Factorisations dans un groupe, action d'Hurwitz, épluchabilité et ordre compatible

01/26/2016 - 15:15
01/26/2016 - 16:30
Speaker: 
Vivien Ripoll, Université de Vienne
Location: 
201, av. du Président-Kennedy, LOCAL PK-4323, Montréal (Qc) H2X 3Y7
Abstract: 

 Seminar LACIM

Soit G un groupe, A un sous-ensemble de G, et M le sous-monoïde de G engendré par A. Tout élément g de M peut s'écrire comme un produit d'éléments de A de longueur minimale (ceci s'appelle une décomposition réduite de g). On définit l'ordre "préfixe" sur M, de telle sorte que les décompositions réduites de g sont en bijection avec les chaînes maximales de l'intervalle [1,g] pour l'ordre préfixe. Sous certaines hypothèses sur A, il existe aussi une action naturelle du groupe de tresses à n brins sur l'ensemble des décompositions réduites d'un élément g de longueur n, qui s'appelle l'action d'Hurwitz. On examine les relations entre la propriété d'épluchabilité du poset [1,g] et la transitivité de l'action d'Hurwitz sur les décompositions réduites de g. Dans le cas où G est un groupe de réflexion, A son ensemble de réflexions, et g un élément de Coxeter, l'intervalle [1,g] est le treillis des partitions non-croisées de G et ces propriétés sont bien connues dans le cadre de la combinatoire de Coxeter-Catalan. On étudie un outil potentiel pour prouver ces propriétés, appelé ordre g-compatible sur A. C'est un ordre total sur A, inspiré par la définition d'ordre de réflexion compatible dans le cas d'un groupe de réflexion. (Travail en commun avec Henri Mühle)

Last edited by on Fri, 01/22/2016 - 10:11

Systèmes et contrôle : enjeux et réussites

01/29/2016 - 19:30
Speaker: 
Enrique Zuazua (Universidad Autónoma de Madrid)
Location: 
Université de Montréal Pavillon Jean-Coutu 2940, chemin de Polytechnique salle S1-151
Abstract: 

 Depuis des générations, au sein de nombreuses civilisations, les mathématiques se sont développées dans le but de quantifier, de mesurer, et d'expliquer le monde qui nous entoure. Notre société moderne ne serait tout simplement pas possible sans l'apport des mathématiques.

Les mathématiques et le langage font probablement partie des attributs qui distinguent les êtres humains des autres espèces. Au cours de leur évolution, les mathématiques sont devenues parties prenantes de presque tous les aspects de notre vie quotidienne. Leurs utilisations sont innombrables et de plus en plus pointues. Ceci est tout particulièrement vrai pour l'automatique moderne.

Dans cet exposé, qui évitera les détails techniques, nous nous attacherons à présenter certains aspects des mathématiques du contrôle, ainsi que leur mise en oeuvre algorithmique. La pertinence de la démarche sera illustrée par des applications au contrôle des fluides et des structures.

Last edited by on Fri, 01/22/2016 - 10:06

Introduction to *-Autonomous categories

02/02/2016 - 16:00
02/02/2016 - 17:00
Speaker: 
M Barr (McGill)
Location: 
BH920
Abstract: 

I will give the background and definition, briefly discuss a few examples and discuss how they are models of linear logic. I will also describe very briefly the Chu construction and its history. The main purpose of this introduction is to determine if there is enough interest to expand the topic into a series of lectures.

Last edited by on Thu, 01/21/2016 - 12:01

The Mathematics of Mathematical Handwriting Recognition

01/25/2016 - 15:00
01/25/2016 - 16:00
Speaker: 
Stephen Watt (University of Waterloo)
Location: 
McGill Burnside Hall 920
Abstract: 

Accurate computer recognition of handwritten mathematics offers to provide a natural interface for mathematical computing, document creation and collaboration. Mathematical handwriting, however, provides a number of challenges beyond what is required for the recognition of handwritten natural languages. On one hand, it is usual to use symbols from a range of different alphabets and there are many similar-looking symbols. Mathematical notation is two-dimensional and size and placement information is important. Additionally, there is no fixed vocabulary of mathematical "words" that can be used to disambiguate symbol sequences. On the other hand, there are some simplifications. For example, symbols do tend to be well-segmented. With these characteristics, new methods of character recognition are important for accurate handwritten mathematics input.

We present a geometric model that we have found useful for recognizing mathematical symbols. Characters are represented as parametric curves approximated by certain truncated orthogonal series in a coordinate or jet space. This maps symbols to a low-dimensional vector space of series coefficients in which the Euclidean distance is closely related to the variational integral between two curves. This can be used to find similar symbols very efficiently. We describe some properties of mathematical handwriting data sets when mapped into this space and compare classification methods and their confidence measures. We also show how, by choosing the functional basis appropriately, the series coefficients can be computed in real-time, as the symbol is being written and, by using integral invariant functions, orientation-independent recognition is achieved. The beauty of this theory is that a single, coherent view provides several related geometric techniques that give a high recognition rate and that do not rely on peculiarities of the symbol set.

Last edited by on Wed, 01/20/2016 - 15:16

Big data & mixed-integer (nonlinear) programming

01/22/2016 - 16:00
Speaker: 
Andrea Lodi, École Polytechnique (Montréal)
Location: 
UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115
Abstract: 

 In this talk I review a couple of applications on Big Data that I personally like and I try to explain my point of view as a Mathematical Optimizer -- especially concerned with discrete (integer) decisions -- on the subject.  I advocate a tight integration of Data Mining, Machine Learning and Mathematical Optimization (among others) to deal with the challenges of decision-making in Data Science.  Those challenges are the core of the mission of the Canada Excellence Research Chair in "Data Science for Real-time Decision Making” that I hold.

Last edited by on Fri, 01/22/2016 - 10:36

On invertibility of adjacency matrices of random d-regular digraphs

01/21/2016 - 16:30
01/21/2016 - 17:30
Speaker: 
Anna Lytova, University of Alberta
Location: 
McGill, Burnside Hall 1205 **Room change**
Abstract: 

We consider d-regular directed graphs on n vertices. Every vertex of such graphs has exactly d in-neighbors and d out-neighbors. We show that  under some minor restrictions on d, the probability that an adjacency matrix of a random d-regular digraph is singular tends to zero with d growing to infinity. To this end, we establish a few expansion properties of d-regular digraphs, in particular, a Littlewood--Offord type anti-concentration property.
This is a joint work with A. Litvak, K. Tikhomirov, N. Tomczak-Jaegermann, and P. Youssef
We consider d-regular directed graphs on n vertices. Every vertex of such graphs has exactly d in-neighbors and d out-neighbors. We show that  under some minor restrictions on d, the probability that an adjacency matrix of a random d-regular digraph is singular tends to zero with d growing to infinity. To this end, we establish a few expansion properties of d-regular digraphs, in particular, a Littlewood--Offord type anti-concentration property.
This is a joint work with A. Litvak, K. Tikhomirov, N. Tomczak-Jaegermann, and P. Youssef
We consider d-regular directed graphs on n vertices. Every vertex of such graphs has exactly d in-neighbors and d out-neighbors. We show that  under some minor restrictions on d, the probability that an adjacency matrix of a random d-regular digraph is singular tends to zero with d growing to infinity. To this end, we establish a few expansion properties of d-regular digraphs, in particular, a Littlewood--Offord type anti-concentration property.
This is a joint work with A. Litvak, K. Tikhomirov, N. Tomczak-Jaegermann, and P. Youssef

Last edited by on Thu, 01/14/2016 - 16:22

Fractional revival in spin chains and orthogonal polynomials

01/19/2016 - 15:30
Speaker: 
Luc Vinet, CRM et Département de physique
Location: 
CRM, UdeM, Pavillon André-Aisenstadt, 2920, ch. de la Tour, salle 4336
Abstract: 

Abstract:

La revitalisation fractionelle (RF) se présente dans un système quand un paquet d’'onde initial se décompose sous l’'évolution dynamique en petits clones localisés se reproduisant de façon périodique. Comme nous le verrons ce phénomène peut être observé dans certaines chaînes de spin qui pourront donc être utilisées pour réaliser le transfert d'’information quantique où la génération d’'états maximalement intriqués. Le cas spécial où le paquet d’'onde est seulement revitalisé à l’'un des sites est appelé transfert d’'état parfait. Les spécifications des Hamiltoniens XX avec FR à deux sites seront analysées. Deux angles vont caractériser cet effet. L’'un correspond à l’'espacement entre les deux réseaux formant l'’ensemble d’'orthogonalité des polynômes de para Krawtchouk. Le second agit comme paramètre de transformations isospectrales des matrices de Jacobi associées à ces polynômes et dont les éléments sont les couplages et champs magnétiques de la chaîne. 

Cet exposé s’'appuit sur des travaux réalisés en collaboration avec Vincent X. Genest (MIT) et Alexei Zhedanov (Donetsk).


Fractional revival (FR) occurs in a quantum system when an initial wave packet evolves into small clones that recur with periodicities in a localized fashion. As we shall see, this phenomenon is observed in certain spin chains that can hence be used to perform tasks such as quantum information transfer or the generation of entangled states. The special case where the wave packet is reproduced at only one site is referred to as perfect state transfer. The specifications of XX Hamiltonians admitting FR at two sites will be analysed. Two angles will be seen to characterize the effect. One will correspond to the spacing of the two lattices forming the orthogonality set of the para Krawtchouk polynomials. The second parametrizes isospectral transformations of the Jacobi matrices associated with these polynomials whose elements are the couplings and magnetic field strengths of the chain. 

Based on joint work with V.X.Genest (MIT) and A.Z. Zhedanov (CRM and Donetsk)


Fractional revival (FR) occurs in a quantum system when an initial wave packet evolves into small clones that recur with periodicities in a localized fashion. As we shall see, this phenomenon is observed in certain spin chains that can hence be used to perform tasks such as quantum information transfer or the generation of entangled states. The special case where the wave packet is reproduced at only one site is referred to as perfect state transfer. The specifications of XX Hamiltonians admitting FR at two sites will be analysed. Two angles will be seen to characterize the effect. One will correspond to the spacing of the two lattices forming the orthogonality set of the para Krawtchouk polynomials. The second parametrizes isospectral transformations of the Jacobi matrices associated with these polynomials whose elements are the couplings and magnetic field strengths of the chain. 

Based on joint work with V.X.Genest (MIT) and A.Z. Zhedanov (CRM and Donetsk)La revitalisation fractionelle (RF) se présente dans un système quand un paquet d’'onde initial se décompose sous l’'évolution dynamique en petits clones localisés se reproduisant de façon périodique. Comme nous le verrons ce phénomène peut être observé dans certaines chaînes de spin qui pourront donc être utilisées pour réaliser le transfert d'’information quantique où la génération d’'états maximalement intriqués. Le cas spécial où le paquet d’'onde est seulement revitalisé à l’'un des sites est appelé transfert d’'état parfait. Les spécifications des Hamiltoniens XX avec FR à deux sites seront analysées. Deux angles vont caractériser cet effet. L’'un correspond à l’'espacement entre les deux réseaux formant l'’ensemble d’'orthogonalité des polynômes de para Krawtchouk. Le second agit comme paramètre de transformations isospectrales des matrices de Jacobi associées à ces polynômes et dont les éléments sont les couplages et champs magnétiques de la chaîne. 

Cet exposé s’'appuit sur des travaux réalisés en collaboration avec Vincent X. Genest (MIT) et Alexei Zhedanov (Donetsk).


Fractional revival (FR) occurs in a quantum system when an initial wave packet evolves into small clones that recur with periodicities in a localized fashion. As we shall see, this phenomenon is observed in certain spin chains that can hence be used to perform tasks such as quantum information transfer or the generation of entangled states. The special case where the wave packet is reproduced at only one site is referred to as perfect state transfer. The specifications of XX Hamiltonians admitting FR at two sites will be analysed. Two angles will be seen to characterize the effect. One will correspond to the spacing of the two lattices forming the orthogonality set of the para Krawtchouk polynomials. The second parametrizes isospectral transformations of the Jacobi matrices associated with these polynomials whose elements are the couplings and magnetic field strengths of the chain. 

Based on joint work with V.X.Genest (MIT) and A.Z. Zhedanov (CRM and Donetsk)

Last edited by on Thu, 01/14/2016 - 15:35

On folding pathways, recycling, and reversible programming

01/18/2016 - 16:00
01/18/2016 - 17:00
Speaker: 
Anne Condon, UBC
Location: 
McGill University, 845 rue Sherbrooke O, salle/room Burnside 1205
Abstract: 

Abstract:

DNA programs execute when sets of interacting molecules follow specific folding pathways, i.e., sequences of secondary structures. Longer pathways imply longer and thus potentially more complex computations.  This motivates the question: is it possible to design a single DNA strand, or set of interacting DNA strands, that follow a folding pathway whose length significantly exceeds the total length of the participating molecules? We'll describe some progress on this problem and connections with the theory of reversible, energy-efficient computing.DNA programs execute when sets of interacting molecules follow specific folding pathways, i.e., sequences of secondary structures. Longer pathways imply longer and thus potentially more complex computations.  This motivates the question: is it possible to design a single DNA strand, or set of interacting DNA strands, that follow a folding pathway whose length significantly exceeds the total length of the participating molecules? We'll describe some progress on this problem and connections with the theory of reversible, energy-efficient computing.

Last edited by on Thu, 01/14/2016 - 15:29

TBA

04/08/2016 - 13:30
04/08/2016 - 14:30
Speaker: 
Jiuyi Zhu (Johns Hopkins University)
Location: 
McGill University, Burnside Hall, 9th floor, BURN 920
Last edited by on Wed, 01/13/2016 - 12:00

Topology, rigid cosymmetries and linearization instability in higher gauge theories

01/29/2016 - 13:30
01/29/2016 - 14:30
Speaker: 
Igor Khavkine (Trento, Italy)
Location: 
McGill University, Burnside Hall, 9th floor, BURN 920
Abstract: 

It is well known that some solutions of non-linear partial differential equations (PDEs), like Einstein or Yang-Mills equations, exhibit linearization instability: some linearized solutions do not extend to families of near-by non-linear solutions. Often, linearized solution fail to extend when some non-linear functional, which we refer to as a linearization obstruction, is non-zero on it. In the case of Einstein and Yang-Mills equations, such linearization obstructions are precisely related to spacetime topology, charges of linearized conservation laws and rigid symmetries of the background solution. I will describe a significant generalization this classic result. It is applicable to both elliptic and hyperbolic equations, to variational and non-variational equations, to determined systems and gauge theories, and to ordinary as well as higher gauge theories.

Last edited by on Wed, 01/13/2016 - 11:58