These seminars are common with the Plume team (ENS Lyon) and are held in the seminar room, second floor of the building Le Chablais, on the Bourget-du-lac (Savoy) site or at ENS Lyon.

## Next seminar:

**Thursday 22nd March 2018 at 10h
**
Oleg Karpenkov
(Department of Mathematical Sciences, University of Liverpool),
*Global relations for toric singularities*

Abstract:(Hide abstracts)

In this talk we will discuss a link between geometry of continued fractions and global relations for singularities of complex projective toric surfaces. The results are based on recent development of lattice trigonometric functions that are invariant with respect to Aff(2,Z)-group action.

The seminar of the team LIMD is under the responsibility of Xavier
Provencal.

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Other years: 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017,
all years together.

# Year 2018

**Thursday 25th January 2018 at 10h
**
Youssef Fares
(Amiens),
*Autour de la conjecture de Poonen sur les polynômes quadratiques*

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Soit c un nombre rationnel. Considérons le polynôme φ(X) = X^2 - c. On s’intéressse aux cycles de φ dans Q. Plus précisément, on s’intéresse à l’une des conjectures de Poonen selon laquelle tout cycle de φ dans Q admet une longueur au plus égale à 3. Dans notre exposé, on discutera de cette conjecture et on rappellera les résultats connus. En suite, on utilisera des moyens arithmetiques, combinatoriaux et analytiques simples pour étudier des cas particuliers de ce problème. Les outils utilisés dans cet exposé sont accessibles aux étudiants de master 2.

**Thursday 1st February 2018 at 10h
**
Thomas Rubiano
(LIPN, Paris 13),
*Implicit Computational Complexity meets Compilers*

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Complexity theory helps us predict and control resources, usually time and space, consumed by programs. Static analysis on specific syntactic criterion allows us to categorize some programs. A common approach is to observe the program’s data’s behavior. For instance, the detection of non-size-increasing programs is based on a simple principle : counting memory allocation and deallocation, particularly in loops. This way, we can detect programs which compute within a constant amount of space. This method can easily be expressed as property on control flow graphs. Because analyses on data's behaviour are syntactic, they can be done at compile time. Because they are only static, those analyses are not always computable or easily computable and approximations need are needed. ``Size-Change Principle'' from C. S. Lee, N. D. Jones et A. M. Ben-Amram presented a method to predict termination by observing resources evolution and a lot of research came from this theory. Until now, these implicit complexity theories were essentially applied on more or less toy languages. This thesis applies implicit computational complexity methods into ``real life'' programs by manipulating intermediate representation languages in compilers. This give an accurate idea of the actual expressivity of these analyses and show that implicit computational complexity and compilers communities can fuel each other fruitfully. As we show in this thesis, the methods developed are quite generals and open the way to several new applications.

**Thursday 8th February 2018 at 10h
**
Séminaire Chocola
(ENS Lyon),
*TBA*

Abstract:(Hide abstracts)

TBA

**Wednesday 28th February 2018 at 10h
**
Eric Goles
(Engineering Faculty of the Adolfo Ibanez University, Santiago, Chile),
*Dynamics and Complexity of Majority Automata: application to some discrete social models*

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A Majority Automata consists of applying over the vertices of a undirected graph (with states 0’s and 1’s) an operator that chooses the most represented state among the neighbors of a vertex. This rule is applied in parallel over all the nodes of the graph. When the graph is a regular lattice ( in one or more dimensions) it is called the Majority Cellular Automata. In this seminar we will study the computational complexity of the following prediction problem: PRED: Given an initial configuration and a specific site initially at state a ( 0 or 1), is there a time step T≥1 such that this site changes state? The complexity of PRED is characterized by the possibility to find an algorithm that give the answer faster than the running of the automata simulation in a serial computer. More precisely, if we are able to determine an algorithm running in a parallel computer in polylog time (class NC). Otherwise, the problem may be P-Complete ( one of the most dificult in class P of Polynomial problems) or … worse. We will applied this kind of results to the discrete Schelling’s segregation model. Also we will present the Sakoda’s Social Discret model.

**Thursday 8th March 2018 at 10h
**
Étienne Miquey
(Nantes),
*The algebraic structure of classical realizability models.*

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Implicative algebras, developed by Alexandre Miquel, are very simple algebraic structures generalizing at the same time complete Boolean algebras and Krivine realizability algebras, in such a way that they allow to express in a same setting the theory of forcing (in the sense of Cohen) and the theory of classical realizability (in the sense of Krivine). Besides, they have the nice feature of providing a common framework for the interpretation both of types and programs. The main default of these structures is that they are deeply oriented towards the λ-calculus, and that they only allows to faithfully interpret languages in call-by-name. To remediate the situation, we introduce two variants of implicative algebras: disjunctive algebras, centered on the “par” (⅋) connective of linear logic (but in a non-linear framework) and naturally adapted to languages in call-by-name; and conjunctives algebras, centered on the “tensor” (⊗) connective of linear logic and adapted to languages in call-by-value. Amongst other properties, we will see that disjunctive algebras are particular cases of implicative algebras and that conjunctive algebras can be obtained from disjunctive algebras (by reversing the underlying order).

**Thursday 15th March 2018 at 10h
**
Séminaire Chocola
(ENS Lyon),
*TBA*

**Wednesday 21st March 2018 at 10h
**
Buket Eren
(Galatasaray University, Istambul, Turquie.),
*Autour de l'équation de Markov*

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Les nombres de Markov sont des entiers positifs qui apparaissent dans les triplets de solutions de l’équation diophantienne, x^2+y^2+z^2 = 3xyz, appelée l’équation de Markov. Il est possible de trouver tous les solutions à partir d’un triplet par un algorithme simple. Pourtant, il y a un célèbre problème ouvert formulé par Frobenius : est-il vrai qu'étant donné un entier positif z, il existe au plus un couple (x,y) d’entiers positifs avec x < y < z tel que (x,y,z) soit une solution? Ces nombres apparaissent dans le contexte des fractions continues et de l’approximation diophantienne des nombres réels irrationnels par des nombres rationnels. Ils apparaissent aussi dans de très nombreux domaines des mathématiques comme les formes quadratiques binaires, la géométrie hyperbolique et la combinatoire des mots etc... Le but de cette exposé est de présenter une partie de la théorie de Markov qui est construite autour de l’équation de Markov et de donner la conjecture d’unicité sur les nombres de Markov. Au final, on introduira une involution des irrationnels susceptible d’être pertinente pour le sujet.

**Thursday 22nd March 2018 at 10h
**
Oleg Karpenkov
(Department of Mathematical Sciences, University of Liverpool),
*Global relations for toric singularities*

Abstract:(Hide abstracts)

In this talk we will discuss a link between geometry of continued fractions and global relations for singularities of complex projective toric surfaces. The results are based on recent development of lattice trigonometric functions that are invariant with respect to Aff(2,Z)-group action.

**Thursday 29th March 2018 at 10h
**
Maxime Lucas
(Nantes),
*TBA*

**Thursday 5th April 2018 at 10h
**
Séminaire Chocola
(ENS Lyon),
*TBA*

**Thursday 17th May 2018 at 10h
**
Séminaire Chocola
(ENS Lyon),
*TBA*

The seminar of the team LIMD is under the responsibility of Xavier
Provencal.

**Settings:**
See
with decreasing date.
Hide abstracts

Other years: 2005, 2006, 2007, 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017,
all years together.