Abstract: After its introduction in the summer of 2016, Pokémon GO quickly became the most popular game around. The game requires players---called trainers---to walk outside to search for and catch Pokémon. Now that the first craze is over, it is time for scientists to analyze various aspects of the game. Since the game requires a mobile device with GPS and is (in part) essentially a search problem played on the streets, we can analyze it using competitive analysis. We define an abstraction of searching for Pokémon using a geometric graph and call it the Pokémon GO search problem. We show that for general geometric graphs, there is no constant competitive ratio to find a Pokémon. However, if the graph has convex faces only, or if the graph has constant-bounded geometric dilation, then there is an O(1)-competitive search strategy.

Abstract

En esta charla abordaremos el problema de Moore en Gráficas Mixtas, el cual fue introducido por Bosàk en 1979, a partir de ese momento este problema ha sido abordado por varios autores y se han logrado distintos resultados de los cuales hablaremos en esta charla, además expondremos nuestras recientes aportaciones en este tema. Por otro lado, buscando generalizar este problema, debido a que dicho problema está relacionado de manera natural con el problema de las Jaulas, plantearemos el problema de Jaulas Mixtas y mostraremos los avances que tenemos en dicho problema. 

In this talk, we present an identification protocol and a signature scheme due to Galbraith, Petit and Silva. We rely on the hardness of an isogeny problem on supersingular elliptic curves, which is believed to be a hard problem, and even the best known quantum algorithms to solve it run in exponential time.

Our identification protocol relies on two key ingredients. First, the good mixing properties of supersingular isogeny graphs, which allow us to move through the graph efficiently and at the same time achieve random-looking outputs.

Second, we make use of Deuring’s correspondence, which identifies endomorphism rings of supersingular elliptic curves with maximal orders in a certain quaternion algebra.  We use the algorithm of Kohel-Lauter-Petit-Tignol (ANTS 2014) to compute ideals of a certain norm between maximal orders in the quaternion algebra. This will allow to simulate the protocol with indistinguishable distribution.

Finally, we use the standard technique of Fiat-Shamir to derive a signature scheme from the identification protocol, and we discuss its security.

Background on elliptic curves, quaternion algebras and expander graphs will be provided at the beginning of the talk, only cryptography definitions are required.

L’any 2016 es commemora el tercer centenari de la mort d’un dels matemàtics més rellevants de la història, Gottfried Wilhelm Leibniz (Leipzig, 1646 – Hannover, 1716). Amb aquest cicle volem commemorar aquest centenari, adherint-nos així a tots els homenatges que la comunitat científica està celebrant arreu del món.

Si cal destacar quelcom de l’obra matemàtica de Leibniz, podríem citar els seus nombrosos treballs sobre el càlcul infinitesimal, els determinants, la combinatòria, la lògica i els jocs d’atzar.

Entendre el pensament matemàtic de Leibniz és molt complex i requereix submergir-se no només en els seus textos matemàtics sinó també en els filosòfics relacionats amb el seu sistema metafísic, amb la seva interpretació dels processos de raonament com una àlgebra del pensament, i en les nombroses cartes i manuscrits recentment editats.

Un dels objectius del cicle és presentar la figura de Leibniz des de la seva vessant com a matemàtic, donant a conèixer la seva obra i el seu impacte. A més, l’estudi de Leibniz i de la seva obra contribuirà a transmetre als participants del cicle una percepció de la matemàtica com a ciència útil, humana, interdisciplinària, dinàmica i heurística.

Amb aquest homenatge a Leibniz, pretenem conèixer millor el seu pensament, així com les seves fonts i l’impacte que va tenir la seva obra tant al segle XVIII, com posteriorment.

El cicle s'estructura en dues sessions, amb dues xerrades cadascuna:

• 4 novembre 2016

M. Rosa Massa (UPC): “Una aproximació a la figura de Leibniz: filòsof, físic, enginyer i matemàtic”
Guillermo Lusa (UPC): “Tras las huellas de Leibniz”

• 18 novembre 2016

Mònica Blanco (UPC): “Algunes qüestions al voltant del càlcul de Leibniz”
Siegmund Probst (Leibniz Archive): “Gottfried Wilhelm Leibniz (1646-1716) and John Wallis (1616-1703)”

Trobareu més informació sobre el cicle a http://arban.espais.iec.cat/2016/10/11/leibniz-300-anys-despres/.

Abstract

En esta charla, se presentará el siguiente resultado:

Sean $t$, $k$ y $q$ enteros tal $q\geq 0$, $0\leq t < k$ y $t \equiv k \,({\rm mod}\, 2)$ y sea $s\in [0,t+1]$ el único entero que satisface $s \equiv q + \frac{k-t-2}{2} \,({\rm mod} \, (t+2))$. Entonces, para todo entero $n$ tal que [n \ge \max\left{k,\frac{1}{2(t+2)}k^2 + \frac{q-s}{t+2}k - \frac{t}{2} + s\right}] y cualquier función $f:[n]\to {-1,1}$ con $|\sum{i=1}^nf(i)| \le q$, existe un subconjunto $B \subseteq [n]$ de $k$ enteros consecutivos tal que $|\sum{y\in B}f(y)| \le t$. Este resultado es justo para todos los parámetros implicados. Daremos también una caracterización de las secuencias extremales. 

Además de este teorema, presentaremos otros resultados similares involucrando diferentes subsecuencias y descomposiciones de secuencias en ciertas subsecuencias de suma acotada.

Este es un trabajo en colaboración con Yair Caro y Amanda Montejano.

This activity is aimed at the researcher who has probably taken an introductory statistics and probability course at some stage and would like a brief introduction to the core methods of statistics and how they are applied. We are going to do a panoramic view by the good practices in scientific methodologies from statistical point of view.

Table of contents:

• Lecture 1 -Datasets and Random Variables
• Lecture 2 -Statistical Models and Probability theory
• Lecture 3 -Likelihood and Inferential Questions

Please note that October 31st, 2016 is the deadline for the registration (or when seats are filled).

You can find more information and register at: http://www.crm.cat/en/Activities/Curs_2016-2017/Pages/Reviewing-the-core-of-statistics.aspx.

• Speaker: Arnau Padrol, Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie (Paris 6).

• Title: Colorful simplicial depth, Minkowski sums, and generalized Gale transforms.

Abstract

The colorful simplicial depth of a collection of d+1 finite sets of points in Euclidean d-space is the number of choices of a point from each set such that the origin is contained in their convex hull. We use methods from combinatorial topology to prove a tight upper bound on the colorful simplicial depth. This implies a conjecture of Deza et al. (2006). Furthermore, we introduce colorful Gale transforms as a bridge between colorful configurations and Minkowski sums. Our colorful upper bound then yields a tight upper bound on the number of totally mixed facets of certain Minkowski sums of simplices. This resolves a conjecture of Burton (2003) in the theory of normal surfaces.

This is joint work with Adiprasito, Brinkmann, Paták, Patáková and Sanyal.

Abstract

The colorful simplicial depth of a collection of d+1 finite sets of points in Euclidean d-space is the number of choices of a point from each set such that the origin is contained in their convex hull. We use methods from combinatorial topology to prove a tight upper bound on the colorful simplicial depth. This implies a conjecture of Deza et al. (2006).

Furthermore, we introduce colorful Gale transforms as a bridge between colorful configurations and Minkowski sums. Our colorful upper bound then yields a tight upper bound on the number of totally mixed facets of certain Minkowski sums of simplices. This resolves a conjecture of Burton (2003) in the theory of normal surfaces.

This is joint work with Adiprasito, Brinkmann, Paták, Patáková and Sanyal.

De la convocatòria "The position is for carrying out postdoctoral research at the highest level in the area of Mathematical Modelling. This includes in particular Applied statistics and probability, Mathematical engineering, and Numerical analysis and simulation. Candidates should identify potential BGSMath researchers or groups in which to develop their research projects."