En els darrers anys hi ha hagut una experiència ben nova en el camp de la matemàtica: entitats nacionals han encarregat a consultores professionals diversos estudis amb l’objectiu d’avaluar l’impacte de l’activitat matemàtica en el producte interior brut (PIB) del país. Els estudis es refereixen al Regne Unit (2012), els Països Baixos (2014), França (2015) i Espanya (abril del 2019). Cadascun dels quatre estudis ha tingut el seu propi recorregut.

L’objectiu d’aquesta conferència és presentar una lectura de les conclusions d’aquests estudis. També hauria d’haver-hi lloc per a una visió crítica d’aquests informes, però potser el més interessant seria poder-ne extreure recomanacions de política científica, aplicables, en particular, a Catalunya en l’àmbit de les matemàtiques o en l’àmbit general de la ciència i la tecnologia.

Canals:
Youtube: www.youtube.com/comunicacioiec
Plataforma Zoom: https://us02web.zoom.us/j/81896034827?pwd=QXdmaVNoRW4wTTl5dHFyMlFCVldNdz09

VLAB: b-Lab Diary of a confinement: Daniel Peralta (I)

In these days of confinement, work in the lab has not stopped! We are having talks by videoconference, both by members of the lab and by guests.

If a talk interests you and you wish to listen to attend, or if you have a proposal for these talks, please contact the organizer: eva.miranda@upc.edu

Contact structures and Beltrami fields on the torus and the sphere

Speaker: Daniel Peralta-Salas

When: Tuesday 28th of April, at 17:00 - 18:00.

Abstract: We present new explicit tight and overtwisted contact structures on the (round) 3-sphere and the (flat) 3-torus for which the ambient metric is weakly compatible. Our proofs are based on the construction of nonvanishing curl eigenfields using suitable families of Jacobi or trigonometric polynomials. As a consequence, we show that the contact sphere theorem of Etnyre, Komendarczyk and Massot (2012) does not hold for weakly compatible metric as it was conjectured. We also establish a geometric rigidity for tight contact structures by showing that any contact form on the 3-sphere admitting a compatible metric that is the round one is isometric, up to a constant factor, to the standard (tight) contact form.

The talk will be tightly related to this article: https://arxiv.org/abs/2004.10185

More information in our webpage:

https://geodys.upc.edu/en/news/b-lab-diary-of-a-confinement-daniel-peralta-i

The Global Poisson Webinar aims at presenting talks in the field of Poisson geometry, understood in a (very) broad sense.

We welcome suggestions of talks for this seminar which should be sent to (one of) the seminar organizers.

We are also happy to publish dates and access data of other Poisson seminars and events. Please address this information to the Zoom Master.

http://www.unige.ch/math/folks/nikolaev/GlobalPoisson.html

Propers conferenciants:

April 9:

Rui Loja Fernandes (Urbana-Champaign)

Local models around Poisson submanifolds

April 16:     Eckhard Meinrenken

April 23:     Eva Miranda

Més informació

Saps quina és la raó o la proporció que ha inspirat més artistes al llarg de la història? Una raó que està relacionada amb la distribució dels pètals en una margarida o de les pipes en un gira-sol... La raó més irracional de totes! Es tracta d'un nombre envoltat de misticisme que s'ha anomenat auri o d'or, perquè representa un cànon occidental de bellesa i harmonia. El més sorprenent és que aquest nombre apareix en molts patrons de la natura.

En aquesta xerrada, la doctora en Matemàtiques Maria Alberich-Carramiñana ens revelarà aquest misteri i també ens farà descobrir propietats matemàtiques curioses del nombre auri, també denominat el nombre de la divina proporció. En particular, ens parlarà de la relació que té aquest nombre amb la successió de Fibonacci, amb els mosaics pentagonals o amb les tessel·lacions de Penrose, i també amb la inesperada troballa dels quasicristalls.

By: Ignacio Cascudo (IMDEA Software, Madrid)

Title: On universally composable secure homomorphic commitment schemes

Abstract: Commitment schemes are the digital equivalent to a safe-box. A committer can put a value in the box (commit), lock it and then send it to a receiver. At a later point the committer can open the commitment (sending the keys to the safe-box). After receiving the box but before receiving the keys, while the receiver cannot see the message, the committer can no longer change it. Commitment schemes are very useful for secure multiparty computation, for which we often want some additional properties: homomorphic properties allow to open some agreed-upon functions of some committed messages; universal composable (UC) security gives strong guarantees of security when commitments are used as a part of larger protocol. In this talk I will describe some highlights of a line of work which constructs UC-secure homomorphic commitments from error-correcting codes and simpler cryptographic primitives.

The talk is based on a series of papers from PKC 2015, Crypto 2016, Asiacrypt 2019 jointly with Ivan Damgård, Bernardo David, Nico Döttling, Rafael Dowsley, Irene Giacomelli, Jesper Buus Nielsen and Roberto Trifiletti.

TALK #1:

By: Ramiro Martínez, MAK-UPC

Title: RLWE-based Zero-Knowledge Proofs for linear and multiplicative relations

Abstract: Ring Learning With Errors (RLWE) samples are pairs of polynomials in $\\mathbb{Z}_q\[x\]/(x^{n}+1)$, obtained from a distribution that depends on a secret polynomial. RLWE samples are computationally indistinguishable from uniformly random pairs of polynomials. We present efficient Zero-Knowledge Proofs of Knowledge (ZKPoK) for linear and multiplicative relations among secret messages hidden as RLWE samples. Our proposed protocols for a ZKPoK are based on the celebrated paper by Stern on identification schemes using coding problems (Crypto'93). Our 5-move protocol achieves a soundness error slightly above 1/2 and perfect Zero-Knowledge.

As an application we present ZKPoK of relations between committed messages. The resulting commitment scheme is perfectly binding with overwhelming probability over the choice of the public key, and computationally hiding under the RLWE assumption. Compared with previous Stern-based commitment scheme proofs we decrease computational complexity, improve the size of the parameters and reduce the soundness error of each round.

TALK #2:

By: Carla Ràfols, UPF

Title: A survey on SNARKs

Abstract: Zero-Knowledge proofs are among the oldest and most useful cryptographic primitives. Efficient proofs for "simple" languages (non NP complete) have been known for a long time, in different security models and based on various different computational assumptions. SNARKs or Succint Non-Interactive Arguments of Knowledge, proposed by Groth in 2010, allow to prove circuit satisfiability in zero-knowledge. The most efficient constructions are not only succinct (independent of the witness size) but also very efficient concretely. SNARKs have had a major impact in cryptographic research and practice, partly due to their application to anonymous financial transactions in cryptocurrencies. In this talk, I will survey some of the main results, techniques and applications in the area.

TALK #1:

By: Michael Olugbenga Bamiloshin, URV Tarragona

Title: Common Information, Matroid Representation, and Secret Sharing for Matroid Ports

Abstract: A secret sharing scheme is a method by which a dealer distributes shares to parties such that only authorized subsets of parties can reconstruct the secret. The information ratio of a secret sharing scheme is the size in bits of the largest share of the scheme divided by the size of the secret. Farràs, Kaced, Martín and Padró presented an improvement in the linear programming technique to derive lower bounds on the information ratio of the schemes for an access structure that use the Ahlswede-Körner lemma and the common information of random variables, avoiding the use of explicit non-Shannon information inequalities (EUROCRYPT 2018). In this work we apply this linear programming technique to the classification of matroids on eight and nine points. Namely, we apply this technique to check if a matroid is multilinearly representable, algebraic or almost entropic. We also present some hitherto unknown non-representable matroids and new bounds on the information ratio of schemes for ports of non-representable matroids.

This is a joint work with Aner Ben-Efraim, Oriol Farràs and Carles Padró.

TALK #2:

By: Victor Peña-Macias, Universidad Nacional de Colombia

Title: Characteristic-Dependent Linear Rank Inequalities and Applications to Network Coding

Abstract: In Linear Algebra over finite fields, a characteristic-dependent linear rank inequality is a linear inequality that holds by ranks of subspaces of a vector space over a finite field of determined characteristic, and does not in general hold over fields with other characteristic. In this talk, we show a new method to produce these inequalities. We also discuss some results of application to Network Coding, among these, for each finite or co-finite set of primes P, we show that there exists a sequence of networks (N(t)) in which each member is linearly solvable over a field if and only if the characteristic of the field is in P; and the linear capacity, over fields whose characteristic is not in P, tends to 0 as t tends to infinity.

Incripció:
https://gcice.upc.edu/fitxa_cursos.asp?id=54476

Two talks in this session:

TALK #1:

By: Chen Yuan, CWI Amsterdam
Title: Towards Optimal Robust Secret Sharing with Security Against a Rushing Adversary

Abstract: Robust secret sharing enables the reconstruction of a secret-shared message in the presence of up to t (out of n) incorrect shares. The most challenging case is when n = 2t + 1, which is the largest t for which the task is still possible, up to a small error probability and with some overhead in the share size. In this work,we propose a new robust secret sharing scheme that offers full security against a rushing adversary. We also answer the open question posed by Cevallos et al.(Eurocrypt 2012) who proposed a scheme with overhead of O(n+K) and asked whether the linear dependency on n was necessary or not.

This is a joint work with Serge Fehr.

TALK #2:

By: Oriol Farras, URV Tarragona
Title: Secret-Sharing Schemes for General Access Structures

Abstract: A secret-sharing scheme allows some authorized sets of parties to reconstruct a secret; the collection of authorized sets is called the access structure. For over 30 years, it was known that any (monotone) collection of authorized sets can be realized by a secret-sharing scheme whose shares are of size $2^{n−o(n)}$ and until recently no better scheme was known. In a recent breakthrough, Liu and Vaikuntanathan (STOC 2018) reduced the share size to $O(2^{0.994n})$. We improved the general construction, obtaining a share size $O(2^{0.892n})$. For the special case of linear secret-sharing schemes, we get an exponent of $0.942$ (compared to $0.999$ of Liu and Vaikuntanathan).

This result was included in the paper "Secret-Sharing Schemes for General and Uniform Access Structures", a joint work with Benny Applebaum, Amos Beimel, Oded Nir and Naty Peter presented in Eurocrypt 2019.