Two 30 Minute Talks

10/27/2015 - 14:30
10/27/2015 - 16:00
Speaker: 
M. Barr (McGill University)
Location: 
Burnside Hall, Rm. 920 (McGill University)
Abstract: 

I will give two talks that should be about 30 minutes each. The first is to help prepare for the Octoberfest in Ottawa next weekend, while the second is the talk I gave at the AMS meeting in Baltimore in Jan., 2014. This is all joint work with John Kennison and Bob Raphael. Titles and abstracts of each follow:

1. Limit closures of some full subcategories

The three subcategories are: 
1. Metric spaces inside the category of separated uniform spaces. 
2. Integrally closed domains inside the category of commutative rings. 
3. Integral domains inside the category of commutative rings.

2. Completions of subcategories of domains

The subcategories of domains include the 2nd and 3rd above, as well as many others. The central hypothesis is that every domain lies inside a field belonging to the subcategory in question.

Last edited by on Mon, 10/26/2015 - 13:01

The multiplier method to construct conservative finite difference schemes for ordinary and partial differential equations

11/02/2015 - 15:00
11/02/2015 - 16:00
Speaker: 
Andy Wan (McGill University)
Location: 
Burnside Hall, 805 Sherbrooke Str. West, Rm. 920 (McGill University)
Abstract: 
Structure-preserving discretizations are numerical methods which preserve important structure of differential equations at the discrete level. For system derived from a Hamiltonian or Lagrangian, symplectic and variational integrators are a class of discretizations which can preserve symplectic and variational structure at the discrete level. In this talk, we introduce the multiplier method of constructing conservative finite difference schemes for ordinary and partial differential equations. The proposed discretization is shown to be consistent for any order of accuracy when the discrete multiplier has a multiplicative inverse. Moreover, we show that by construction, the discrete densities can be exactly conserved. In particular, the multiplier method does not require the system to possess a symplectic or variational structure. Examples, including dissipative problems, are given to illustrate the method. In the case when the inverse of the discrete multiplier becomes singular, consistency is also established for scalar ODEs provided the discrete multiplier and density are zero-compatible. Long-term stability for such method is also discussed. This is joint work with Alexander Bihlo at Memorial University and Jean-Christophe Nave at McGill University.
Last edited by on Wed, 10/21/2015 - 09:19

Stability of Active Muscle Tissue

10/26/2015 - 15:00
10/26/2015 - 16:00
Speaker: 
Luis Dorfmann (Tufts University)
Location: 
Burnside Hall, 805 Sherbrooke Str. West, Rm. 920 (McGill University)
Abstract: 

In this talk we examine the notion of material stability in modeling active muscle tissue where the nonlinear constitutive law is dependent on the physiologically-driven muscle contraction and on finite mechanical deformation. First, the governing equations and constitutive laws for a general active-elastic material are linearized about a homogeneous underlying configuration. In order to obtain mathematical restrictions analogous to those found in elastic materials, stability conditions are derived based on the propagation of homogeneous plane waves with real wave speeds, and the generalized acoustic tensor is obtained. Focusing on 2D motions, and considering a simplified, decoupled transversely isotropic energy function, the restriction on the active acoustic tensor is recast in terms of a generally applicable constitutive law, with specific attention paid to the fiber contribution. The implication of the material stability conditions on material parameters, active contraction and elastic stretch is investigated for prototype material models of muscle tissue.

Last edited by on Wed, 10/21/2015 - 09:18

Colloque des sciences mathématiques du Québec -- Weighted Hurwitz Numbers: Classical and Quantum

10/23/2015 - 16:00
10/23/2015 - 17:00
Speaker: 
John Harnad (Concordia University et CRM)
Location: 
UQAM, Pavillon Sherbrooke, Salle SH-2420
Abstract: 

Hurwitz numbers enumerate branched coverings of the Riemann sphere. An equivalent combinatorial problem consists of enumeration of factorizations of elements of the symmetric group. The study of these enumerative invariants is classical, dating back to the pioneering work of Hurwitz, Frobenius and Schur. In 2000, Okounkov and Pandharipande began their program relating Hurwitz numbers to other combinatorial/topological invariants associated to Riemann surfaces, such as Gromov-Witten and  Donaldson-Thomas invariants. A key result was the expression generating functions for Hurwitz numbers of branched covers with only simple branching, plus one, or two other branch points, as Tau functions of of the KP and Toda hierarchies, using the associated semi-infinite wedge product representation.  

In recent work, these ideas were extended to generating functions for a very wide class of weighted branched coverings, making use of the six standard bases for the ring of symmetric functions, such as Schur functions, and monomomial sum symmetric and also their “quantum” deformations, involving the Macdonald polynomials.  The general theory of weighted Hurwitz numbers, together with various applications and examples coming from Random Matrix theory and enumerative geometry will be explained in a simple, unified way, using bases for the center of the symmetric group algebra, the characteristic map to the ring of symmetric polynomials. and multiplicatively defined symmetric functions evaluated on the Jucys-Murphy elements of the group algebra.   The simplest quantum case gives a special weighted enumeration of branched coverings that is closely related to the statistical mechanics of Bose-Einstein gases with linear energy spectrum.

Last edited by on Mon, 10/19/2015 - 16:23

Lecture Chaire André Aisenstadt -- CFT amplitudes and Hitchin systems

10/23/2015 - 14:00
10/23/2015 - 15:00
Speaker: 
Bertrand Eynard (CPT, CEA Saclay)
Location: 
CRM, UdeM, Pavillon André-Aisenstadt, 2920, chemin de la tour, Salle 5340
Abstract: 

(Conférence s'adressant à un large auditoire/Suitable for a general audience)

Checking that the amplitudes satisfy the CFT axioms: OPEs, Ward identities. Modular invariance and the crossing symmetry, from the geometry of Higgs bundles.

http://www.crm.math.ca/Eynard/

Last edited by on Mon, 10/19/2015 - 16:20

Seminar LACIM -- Compter les palindromes dans les arbres

10/23/2015 - 13:30
10/23/2015 - 14:30
Speaker: 
Nadia Lafrenière (Université du Québec à Montréal)
Location: 
201, av. du Président-Kennedy, LOCAL PK-4323, Montréal (Qc) H2X 3Y7
Abstract: 

La question du dénombrement des palindromes est un problème largement étudié en combinatoire des mots. Il est entre autres connu que le nombre maximal de palindromes non vides dans les mots d'une longueur fixée est donné par sa longueur. Cette borne n'est cependant pas valide dans le cas des arbres étiquetés, où le langage est défini comme l'ensemble des traces des chemins entre les sommets. Nous avons récemment construit une famille infinie d'arbres de taille $n$ contenant $cn^{3/2}$ palindromes, où $c$ est une constante, et démontré que, sous certaines hypothèses, ce nombre est maximal. Nous conjecturons que cette borne est vraie en général et donnons des indices pour sa démonstration. Ce travail a été réalisé conjointement avec Xavier Provençal.

Last edited by on Mon, 10/19/2015 - 16:18

A new approach to the L^p theory of -Delta + b \nabla, and its applications to Feller processes with general drifts

10/23/2015 - 13:30
10/23/2015 - 14:30
Speaker: 
D. Kinzebulatov (CRM & McGill University)
Location: 
Burnside Hall, 805 Sherbrooke Str West, Rm. 920 (McGill University)
Last edited by on Mon, 10/19/2015 - 16:16

Minicourse II: Integrable systems, random matrices, Hitchin systems and CFT : Random matrices, orthogonal polynomials isospectra

10/22/2015 - 16:00
10/22/2015 - 18:00
Speaker: 
Bertrand Eynard (CPT, CEA Saclay)
Location: 
Concordia University, Math Help Center, Rm. 912.00 / Library Building, 1400 de Maisonneuve Blvd. West, Montréal
Abstract: 

Random matrices and orthogonal polynomials, expectation values of resultants, and expectation values of characteristic polynomials. Isospectral systems from the ODEs satisfied by orthogonal polynomials Notion of Miwa-Jimbo Tau function, Fay identities, Hirota equations, Sato relations.

Last edited by on Mon, 10/19/2015 - 16:13

Minicourse II - Integrable systems, random matrices, Hitchin systems and CFT : Introduction to integrable systems and solutions

10/21/2015 - 16:00
10/21/2015 - 17:00
Speaker: 
Bertrand Eynard (CPT, CEA Saclay)
Location: 
Concordia University, Rm. 921.04 / Library Building, 1400 de Maisonneuve Blvd. West, Montréal
Abstract: 

The Lax formalism, isospectral systems, algebro-geometric solutions (Baker Akhiezer functions), prime forms, and theta functions. Hitchin systems.

Last edited by on Mon, 10/19/2015 - 16:12

Seminar Biostatistique -- How SMART is your trial? Obtain quality data about dynamic treatment regimes

10/20/2015 - 15:30
10/20/2015 - 16:30
Speaker: 
Erica Moodie, PhD (McGill University)
Location: 
Purvis Hall, 1020 Pine Ave. West, Room 24
Abstract: 

Current practice in randomized trials typically focuses on identifying the single best treatment for a particular condition. Clinical practice, however, has consistently been more concerned with a patient- rather than disease-centric approach. Dynamic treatment regimes are part of a rapidly expanding area of research whereby such personalized treatment strategies can be identified. These methods can lead to improved results over standard 'one size fits all' approaches, and provide a route to formalizing treatment adjustments in an evidence-based manner. In this talk, I will give an introduction to dynamic treatment regimes, focusing primarily on sequential multiple assignment randomized trials (SMARTs), the best means of obtaining high-quality data to determine optimal treatment regimes, and will present some new findings on the purported benefits of such trials from a case study involving the Clinical Antipsychotic Trials of Invervention Effectiveness (CATIE) Schizophrenia study.

Last edited by on Mon, 10/19/2015 - 16:09