Recerca | Blog de la Biblioteca de Matemàtiques i Informàtica

30/05/2022
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SIMBa: The LLL algorithm and its application to number theory

El proper dimecres, 1 de juny, se celebrarà una nova xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Shehzad Hathi
Universitat: UNSW Canberra at ADFA

Data: Wednesday, June 1st, 2022.
Hora: 11:00, coffee break; 11:20, talk.
Lloc: UB (FMI aula B1) and Zoom
Idioma: English

Títol: The LLL algorithm and its application to number theory
Resum: The Lenstra-Lenstra-Lovász algorithm is a polynomial-time algorithm to find a short and nearly orthogonal basis of a lattice. Besides applications in cryptanalysis, it was also used by Odlyzko and te Riele (in 1985) to disprove Merten’s conjecture. We will look at how this algorithm can be adapted for a number-theoretic problem like Merten’s 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.

28/04/2022
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SIMBa: Taula rodona d’ajuts predoctorals

Des de l’organització del Seminari Informal de Matemàtiques de Barcelona us convidem a la Taula rodona d’orientació d’ajuts predoctorals que se celebrarà el dimecres 4 de maig de 2022 a les 12:00 (amb el coffee break a les 11:40). L’acte se celebrarà a l’aula B1 de la Facultat de Matemàtiques i Informàtica de la Universitat de Barcelona i es retransmetrà per Zoom.

El propòsit de la xerrada és resoldre els dubtes i inquietuds sobre ajuts predoctorals. També donarem una visió des de dins dels programes de doctorat de matemàtiques que hi ha les diverses universitats catalanes, així com dels màsters. Convidem als assistents a enviar preguntes per avançat, amb la possibilitat de l’anonimat, en aquest formulari i els participants de la taula les respondran.

Els participants de la taula rodona són:

Clara Cufí (UAB)
Ainoa Murillo (UB)
Aina Ferrà (UB)
Pau Mir (UPC)
Enric Florit (UB)

La sessió es desenvoluparà de la següent manera:

Breu presentació dels ajuts i programes de doctorat a Catalunya i Espanya.
Experiència i trajectòria dels membres de la taula rodona.
Torn obert de preguntes.

Després de la sessió us animem a dinar amb els membres de la taula i del SIMBa per a una
discussió més relaxada.

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

14/04/2022
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SIMBa: Undecidability in dynamical systems: from Turing machines to hydro-dynamics

El proper dimecres, 6 dabril, se celebrarà una nova xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Robert Cardona
Universitat: Université de Strasbourg

Data: Wednesday, April 20th, 2022.
Hora: 12:00, coffee break; 12:20, talk.
Lloc: UPC (FME aula 002) and Zoom
Idioma: English.

Títol: Undecidability in dynamical systems: from Turing machines to hydrodynamics
Resum: Logical and computational undecidability are notions that date back to the foundational works of Gödel and Turing developed during the first half of the 20th century. Since then, several questions in mathematics have been shown to be undecidable. In this talk, we first introduce Turing machines and explain how they can be related to the theory of dynamical systems to prove that some of their properties can be undecidable. In the context of hydrodynamics, we will be interested in the Euler equations for ideal fluids, and the undecidability properties of its solutions. We will discuss informally some recent results establishing the existence of undecidability phenomena in hydrodynamics. These results are based on several joint works with Eva Miranda, Daniel Peralta-Salas, and some of them also with Francisco Presas.

30/03/2022
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SIMBa: Degree of symmetry of manifolds and the toral rank conjecture

El proper dimecres, 6 dabril, se celebrarà una nova xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Jordi Daura Serrano
Universitat: Universitat de Barcelona

Data: Wednesday, April 6th, 2022.
Hora: 12:00, coffee break; 12:20, talk.
Lloc: UB (FMI, aula B1) and Zoom
Idioma: English.

Títol: Degree of symmetry of manifolds and the toral rank conjecture
Resum: The aim of the theory of transformation groups is to study the symmetry of spaces like manifolds, by studying group actions on them. One of the fundamental questions is the following: given a manifold M, how “big” a compact Lie group acting effectively on M can be? Although the most well-known manifolds are highly symmetric, like spheres and tori, it is conjectured that most manifolds admit few or no compact group actions. In order to make this question more precise,
it is possible to associate to a manifold its degree of symmetry, a value which tells us how symmetric this manifold is. Moreover, we may try to compute it by using topological and geometric information of the manifold. These type of computations are really hard and they lead to interesting questions, like the toral rank conjecture, formulated by S.Halperin in 1985. In the first part of the talk will be a brief introduction to the theory of compact transformation groups and the
various definitions of degree of symmetry, while in the second part I will explain the statement of the toral rank conjecture.

15/03/2022
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SIMBa: Numerical computation of invariant objects using Daubechies wavelets

El proper dimecres, 16 de març, se celebrarà una nova xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Salvador Borrós Cullell
Universitat: Universitat Autònoma de Barcelona

Data: Wednesday, March16th, 2022.
Hora: 12:00, coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website)
Idioma: English.

Títol: Numerical Computation of Invariant Objects Using Daubechies
Wavelets
Resum: We present a method to compute the truncated wavelet expansion of an invariant object in a quasi-periodic skew product using periodic Daubechies Wavelets. To obtain the wavelet coefficients, we need to solve the invariance equations of the system in a mesh of points, desirably as dense as possible. This requires quite a bit of numerical finesse, since Daubechies Wavelets do not have closed expressions. Once we have obtained the truncated wavelet expansion of the invariant object, we can compute its Besov regularity of said invariant objects. In particular, we will compute the regularity of Strange Non-Chaotic Attractors stemming from a Keller-GOPY biparametric family of systems as a proof of concept.

24/02/2022
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SIMBa: Unlikely Intersections in Dynamics

El proper dimecres, 2 de març, se celebrarà una nova xerrada del Seminari Informal de Matemàtiques de Barcelona (SIMBa).

Speaker: Andriana Karuk
Universitat:

Data: Wednesday, March 2nd, 2022.
Hora: ~~12:00, coffee break; 12:20, talk~~. Actualització: 12:00, virtual coffee break ; 12:20, talk.
Lloc: Zoom, UB (aula B1).
Idioma: English.

Títol: Unlikely Intersections in Dynamics
Resum: Arithmetic dynamics is an encounter of number theory and dynamical systems. In arithmetic dynamics, one focuses on studying properties of self-maps with a flavour of number theory. In particular, the study of unlikely intersections in arithmetic geometry leads to dynamical problems of an arithmetic nature. The guiding principle is that families of objects should not intersect unless there is a geometric reason forcing the converse. Our object of study is the set of parameters $c \in \mathbb{C}$ such that both $a$ and $b$ are preperiodic for $f_{c}(z)=z^{d}+c$ . We will see that for any fixed $a, b \in \mathbb{Z}$ and any integer $d \geqslant 2$ , the set of $c \in \mathbb{C}$ for which both $a$ and $b$ are preperiodic for $z^{d}+c$ is infinite if and only if $a^{d}=b^{d}$ . The proof combines complex-analytic and arithmetic tools to prove this statement, which we will have a glimpse of.

28/01/2022
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SIMBa: From far-out mystery to a useful tool

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

Speaker: Carlos Caralps Rueda
Universitat: Universitat Autònoma de Barcelona

Data: Wednesday, February 9th, 2022.
Hora: 12:00, coffee break; 12:20, talk.
Lloc: Zoom (the link will be posted on our website)
Idioma: English.

Títol: From far-out mystery to a useful tool
Resum: This talk aims to redefine topological filters in order to obtain a helpful tool that can be used to prove some propositions in topology using semiring theory. In this talk, we will see the first definition of filters provided by Henri Cartan, which is used to define limits in general topological spaces, and we will state some famous theorems about filters and topology. Changing the definition slightly allows us to prove some propositions by using group theory identities, we will show this by solving some topology-undergraduate problems as trivial algebraic identities.

13/12/2021
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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.

25/11/2021
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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.

12/11/2021
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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
Universitat: Universidad de La Rioja

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).