Blog de la Biblioteca de Matemàtiques i Informàtica

SIMBa: On Zero-Knowledge Proofs

El proper dimecres, 15 de desembre, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Marta Bellés Muñoz
Universitat: Universitat Pompeu Fabra

Data: Wednesday, December 15th, 2021.
Hora: 12:00, coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website)
Idioma: English.

Títol: On Zero-Knowledge Proofs
Resum: Informally speaking, zero-knowledge protocols are cryptographic tools that allow you to prove that you know a secret without revealing it. More precisely, a zero-knowledge proof allows one party to convince another that a statement is true without revealing anything other than the veracity of the statement. This type of proofs were introduced in 1989 as theoretical cryptographic objects, but the appealing properties of the protocols have made them become crucial tools in many real-world applications with strong privacy issues. In this presentation I will explain the main ideas behind zero-knowledge, I will talk about the type of statements that we know can be proved with zero knowledge, and present some of the most outstanding applications of this technology.

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: Invariant manifolds and transport in an Earth-Moon system perturbed by Sun’s gravity field

El proper dimecres, 1 de desembre, se celebrarà una nova xerrada —en format virtual— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Begoña Nicolás
Universitat: Universitat de Barcelona

Data: Wednesday, December 1st, 2021.
Hora: 12:00, coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website)
Idioma: English.

Títol: Invariant manifolds and transport in an Earth-Moon system perturbed
by Sun’s gravity field
Resum: The mathematical model we use to study the Sun-Earth-Moon system is the Bicircular Problem (BCP), that can be thought as a time-periodic perturbation of the autonomous system described by the Restricted Three-Body Problem (RTBP). Our main concern on the BCP is regarded to a family of two-dimensional quasi-periodic solutions that have stable and unstable invariant manifolds associated. These manifolds give the skeleton for different dynamical transport phenomena that take place in our system.

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: Computation, Complexity, P-NP (and the fistful of sand that learned how to think)

El proper dimecres, 17 de novembre, se celebrarà una nova xerrada —en format virtual i, alerta, presencial!— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Javier Villar

Data: Wednesday, November 17th, 2021.
Hora: 12:00, coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website)
Idioma: English.

Títol: Computation, Complexity, P-NP (and the fistful of sand that learned
how to think)
Resum: Worst-time complexity, Blum’s complexity measures, and the complexity classes derived from them, are some of the most basic tools of modern Computer Science. The theory developed from the problem of classifying computational problems is a rich and popular piece of Math, with many applications to fields like Cryptography or Statistical Physics.
In this presentation we try to give a minimum-prerequisite insight into the current understanding of computability, machine-independent complexity, the P-NP problem and the reasons behind why we haven’t been able to solve it (yet).

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: Topological models of ∞-groupoids

El proper dimecres, 3 de novembre, se celebrarà una nova xerrada —en format virtual i, alerta, presencial!— del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: David Martínez Carpena
Universitat: Universitat de Barcelona

Data: Wednesday, November 3rd, 2021.
Hora: 12:00, coffee break; 12:20, talk.
Lloc: Zoom | Presencial: Aula B2
Idioma: English.

Títol: Topological models of ∞-groupoids
Resum: In higher category theory, ∞-groupoids are ∞-categories whose morphisms are weakly invertible at all orders. Every topological space has an associated ∞-groupoid, named its fundamental ∞-groupoid, which encodes the information of higher paths over the space. The statement that every space can be recovered up to homotopy from its fundamental ∞-groupoid is known as Grothendieck’s homotopy hypothesis. In this presentation, we choose a model of ∞-categories based on topologically enriched categories, and discuss the homotopy hypothesis in this context.

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: Supercritical diffusion: memes, stonks and more

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.

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

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.

SIMBa: An introduction to theorem provers

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.

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

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.

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.

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
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.