2006-2007 Colloquium
Department of Mathematical Sciences.
2006-2007 Colloquium Schedule
Colloquia are on Tuesdays, at 1:00 pm in RB3023.
Please feel free to bring your lunch!
September 26, 2006. Dr. Fridolin Ting, Lakehead University
"Asymptotic stability of pinned fundamental vortices."
We consider asymptotic stability of pinned fundamental vortices to the Ginzburg-Landau equations with external potentials in U2. For smooth and sufficiently small external potentials, there exists a perturbed vortex solution centred near each critical point of the potential. It is known that perturbed vortex solutions which are concentrated near maxima/minima are dynamically stable/unstable in the gradient and Hamiltonian case. In fact, for the gradient case, the pinned vortices corresponding to maxima are asymptotically stable. This is joint work with S. Gustafson.
We consider asymptotic stability of pinned fundamental vortices to the Ginzburg-Landau equations with external potentials in U2. For smooth and sufficiently small external potentials, there exists a perturbed vortex solution centred near each critical point of the potential. It is known that perturbed vortex solutions which are concentrated near maxima/minima are dynamically stable/unstable in the gradient and Hamiltonian case. In fact, for the gradient case, the pinned vortices corresponding to maxima are asymptotically stable. This is joint work with S. Gustafson.
October 13, 2006 Dr. Mei Ling Huang, Brock University
3:00 - 4:00 p.m. Ryan Building-1047
"Hermite Series for Probability Density Estimation"
The paper discusses Hermite series density estimator of an unknown density function f(x) using an random sample X1,X2,...,Xn of i.i.d. random variables. We study its convergence rate and other properties. The paper compares this estimator with the kernel density estimator and other density estimators, and shows that there are some improvements of this Hermite series density estimator. Monte Carlo simulation results confirm the theoretical conclusions. Applications and numerical examples are also given.
3:00 - 4:00 p.m. Ryan Building-1047
"Hermite Series for Probability Density Estimation"
The paper discusses Hermite series density estimator of an unknown density function f(x) using an random sample X1,X2,...,Xn of i.i.d. random variables. We study its convergence rate and other properties. The paper compares this estimator with the kernel density estimator and other density estimators, and shows that there are some improvements of this Hermite series density estimator. Monte Carlo simulation results confirm the theoretical conclusions. Applications and numerical examples are also given.
November 21, 2006 Dr. Adam Van Tuyl, Lakehead University
1:00 - 2:00 p.m. in RB-3023.
"What is a syzygy?"
According to the dictionary, a syzygy is a kind of unity, especially through alignment. In this talk, I'll describe what we mean by a syzygy in mathematics. Roughly speaking, a syzygy is an abstraction of the notion of linear dependence relation from linear algebra. This (mostly) expository talk should be accessible to anyone with some linear algebra background (although some ring theory will also be used).
1:00 - 2:00 p.m. in RB-3023.
"What is a syzygy?"
According to the dictionary, a syzygy is a kind of unity, especially through alignment. In this talk, I'll describe what we mean by a syzygy in mathematics. Roughly speaking, a syzygy is an abstraction of the notion of linear dependence relation from linear algebra. This (mostly) expository talk should be accessible to anyone with some linear algebra background (although some ring theory will also be used).
March 6, 2007 Dr. Clement Kent, Lakehead University
10:00 - 11:00 a.m. in RB-1047
"Fulfillment (Part I)"
One of the outstanding ideas in the foundations of mathematics in the 20 th. Century was Godel's proof of the incompleteness of almost all mathematics. Godel used techniques of arithmetization of syntax and self reference which some mathematicians still find artificial. Since 1977 more "mathematical" truths have been shown to be independent of basic axiomatic theories, but the independence often falls back on Godel's results. But, hidden in the "mathematical forklore" has lingered a construction called "fulfilment" by which Saul Kripke produced directly a non-provable truth of arithmetic not using Godel's results. Kripke never published and only an incomplete summary, by Hilary Putnam, appeared in 2003. Kripke employed ideas of Non-Standard Analysis. I plan one hour of informal historical discussion of some of the pleasant facts about non-standard models, and a second hour on how Kripke used them in arithmetic, suppressing messy details. This should be accessible to students in Andrew Dean's second year analysis course who have solved problem 1.154. All of this should have been acceptable to Euler, in 1740, when he wrote on "infinitesimal analysis".
10:00 - 11:00 a.m. in RB-1047
"Fulfillment (Part I)"
One of the outstanding ideas in the foundations of mathematics in the 20 th. Century was Godel's proof of the incompleteness of almost all mathematics. Godel used techniques of arithmetization of syntax and self reference which some mathematicians still find artificial. Since 1977 more "mathematical" truths have been shown to be independent of basic axiomatic theories, but the independence often falls back on Godel's results. But, hidden in the "mathematical forklore" has lingered a construction called "fulfilment" by which Saul Kripke produced directly a non-provable truth of arithmetic not using Godel's results. Kripke never published and only an incomplete summary, by Hilary Putnam, appeared in 2003. Kripke employed ideas of Non-Standard Analysis. I plan one hour of informal historical discussion of some of the pleasant facts about non-standard models, and a second hour on how Kripke used them in arithmetic, suppressing messy details. This should be accessible to students in Andrew Dean's second year analysis course who have solved problem 1.154. All of this should have been acceptable to Euler, in 1740, when he wrote on "infinitesimal analysis".
March 13, 2007 Dr. Clement Kent, Lakehead University
10:00 - 11:00 a.m. in RB-1047
"Fulfillment (Part II)"
One of the outstanding ideas in the foundations of mathematics in the 20 th. Century was Godel's proof of the incompleteness of almost all mathematics. Godel used techniques of arithmetization of syntax and self reference which some mathematicians still find artificial. Since 1977 more "mathematical" truths have been shown to be independent of basic axiomatic theories, but the independence often falls back on Godel's results. But, hidden in the "mathematical forklore" has lingered a construction called "fulfilment" by which Saul Kripke produced directly a non-provable truth of arithmetic not using Godel's results. Kripke never published and only an incomplete summary, by Hilary Putnam, appeared in 2003. Kripke employed ideas of Non-Standard Analysis. I plan one hour of informal historical discussion of some of the pleasant facts about non-standard models, and a second hour on how Kripke used them in arithmetic, suppressing messy details. This should be accessible to students in Andrew Dean's second year analysis course who have solved problem 1.154. All of this should have been acceptable to Euler, in 1740, when he wrote on "infinitesimal analysis".
One of the outstanding ideas in the foundations of mathematics in the 20 th. Century was Godel's proof of the incompleteness of almost all mathematics. Godel used techniques of arithmetization of syntax and self reference which some mathematicians still find artificial. Since 1977 more "mathematical" truths have been shown to be independent of basic axiomatic theories, but the independence often falls back on Godel's results. But, hidden in the "mathematical forklore" has lingered a construction called "fulfilment" by which Saul Kripke produced directly a non-provable truth of arithmetic not using Godel's results. Kripke never published and only an incomplete summary, by Hilary Putnam, appeared in 2003. Kripke employed ideas of Non-Standard Analysis. I plan one hour of informal historical discussion of some of the pleasant facts about non-standard models, and a second hour on how Kripke used them in arithmetic, suppressing messy details. This should be accessible to students in Andrew Dean's second year analysis course who have solved problem 1.154. All of this should have been acceptable to Euler, in 1740, when he wrote on "infinitesimal analysis".
March 15, 2007 Dr. Thomas Schlumprecht, Texas A & M University
10:00 - 11:00 a.m. in RB-2024
"Coefficient Quantization in Banach Spaces"
Let (ei) be a dictionary for a separable Banach space X. We consider the problem of approximation by linear combinations of dictionary elements with quantized coefficients drawn usually from a ‘finite alphabet’. We investigate several approximation properties of this type and connect them to the Banach space geometry of X. The existence of a total minimal system with one of these properties, namely the coefficient quantization property, is shown to be equivalent to X containing co.
10:00 - 11:00 a.m. in RB-2024
"Coefficient Quantization in Banach Spaces"
Let (ei) be a dictionary for a separable Banach space X. We consider the problem of approximation by linear combinations of dictionary elements with quantized coefficients drawn usually from a ‘finite alphabet’. We investigate several approximation properties of this type and connect them to the Banach space geometry of X. The existence of a total minimal system with one of these properties, namely the coefficient quantization property, is shown to be equivalent to X containing co.
March 20, 2007 Mr. Benjamin Lavoie, Lakehead University
10:00 - 11:00 a.m. in RB-1047
"Su(2) and su(3) Intelligent States"
We show how all su(2) and su(3) intelligent states can be obtained by coupling su(2) and su(3) coherent states. The construction leads to a discussion of some general properties of these intelligent states.
10:00 - 11:00 a.m. in RB-1047
"Su(2) and su(3) Intelligent States"
We show how all su(2) and su(3) intelligent states can be obtained by coupling su(2) and su(3) coherent states. The construction leads to a discussion of some general properties of these intelligent states.
March 27, 2007 Ms. Jane He, Lakehead University
10:00 - 11:00 a.m. in RB-1047
"The path ideal of a tree and its properties"
For a tree T we consider the path ideal It(T), that is, an ideal where every generator corresponds to a path of length tin T. When this path ideal is regarded as a facet ideal of a simplicial complex, that is, we view every generator of path ideal as a facet of this simplicial complex, we show this simplicial complex is actually a simplicial tree. By using a property of a simplicial tree due to Faridi, we get R=It(T) is sequentially Cohen-Macaulay.