Présentations des invités vedettes
Constant Curiosity
by Norman Do
Abstract: Not all numbers were created equal. Mathematically minded folk are
all aware of the ubiquity of Archimedes' constant $\pi$, the importance of
Euler's constant $e$ and the beauty of the golden ratio $\phi$. However,
let's spare a thought for a few of the lesser known mathematical constants
--- ones which might not permeate the various fields of mathematics but
have nevertheless been immortalized in the mathematical literature in one
way or another. In this seminar, we'll consider a few of these numerical
curios and their rise to fame.
by Norman Do
Abstract: Not all numbers were created equal. Mathematically minded folk are
all aware of the ubiquity of Archimedes' constant $\pi$, the importance of
Euler's constant $e$ and the beauty of the golden ratio $\phi$. However,
let's spare a thought for a few of the lesser known mathematical constants
--- ones which might not permeate the various fields of mathematics but
have nevertheless been immortalized in the mathematical literature in one
way or another. In this seminar, we'll consider a few of these numerical
curios and their rise to fame.
Pourquoi tant d’intérêt pour la combinatoire algébrique?
Why is Algebraic Combinatorics so Hot?
by François Bergeron
Résumé: Abstract :
Au cours de cette présentation bilingue, In this bilingual talk,
je vais illustrer diverses interactions I will illustrate various current interactions
récentes de la combinatoire algébrique between algebraic combinatoricsand other
avec d’autres domaines passionnants des exciting fields of mathematics.
mathématiques.
Why is Algebraic Combinatorics so Hot?
by François Bergeron
Résumé: Abstract :
Au cours de cette présentation bilingue, In this bilingual talk,
je vais illustrer diverses interactions I will illustrate various current interactions
récentes de la combinatoire algébrique between algebraic combinatoricsand other
avec d’autres domaines passionnants des exciting fields of mathematics.
mathématiques.
Domino tilings of Aztec Diamonds
by Benjamin Young
This is an introduction to the combinatorics of tilings.
We'll start by counting the number of ways in which a certain region
(the aztec diamond) can be covered with dominos, using a technique called
Graphical Condensation (discovered by Eric Kuo, as an undergraduate
research project). We'll then take a brief look at what a randomly
chosen tiling of a large aztec diamond looks like.
The talk has no prerequisites and will involve many nice (and relevant) pictures
by Benjamin Young
This is an introduction to the combinatorics of tilings.
We'll start by counting the number of ways in which a certain region
(the aztec diamond) can be covered with dominos, using a technique called
Graphical Condensation (discovered by Eric Kuo, as an undergraduate
research project). We'll then take a brief look at what a randomly
chosen tiling of a large aztec diamond looks like.
The talk has no prerequisites and will involve many nice (and relevant) pictures
Présentations au Programme:
What is a number? An introduction to axiomatic set theory
by Jifeng Shen
Abstract: What is 2, after all? The most intuitive answer seems to be: what is common to all collections of 2 objects. In the language of set theory, it appears to be natural to say that 2 is the set of all sets with 2 elements. However, this definition relies on a very naive conception of sets, a conception that leads to some inevitable paradoxes (e.g. the infamous Russell's paradox). A better definition of numbers, grounded on a consistent conception of sets, is needed. In fact, a new approach to set theory, a new approach to the heart of mathematics itself, is required. This approach is axiomatic set theory.
by Jifeng Shen
Abstract: What is 2, after all? The most intuitive answer seems to be: what is common to all collections of 2 objects. In the language of set theory, it appears to be natural to say that 2 is the set of all sets with 2 elements. However, this definition relies on a very naive conception of sets, a conception that leads to some inevitable paradoxes (e.g. the infamous Russell's paradox). A better definition of numbers, grounded on a consistent conception of sets, is needed. In fact, a new approach to set theory, a new approach to the heart of mathematics itself, is required. This approach is axiomatic set theory.
Asset Pricing
by Sheisha Kulkarni
A short summary and analysis on the two major theories of asset pricing and how limitations may have contributed to a global financial crisis. A short discussion as well of new developments in the field including behavioral finance. The presentation will be done in English and a projector would be great!
by Sheisha Kulkarni
A short summary and analysis on the two major theories of asset pricing and how limitations may have contributed to a global financial crisis. A short discussion as well of new developments in the field including behavioral finance. The presentation will be done in English and a projector would be great!
Item Response Theory
by Daphna Harel
Abstract: In this talk, we will explore how tests, such as the LSATs, or other questionnaires use probabilistic models to measure a latent trait, such as intelligence. I'll start with the theory behind latent trait modeling, and then use this to analyze a data set. Basic knowledge of probability is helpful for this talk, but not completely necessary.
by Daphna Harel
Abstract: In this talk, we will explore how tests, such as the LSATs, or other questionnaires use probabilistic models to measure a latent trait, such as intelligence. I'll start with the theory behind latent trait modeling, and then use this to analyze a data set. Basic knowledge of probability is helpful for this talk, but not completely necessary.
Groupes de Coxeter
par Maxime Bergeron, Maxime Scott, et Marco Robado
Nous introduirons des concepts d'Algèbre nécessaire à la compréhension du sujet. Ensuite nous donnerons une vision géométrique de ces groupes et nous explorerons plusieurs aspects intéressants de ceux-ci.
par Maxime Bergeron, Maxime Scott, et Marco Robado
Nous introduirons des concepts d'Algèbre nécessaire à la compréhension du sujet. Ensuite nous donnerons une vision géométrique de ces groupes et nous explorerons plusieurs aspects intéressants de ceux-ci.
Discussion of Schoof's paper on counting points on elliptic curves over finite fields
by Daniel Bernucci
Description of the algorithm and applications to elliptic curve cryptography and/or, as per Schoof's original paper, the computation of square roots modulo p.
by Daniel Bernucci
Description of the algorithm and applications to elliptic curve cryptography and/or, as per Schoof's original paper, the computation of square roots modulo p.
Unitary t-Design
By Artem Kaznatcheev
Unitary t-designs provide a method to simplify integrating polynomials of degree less than t over U(d). Designs allow us to replace the average over U(d) (an integral) by an average over the design (a finite sum). I will motivate and introduce this theoretical tool and present a few nice results. As an example I will prove that un! itary orthonormal bases of the space of d-by-d matrices are 1-designs. This allows me to show that t-designs are non-commuting sets, supporting our intuition that the elements of a design are well ‘spread out’. A (very) brief introduction to quantum mechanics will be given, and the majority of the talk should be self-contained.
By Artem Kaznatcheev
Unitary t-designs provide a method to simplify integrating polynomials of degree less than t over U(d). Designs allow us to replace the average over U(d) (an integral) by an average over the design (a finite sum). I will motivate and introduce this theoretical tool and present a few nice results. As an example I will prove that un! itary orthonormal bases of the space of d-by-d matrices are 1-designs. This allows me to show that t-designs are non-commuting sets, supporting our intuition that the elements of a design are well ‘spread out’. A (very) brief introduction to quantum mechanics will be given, and the majority of the talk should be self-contained.
Formes quadratiques binaires
par François Séguin
Nous étudierons les formes quadratiques binaires entières, et nous verrons comment la loi de composition sur le groupe de classes peut être approchée de différentes manières, certaines intuitives et d'autres moins.
par François Séguin
Nous étudierons les formes quadratiques binaires entières, et nous verrons comment la loi de composition sur le groupe de classes peut être approchée de différentes manières, certaines intuitives et d'autres moins.
Factorization by the quadratic sieve method
by Maya Kaczorowoski
Number sieving factorization methods are based on factorization by difference of squares. For fast factorization, these algorithms require that we come up with a large list of B-smooth numbers. In practice, it is difficult and time-consuming to divide many numbers by long lists of primes hoping to find B-smooth numbers. Instead, the quadratic and number field sieves provides a way to apply this division simultaneously to a longer list, limiting the calculations required. We will examine Fermat's factorization by difference of squares, Dixon's algorithm, and finally the quadratic sieve.
by Maya Kaczorowoski
Number sieving factorization methods are based on factorization by difference of squares. For fast factorization, these algorithms require that we come up with a large list of B-smooth numbers. In practice, it is difficult and time-consuming to divide many numbers by long lists of primes hoping to find B-smooth numbers. Instead, the quadratic and number field sieves provides a way to apply this division simultaneously to a longer list, limiting the calculations required. We will examine Fermat's factorization by difference of squares, Dixon's algorithm, and finally the quadratic sieve.
La théorie des jeux combinatoires
par Karl-Alexander Berg-Briseboix
Introduction du concept de jeu combinatoire et de somme de deux jeux combinatoires. Si le temps permet, développement de différentes méthodes pour évaluer le résultat de jeux combinatoires.
par Karl-Alexander Berg-Briseboix
Introduction du concept de jeu combinatoire et de somme de deux jeux combinatoires. Si le temps permet, développement de différentes méthodes pour évaluer le résultat de jeux combinatoires.
Fourier Transforms
by Daniel Shapero
Basic properties of the Fourier transform. In particular, showing how the Fourier transform can be used to solve the wave equation and how it can be used to understand some basic facts of turbulence theory.
by Daniel Shapero
Basic properties of the Fourier transform. In particular, showing how the Fourier transform can be used to solve the wave equation and how it can be used to understand some basic facts of turbulence theory.
A Brief Introduction to Survival Analysis
by Ana Best
This talk will comprise an introduction to survival analysis, including why survival analyses are necessary, and basic nonparametric and semi-parametric methods. Prerequisite: Some familiarity with probability and statistics.
by Ana Best
This talk will comprise an introduction to survival analysis, including why survival analyses are necessary, and basic nonparametric and semi-parametric methods. Prerequisite: Some familiarity with probability and statistics.
Statistical Mechanics via Hamiltonian Formalism
by Alexandre Tomberg
I will talk about statistical mechanics from the point of view of Hamiltonian formalism. I will discuss the non-equilibrium statistical mechanics and the project that I worked on during summer 2009 under the supervision of Prof. Vojkan Jaksic (McGill).
by Alexandre Tomberg
I will talk about statistical mechanics from the point of view of Hamiltonian formalism. I will discuss the non-equilibrium statistical mechanics and the project that I worked on during summer 2009 under the supervision of Prof. Vojkan Jaksic (McGill).
Divergence of the Harmonic Series
by Cyndie Cottrell
Discussion of the mind-boggling fact that the harmonic series diverges.
by Cyndie Cottrell
Discussion of the mind-boggling fact that the harmonic series diverges.
Quasi Monte Carlo Simulation
by Angie King
A brief overview of Monte Carlo and Quasi Monte Carlo methods will be presented. I will discuss the application of Quasi Monte Carlo techniques to solving high dimensional integrals in mathematical finance. Some background in probability and statistics is helpful.
by Angie King
A brief overview of Monte Carlo and Quasi Monte Carlo methods will be presented. I will discuss the application of Quasi Monte Carlo techniques to solving high dimensional integrals in mathematical finance. Some background in probability and statistics is helpful.
