Elliptic PDEs in two dimensions

01/19/2016 - 16:00
01/19/2016 - 17:00
Speaker: 
Ovidiu Savin, Columbia University
Location: 
UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115
Abstract: 

Resume/Abstract :

I will give a short survey of the several approaches to the regularity theory of elliptic equations in two dimensions. In particular I will focus on some old ideas of Bernstein and their application to the infinity Laplace equation and to the Bellman equation in two dimensions.

 

Last edited by on Fri, 01/29/2016 - 15:27

Sharp asymptotic profiles for singular solutions to an elliptic equation with a sign-changing nonlinearity

02/17/2016 - 13:30
02/17/2016 - 14:30
Speaker: 
Frederic Robert (Universite de Lorraine, France)
Location: 
McGIll University, Burnside Hall, BURN 920, 9th Floor
Abstract: 

We consider a positive solution to a nonlinear elliptic equation on a punctured ball. The linear part is the classical Laplacian. When the nonlinear part is positive and critical, this is similar to the classical problem studied by Caffarelli-Gidas-Spruck. When the nonlinear part is negative and a pure power, the problem is associated to a natural convex functional and the singularities are completely understood. In the present work, we mix the two nonlinearities. We show the existence of several potential behaviors. Two of them are natural extensions of the case of constant-sign nonlinearity. Two other behaviors are arising from the interaction of the two nonlinearity. In this talk, I will describe all the possible behaviors and I will show how the methods of apriori analysis in nonlinear elliptic problems are helping understanding this problem. This is joint work with Florica Cirstea (Sydney).

Last edited by on Wed, 02/10/2016 - 11:08

Optimal shapes and isoperimetric inequalities for spectral functionals

02/12/2016 - 16:16
Speaker: 
Dorin Bucur, Université de Savoie
Location: 
CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle 6214
Abstract: 

Resume/Abstract :

In this talk I will discuss isoperimetric inequalities involving the spectrum of the Laplace operator (of Faber-Krahn, Saint-Venant or Mahler type) seen from the perspective of "shape optimization". Techniques inspired from applied mathematics, like the image segmentation theory, or the use of the computer for numerical approximations, can lead to rigorous mathematical proofs of some of those inequalities. I will describe more in detail problems involving the spectrum of the Robin-Laplacian and a Mahler type inequality for the first Dirichlet eigenvalue, and show how those techniques can be applied.

 

Last edited by on Fri, 01/29/2016 - 15:17

Chain reactions

02/05/2016 - 16:00
02/05/2016 - 17:00
Speaker: 
Tadashi Tokieda (Cambridge / Stanford)
Location: 
UQAM, Pavillon Président-Kennedy, 201, ave du Président-Kennedy, salle PK-5115
Abstract: 
Resume/Abstract :

To every action, there is an equal and opposite reaction. However, there turn out to exist in nature situations where the reaction seems to be neither equal in magnitude nor opposite in direction to the action. We will see a series of table-top demos and experimental movies, apparently in more and more violation of Newton's 3rd law, and give a full analysis of what is happening, discovering in the end that this phenomenon are in a sense generic. The keys are shock, singular material property, and supply of `critical geometry'

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

Distributed Optimization for Networked Systems

02/08/2016 - 16:00
Speaker: 
Soomin Lee, Duke University
Location: 
BURN 1205
Abstract: 
We witness a growing interest in distributed multi-agent systems. The Internet, electric power systems, mobile communication networks, and social networks are just a few examples of the myriad network systems that have become a part of everyday life for many people. Lots of interesting optimization problems arise in such network systems. The agents on these networks are geographically distributed, so there is no data fusion center that can see the problem as a whole, gather the information globally, or synchronize actions. Furthermore, the network agents might have varying restrictions on energy, data storage and computational capabilities. In this talk, I will present efficient static and online decentralized optimization algorithms for such systems that allow the network agents to achieve provable consensus to the global optimum.  Applications of the algorithms in various engineering disciplines will be discussed as well. 
Last edited by on Tue, 01/26/2016 - 14:51

Ambiguous Joint Chance Constraints under Mean and Dispersion Information

02/15/2016 - 16:00
Speaker: 
Grani Hanansusanto, Ecole polytechnique Federale de Lausanne
Location: 
BURN 1205
Abstract: 

Abstract: We study joint chance constraints where the distribution of the uncertain parameters is only known to belong to an ambiguity set characterized by the mean and support of the uncertainties and by an upper bound on their dispersion. This setting gives rise to pessimistic (optimistic) ambiguous chance constraints, which require the corresponding classical chance constraints to be satisfied for every (for at least one) distribution in the ambiguity set. We provide tight conditions under which pessimistic and optimistic joint chance constraints are computationally tractable, and we show numerical results that illustrate the power of our tractability results.

Bio: Grani A. Hanasusanto is a postdoctoral researcher at the École Polytechnique Fédérale de Lausanne. He holds a PhD degree in Operations Research from Imperial College London and an MSc degree in Financial Engineering from the National University of Singapore. His research focuses on the design and analysis of tractable solution schemes for decision-making problems under uncertainty, with applications in operations management, energy systems, machine learning and data analytics.

 

Last edited by on Tue, 01/26/2016 - 14:52

Stability and instability for nonlinear elliptic PDE with slight variations to the data

01/29/2016 - 16:00
Speaker: 
Jérôme Vétois, McGill University
Location: 
Colloque des sciences mathématiques du Québec CRM, UdeM, Pav. André-Aisenstadt, 2920, ch. de la Tour, salle
Abstract: 

 We will consider the question of stability of solutions to nonlinear elliptic PDE when slightly varying the data. We will take as a model the Standing Wave Equation for critical nonlinear Schrödinger and Klein-Gordon Equations on a closed manifold, and we will look at variations to the potential functions in these equations. A number of results have been obtained on this question in the last two decades, and we now have an accurate picture of the stability and instability of solutions to these equations. I will give an overview of these results and explain why certain types of unstable solutions can exist for some potential functions or in some geometries, and not others.

Last edited by on Fri, 01/22/2016 - 10:32

An introduction to the RSK correspondence, growth diagrams, and dimer models

01/28/2016 - 16:00
01/28/2016 - 17:30
Speaker: 
Guillaume Chapuy
Location: 
Working Seminar Mathematical Physics / Probabilités-Probability - Concordia University, Math Help Center, room 912.00 / Library Building, 1400 de Maisonneuve Blvd. West, Montréal
Abstract: 

 This is the introductory session of a series of three talks on dimer models, RSK, random polymers joint between the probability and math/physics seminar (next two given by Janosch Ortmann on Feb 4, and in March). I will mainly talk about the Robinson-Schensted-Knuth (RSK) correspondence and some of its variations. This subject keeps appearing in many places in probability but it is often used as a black box. The primary goal of this talk is to take the time to enjoy it for itself and understand where it comes from. I will take the viewpoint of random generation algorithms for dimer models via growth diagrams and the Fermionic Fock space. If time allows, I may also mention some more recent and original work about the interpretation in terms of dimer models of mixed primal/dual interlacing rules via Rail Yard Graphs, and the corresponding mixed versions of the algorithms, based on joint works involving Jérémie Bouttier, Cédric Boutillier, Sylvie Corteel, Sanjay Ramassamy, Dan Betea and Mirjana Vuletic. The next talk by Janos will introduce a "tropical version" and study applications to random polymers.

Last edited by on Fri, 01/22/2016 - 10:29

Interior C^2 estimate of Monge-Ampere equation in 2-dimension

01/27/2016 - 13:30
Speaker: 
Siyuan LU, McGill University
Location: 
McGIll University, Burnside 920
Abstract: 

 Heinz's work and related development. 

Last edited by on Fri, 01/22/2016 - 10:27

A q-hypergeometric approach to integrable systems related with the q-Onsager algebra

01/26/2016 - 15:30
Speaker: 
Pascal Baseilhac, Université de Tours
Location: 
CRM, UdeM, Pavillon André-Aisenstadt, 2920, ch. de la Tour, salle 4336
Abstract: 

A q-hypergeometric framework for a class of quantum integrable models generated from the q-Onsager algebra will be presented. By analogy with the basic example of the quantum harmonic oscillator which eigenfunctions are the Hermite polynomials, I will explain that the bispectral family of multivariable Gasper-Rahman polynomials (generalizing those of Askey-Wilson) provide a natural basis for studying integrable models generated from the basic generators of the q-Onsager algebra. In this talk, I will present an overview (motivations/aims/applications/perspectives) and the main results. Work done in collaboration with Xavier Martin. See: arXiv:1506.06902.

Last edited by on Fri, 01/22/2016 - 10:25