2015 CAP-CRM Prize: "QCD under extreme conditions: Hot, shiny fluids and sticky business"

03/11/2016 - 16:00
Speaker: 
Charles Gale, McGill University
Location: 
CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214
Abstract: 

The phase diagram of Quantum Chromodynamics (QCD, the theory of the strong interaction) is only poorly known. There is currently a vibrant experimental and theoretical program that concentrate on the study and the characterization of the quark-gluon plasma, a fundamental state of matter that existed a few microseconds after the Big Bang. I will describe the theoretical aspects of this endeavour, and highlight some of the surprises uncovered along the way.
 

Last edited by on Thu, 03/03/2016 - 15:47

The binomial species $(1+X)^Y$

03/11/2016 - 13:30
03/11/2016 - 14:30
Speaker: 
Gilbert Labelle, LaCIM
Location: 
Seminar LACIM 201, av. du Président-Kennedy, LOCAL PK-4323, Montréal (Qc) H2X 3Y7
Abstract: 

Nous introduisons l'espèce binomiale virtuelle $B(X,Y) = (1+X)^Y = E(Y Lg(!+X))$ où $E$ est l’espèce des ensembles finies et $Lg$ est le logarithme combinatoire. Le développement de $B$ inclut, par spécialisation des variables, le développement binomial classique, des développement binomiaux pour les fonctions symétriques et $(q,t)$-séries. Nous définissons aussi une nouvelle opération d’exponentiation, $F^G$, entre espèces.

Last edited by on Thu, 03/03/2016 - 15:44

KPZ universality, particle systems and polymer models

03/10/2016 - 16:00
03/10/2016 - 17:30
Speaker: 
Janosch Ortmann
Location: 
Concordia University, Math Help Center, room 912.00 / Library Building, 1400 de Maisonneuve Blvd. West, Montréal
Abstract: 

The Kardar-Parisi-Zhang (KPZ) universality conjecture describes the long-time behaviour of a number of mathematical models of physical processes, which differs from the Central Limit Theorem by the size of the fluctuations as well as the limiting distribution. 

Physicists have predicted that a large number of models, including interacting particle systems and polymers, belong to this class. However, mathematical proofs have turned out to be very difficult to obtain, even for special cases. Such proofs have shown deep connections with, amongst others, algebra, combinatorics and queueing theory.  I will give an overview over some aspects of recent progress in this area.  The talk is based on joint work with Neil O'Connell (Warwick), Jeremy Quastel (Toronto) and Daniel Remenik (Santiago).

Last edited by on Thu, 03/03/2016 - 15:40

Risk neutral and risk averse approaches to multistage stochastic programming

03/10/2016 - 15:45
03/10/2016 - 17:00
Speaker: 
Alexander Shapiro, (Georgia Tech)
Location: 
UdeM, Pavillon André-Aisenstadt, 2920 chemin de la Tour, salle 5340
Abstract: 

In many practical situations one has to make decisions sequentially based on data available at the time of the decision and facing uncertainty of the future. This leads to optimization problems which can be formulated in a framework of multistage stochastic optimization. In this talk we consider risk neutral and risk averse approaches to multistage stochastic programming. We discuss conceptual and computational issues involved in formulation and solving such problems. As an example we give numerical results based on the Stochastic Dual Dynamic Programming method applied to planning of the Brazilian interconnected power system.

Last edited by on Thu, 03/03/2016 - 15:35

Régression bayésienne semi-paramétrique par le modèle de Potts

03/10/2016 - 15:30
03/10/2016 - 16:30
Speaker: 
Alejandro Murua, (Université de Montréal)
Location: 
Seminar Statistique Sherbrooke,2500, boul. de l'Université, Salle D4-2019, Sherbrooke
Abstract: 

Nous considérons la régression non-paramétrique bayésienne à travers des modèles de partitions aléatoires. Notre approche consiste en la construction d'une distribution a priori dépendant des covariables sur des partitions des individus. Notre objectif est d'utiliser les informations données par les covariables pour améliorer l'inférence prédictive. Pour ce faire, nous proposons une loi a priori sur les partitions basée sur le modèle de classification de Potts associé aux covariables observées. Par la proximité entre covariables, cela conduit simultanément à la formation de grappes et à la distribution prédictive a priori. Ce modèle a priori est suffisamment flexible pour supporter de nombreux types de modèles de vraisemblance. Nous nous concentrons sur le modèle de régression. Les détails de mise en oeuvre sont examinés pour le cas spécifique de la régression linéaire multiple multivariée. Le modèle proposé fonctionne bien en termes d'ajustement du modèle et de prévision! par rapport à d'autres approches de régression non paramétriques alternatives. Nous illustrons la méthodologie avec une application à l'état de santé des nations au tournant du 21e siècle. Ceci est un travail conjoint avec Fernando Quintana, Pontificia Universidad Catolica de Chile.

Last edited by on Thu, 03/03/2016 - 15:32

Completions of group algebras, growth and nuclearity

03/10/2016 - 15:30
03/10/2016 - 16:30
Speaker: 
Simone Gutt, (Université Libre de Bruxelles)
Location: 
McGill University, Burnside 719A, 805 Sherbrooke West - McGill University
Abstract: 

If G is a finitely generated infinite group, we define completions Asigma(G) of the group algebra C[G] in the space of formal power series in G, using norms which are defined using a growth functionsigma, i.e. an unbounded nowhere decreasing function sigma: N o [1,infty) which is submultiplicative (i.e. sigma(n + m) <= sigma(n)sigma(m)) or almost submultiplicative (i.e. for every epsilon > 0, there exists a constant c > 0 such that sigma(n + m) <= csigma(n)^{1+epsilon} sigma(m)^{1+epsilon}. We show that Asigma(G) is a Frechet-Hopf *-algebra. We relate nuclearity of such a completion to a growth property of the group. This is joint work with Michel Cahen and Stefan Waldmann.

Last edited by on Thu, 03/03/2016 - 15:26

Ridges and valleys in the high excursion sets of Gaussian random fields

03/10/2016 - 15:30
03/10/2016 - 16:30
Speaker: 
Gennady Samorodnitsky,(Cornell University)
Location: 
McGill University, 801 Sherbrooke St. West, Otto Maass Building , Room: MAASS 217
Abstract: 

It is well known that normal random variables do not like taking large values. Therefore, a continuous Gaussian random field on a compact set does not like exceeding a large level. If it does exceed a large level at some point, it tends to go back below the level a short distance away from that point. One, therefore, does not expect the excursion set above a high for such a field to possess any interesting structure. Nonetheless, if we want to know how likely are two points in such an excursion set to be connected by a path ("a ridge") in the excursion set, how do we figure that out? If we know that a ridge in the excursion set exists (e.g. the field is above a high level on the surface of a sphere), how likely is there to be also a valley (e.g. the field going to below a fraction of the level somewhere inside that sphere)?

We use the large deviation approach. Some surprising results (and pictures) are obtained.

Last edited by on Mon, 03/07/2016 - 10:40

Random loop representations of quantum spin systems and their universal behaviour 1-2

03/10/2016 - 14:30
03/10/2016 - 17:00
Speaker: 
Daniel Ueltschi, (University of Warwick)
Location: 
McGill University, Department of Mathematics, 805 Sherbrooke St. West, Burnside Hall, Burn 1120
Abstract: 

I will describe the representations of Tóth and Aizenman-Nachtergaele of quantum Heisenberg models. They constitute an example of “loop soup” models that display  a universal behaviour in dimensions 3 and higher: At low temperatures, the system contains macroscopic loops and the joint distribution of their lengths is given by a Poisson-Dirichlet distribution. This can be understood (and calculated) by viewing the loop distribution as the invariant measure of an effective spit-merge process.

I will explain the relevant notions. If time permits, I will derive some consequences of this universal behaviour regarding the nature of symmetry breaking in quantum spin systems.

Last edited by on Thu, 03/03/2016 - 15:15

Monopoles on circle bundles

03/08/2016 - 15:30
03/08/2016 - 16:30
Speaker: 
Jacques Hurtubise,(McGill University)
Location: 
CRM, UdeM, Pavillon André-Aisenstadt, 2920, ch. de la Tour, salle 4336
Abstract: 

I will describe the moduli of monopoles with Dirac type singularities on a circle bundle over a Riemann surface, in terms of holomorphic data.

Last edited by on Thu, 03/03/2016 - 15:08

Magneto-acoustic Tomography - Analysis and Algorithms

03/07/2016 - 15:00
03/07/2016 - 16:00
Speaker: 
Fadil Santosa, (School of Mathematics, University of Minnesota)
Location: 
McGill University, Department of Mathematics, 805 Sherbrooke St. West, Burnside Hall, Burn 920
Abstract: 

Magneto-acoustic tomography with magnetic induction (MAT-MI) is a coupled-physics medical imaging modality for determining conductivity distribution in biological tissue. The capability of MAT-MI to provide high resolution images has been demonstrated experimentally. The presentation will go over the science behind the imaging method, followed by an analysis of the well-posedness of the partial differential equations that model the system. A numerical approach for recovering the conductivity is proposed and results from computational experiments are presented.

Last edited by on Thu, 03/03/2016 - 15:03