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SIMBa: Supercritical diffusion: memes, stonks and more

SIBMa

El proper dimecres, 20 d’octubre, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Damià Torres Latorre
Universitat: Universitat de Barcelona

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

Títol: Supercritical diffusion: memes, stonks and more
Resum: In this talk, I will explain the foundations of the theory of elliptic nonlocal PDE, focusing on the fractional Laplacian, (-\Delta)^{s} a model example, and then some recent results on the supercritical fractional obstacle problem.

The first part will start with the relation of fractional operators to jump-diffusion (Lévy) processes and some physical applications. Then, I will give an overview of the basic properties of solutions and compare them to harmonic functions, and also comment on the Caffarelli-Silvestre extension.

In the second part, I will give an idea of how stock prices can be modelled with a nonlocal parabolic obstacle problem, compare the scaling properties of the problem depending on the value of sand present the main points of a recent work with X. Ros-Oton where we study the regularity of the solutions in the supercritical case.

 

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.


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SIMBa: On the possible ranks of universal quadratic forms over totally realnumber fields

SIBMa

El proper dimecres, 6 d’octubre, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Daniel Gil Muñoz
Universitat: Charles University in Prague

Data: Wednesday, October 6th, 2021.
Hora: 12:00,virtual coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website).
Idioma: English.

Títol: On the possible ranks of universal quadratic forms over totally realnumber fields
Resum: A quadratic form Q\left(X_{1}, \ldots, X_{n}\right) over the integer numbers is said to be universal if it represents all positive integers, that is, for every a \in \mathbb{Z}_{>0} there is a vector \left(\alpha_{1}, \ldots, \alpha_{n}\right) \in \mathbb{Z}^{n} such that Q\left(\alpha_{1}, \ldots, \alpha_{n}\right)=a. The topic of universal quadratic forms is quite classical in arithmetic; for instance, Langrange’s 1770 four square theorem asserts that the sum of four squares is a universal quadratic form over \mathbb{Z}. In this talk we consider the suitable generalization of universality for quadratic forms over the number ring \mathcal{O}_{K} of a totally real number field K and view some recent results on the possible ranks (number of variables X_{i} ) of universal quadratic forms over different families of totally real number fields.

 

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.


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SIMBa: An introduction to theorem provers

SIBMa

El proper dimecres, 2 de juny, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Eloi Torrents
Universitat: Universitat Autònoma de Barcelona

Data: Wednesday, June 2nd, 2021.
Hora: 12:00,virtual coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website).
Idioma: English.

Títol: An introduction to theorem provers
Resum: In this talk, we will introduce proof assistants, pieces of softwarethat formally verify mathematical proofs.Lean has a very extensivedatabase with mathematical results at the undergraduate level for-mally verified, and it is even used to verify new research. This hasseveral applications, including teaching, automatically verifying publi-cations, and even automated theorem proving. At the end of this talk,we will carry out a demo of Lean to show the basics and how you canget started.

 

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.


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SIMBa: p-adic modular forms: why do we care?

SIBMa

El proper dimecres, 19 de maig, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Guillem García Tarrach
Universitat: University of Cambridge

Data: Wednesday, May 19th, 2021.
Hora: 12:00,virtual coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website).
Idioma: English.

Títol: p-adic modular forms: why do we care?
Resum: Since their introduction in the seventies, p-adic modular forms have become an important topic in algebraic number theory and have seen many applications to problems in this area. In this talk I will be explaining some of the motivation for p-adic modular forms and talk about some of the important results in the theory.

 

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.


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SIMBa: Spectral data of Higgs bundles

SIBMa

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.


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SIMBa: Entering the tower with Iwasawa theory

SIBMa

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.

 

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.


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SIMBa: Coeficients de Fourier al p-èsim intèrval de Ramanujan-Petersson

SIBMa

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.

 

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.


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

SIBMa

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.

 

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.


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SIMBa: Identities in prime rings

SIBMa

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.


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SIMBa: Persistent homology and barcode distance

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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.