbers? This question will move us to the $p$-adic world, where new phenomen aappear, leading us to suggestive points of view about the conjecture

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.

## SIMBa: The circle method and Linnik–Goldbach problems

El proper dimecres, 7 d’octubre, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Universitat: UNSW Canberra at ADFA.

Data: Wednesday, October 7th, 2020
Hora: 12:00,virtual coffee break; 12:20, talk.
Lloc: Zoom (L’enllaç apareixerà al web del SIMBA el mateix dia de cada xerrada.)
Idioma: English

Títol: The circle method and Linnik–Goldbach problems
Resum: The circle method has its roots in a 1918 paper by Hardy and Ra-manujan which dealt mainly with the partition function, but also withthe representation of numbers as sums of squares. Since then, it hasbeen used with remarkable success by Hardy, Littlewood, Vinogradov,among others, in the field of additive number theory. In this talk, wewill focus on the main ideas of the circle method and illustrate its usein the Linnik–Goldbach problems.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.

## SIMBa (confinat): There are no Banach function spaces, only weighted L2

El proper dimarts, 23 de juny, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Sergi Baena i Miret.
Universitat: Universitat de Barcelona.

Data: Tuesday, 23th of June
Hora: 12:00, virtual coffee break (bring your coffee); 12:20, talk.
Lloc: Zoom meeting. A link will be sent via email, please sign up in our web.
Idioma: English

Títol: There are no Banach function spaces, only weighted $L^{2}$
Resum: An important property of the $A_{p}$ weights is the extrapolation theorem of Rubio de Francia. It was announced in 1982 and givenwith a detailed proof in 1984, both by J.L. Rubio de Francia. Inits original version, reads as follows: if $T$ is a sublinear operator which satisfies the strong type boundedness:

$T: L^{2}(v) \rightarrow L^{2}(v)$

for every weight $v \in A_{2}$ with constant only depending onv, then for $1,

$T: L^{p}(v) \rightarrow L^{p}(v)$

is bounded for every $v \in A_{p},$ with constant depending only on $v$ We will make a review of some of the different versions that have been appeared since then.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.

## SIMBa (confinat): El método de reducción: Determinando el orden asociado en las estructuras Hopf Galois de una extensión de cuerpos p-ádicos

El proper dimecres, 10 de juny, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Daniel Gil Muñoz.
Universitat: Universitat de Barcelona.

Data: Wednesday, 10th of June
Hora: 12:00, virtual coffee break (bring your coffee); 12:20, talk.
Lloc: Zoom meeting. A link will be sent via email, please sign up in our web.
Idioma: Catalan

Títol: El método de reducción: Determinando el orden asociado en lasestructuras Hopf Galois de una extensión de cuerpos $p$-ádicos
Resum: La teoría Hopf Galois es una generalización de la teoría de Galois mediante el uso de álgebras de Hopf. Más concretamente, una estructura Hopf Galois de una extensión de cuerpos $L/K$ es un par ($H$,·) formado por un álgebra de Hopf $H$ y una acción lineal de $H$ sobre $L$ con unas propiedades análogas a las que satisfacen, para una extensión de Galois, su grupo de Galois y la acción clásica. Este enfoque puede ser aplicado a la teoría de módulos de Galois clásica, dando lugar a una teoría de módulos de Hopf Galois. El objetivo es encontrar versiones más generales del ya conocido teorema de la base normal, que asegura que toda extensión de Galois tiene una base formada por conjugados galoisianos de un cierto elemento primitivo. En el caso de una extensión decuerpos $p$– ádicos $L/K$, el estudio de este tipo de cuestiones está́ estrechamente relacionada con el orden asociado en una estructura Hopf Galois ($H$,·), definido como el subconjunto de $H$ cuyos elementos dejan invariante el anillo de enteros de $L$ bajo. En esta charla, presentaremos un método para determinar una base del orden asociado y lo particularizaremos al caso de estructuras Hopf Galois inducidas, que son aquellas que están construidas a partir de estructuras Hopf Galois de subextensiones.

Si voleu estar al cas de les xerrades previstes, podeu consultar el calendari. Si voleu proposar una xerrada, ompliu el formulari. Si voleu contactar amb els responsables podeu escriure un missatge a seminari(dot)simba(at)ub(dot)edu.