Recerca | Blog de la Biblioteca de Matemàtiques i Informàtica

02/05/2021
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SIMBa: Spectral data of Higgs bundles

El proper dimecres, 5 de maig, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Raffaele Carbone
Universitat:

Data: Wednesday, May 5th, 2021.
Hora: 12:00,virtual coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website).
Idioma: English.

Títol: Spectral data of Higgs bundles
Resum: Higgs bundles play an important role across many different areas of modern mathematics and physics: algebraic geometry, representation theory, Gauge theory, dynamical systems. In this seminar I will show how Higgs bundles on curves are studied by algebraic geometry by comparing them to torsion-free sheaves of rank 1 on associated spectral curves.

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.

19/04/2021
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SIMBa: Entering the tower with Iwasawa theory

El proper dimecres, 21d’abril, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Marta Sánchez Pavón
Universitat: Universidad de Sevilla

Data: Wednesday, April 21th, 2021.
Hora: 12:00,virtual coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website).
Idioma: English.

Títol: Entering the tower with Iwasawa theory
Resum: Proving Fermat Last Theorem has been one of the most famous mathematical challenges during the last years. Most importantly, it served as a key starting point for developing deep theories in arithmetic geometry; and Iwasawa theory has been one of such. The fundamental idea of Iwasawa theory is studying the growth of arithmetic objects (such as the ideal class group of number fields or Selmer groups of elliptic curves and abelian varieties) in an infinite tower of $p$ -adic extensions. Furthermore, much of the recent progress in the Birch and Swinnerton-Dyer conjecture is due to these methods. In this talk, we present a brief introduction to Iwasawa theory with an eye on elliptic curves.

01/04/2021
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SIMBa: Coeficients de Fourier al p-èsim intèrval de Ramanujan-Petersson

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

Speaker: Eduard Soto Ballesteros
Universitat: Universitat de Barcelona

Data: Wednesday, April 7th, 2021.
Hora: 12:00,virtual coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website).
Idioma: English.

Títol: Coeficients de Fourier al $p$ -èsim intèrval de Ramanujan-Petersson
Resum: L’expansió de Fourier d’una forma modular nova de pes 2 y caràcter trivial és una sèrie de potències amb coeficients enters algebraics en un cos totalment real. Els coeficients d’índex primer tenen un rol protagonista per motius diversos. La conjectura de Ramanujan-Petersson, demostrada por Deligne, prediu que el $p$ -èsim coeficient de Fourier d’una forma modular de pes 2 té norma en $[0,2 \sqrt{p}] .$ En aquesta xerrada discutirem quins cossos totalment reals tenen elements primitius enters en $[0,2 \sqrt{p}]$ . Aquest treball en col·laboració amb Samuele Anni té orígens en un estudi computacional d’una conjectura de Coleman.

05/03/2021
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SIMBa: ¿How far is an extension of $p$-adic fields from having a normal integral basis?

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

Speaker: Fabio Ferri
Universitat: University of Exeter

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

Títol: ¿How far is an extension of $p$ -adic fields from having a normal integral basis?
Resum: Let $L / K$ be a Galois extension of $p$ -adic fields with Galois group $G$ . Denote by $K[G]$ the group ring $\left\{\sum_{g \in G} a_{g} g: a_{g} \in K\right\} ;$ the classical normal basis theorem shows that $L$ is a free $K[G]$ -module of rank 1 . that is, there exists an element $\alpha \in L$ such that $\{g(\alpha)\}_{g \in G}$ is a basis of $L$ as a $K$ -vector space. It is natural to ask whether $\mathcal{O}_{L}$ is also a free $\mathcal{O}_{K}[G]$ -module of rank 1 , where $\mathcal{O}_{L}$ and $\mathcal{O}_{K}$ denote the rings of integers of $L$ and $K$ , respectively. A theorem of Noether tells us that this is the case if and only if the extension is (at most) tamely ramified. When $L / K$ is wildly ramified, we can still note that there always exists a free $\mathcal{O}_{K}[G]$ -submodule of $\mathcal{O}_{L}$ with finite index. The purpose of this talk is to study the minimal such index, i.e. the quantity $m(L / K):=$ $\min _{\alpha \in \mathcal{O}_{L}}\left[\mathcal{O}_{L}: \mathcal{O}_{K}[G] \alpha\right] .$ We will provide a general bound that only depends on the invariants of the extension, a complete formula for $m(L / K)$ when $L / \mathbb{Q}_{p}$ is abelian and a complete formula when $L / K$ is cyclic of degree $p$ . This is joint work with Ilaria Del Corso and Davide Lombardo.

08/02/2021
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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.

24/01/2021
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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.

08/01/2021
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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.

14/12/2020
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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
Universitat: Universidad Complutense de Madrid.

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.

04/12/2020
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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).

16/11/2020
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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.