Mar 24/04

Undergraduate Seminar by Benjamin Moull Friday, March 26, 2004 Sidney Smith 2115 at 5pm Dynamical Systems and Sharkovskii's Theorem With the proliferation of computers, there has been an explosion of interest in dynamical systems in recent years. They have proved useful in modeling and understanding phenomena in numerous fields, ranging from physics to biology to economics. Interesting and important theoretical results have also been established. One such result is a theorem due to the Russian mathematician Sharkovskii. Though first proved by him in 1962, this result remained unknown to the English speaking math community until 1976. This theorem completely describes the periods of periodic orbits of a continuous map of the real line that can simultaneously occur. In this talk, I will give a brief introduction to dynamical systems in general, followed by an elementary proof of Sharkovskii's theorem. No advance knowledge is needed. Refreshments will be served after the talk.

Mar 17/04

Academic Seminar by Professor James Arthur Monday March 22nd, 5-6pm Sidney Smith 1070 An Introduction to the Langlands Programme The Langlands programme is one of the central areas of modern mathematical research. It proposes far-reaching relations between fundamental arithmetic information and equally fundamental analytic information. The arithmetic information arises from solutions of algebraic equations, and includes data that classify algebraic number fields. The analytic information arises from spectra of differential equations, and includes data that classify representations of locally compact groups. A completion of the Langlands programme would represent a grand unification of two great streams of traditional mathematics. The lecture will be an attempt to describe some of these ideas in elementary terms. Refreshments will be served after the talk.

MASSU Social Friday, March 26th, 2pm till whenever! Sidney Smith 5017B Come out to meet other students, eat food and have a good time!

MASSU Movie Night Thursday, April 8th, 5pm till whenever! Sidney Smith 5017B Movie nights are a great time for everyone. Come out to sit back, relax, eat some food, and enjoy the movies! Suggestions for movies are welcome and can be emailed to massu@math.utoronto.ca

Mar 16/04

Undergraduate Seminar by Lucy Liuxuan Zhang Friday, March 19th, 2004 Sidney Smith 2115 at 5pm Physics & Astrophysics of Magnetohydrodynamical Turbulence (with emphasis on the numerical simulations) Turbulence is intrinsically nonlinear, which is almost equivalent to 'unsolvable'. The good news is, in a magnetized fluid, which is a seemingly more complicated environment, there exists a weak regime where the MHD equations can be solved analytically. The theory of turbulence is constructed by a handful of great theorists. The mathematician Kolmogorov derives the famous Kolmogorov spectrum which describes a turbulent fluid in the absence of magnetic field. In the last 50 years, Goldreich and Sridhar developed the theory of MHD turbulence, that is turbulence in the the presence of magnetic field. Most of the population currently working on astrophysical turbulence are busy running ever larger simulations in order to verify the theory. In the talk, I describe the current state of turbulent research, and maybe some theory. I shall mention the role of MHD turbulence in astrophysical settings, in particular, star formation. I write down the MHD equations, and explain how they are solved numerically. I will cover the boundary condition, initial condition and turbulence driving method. Refreshments will be served after the talk.

Mar 10/04

Academic Seminar by Professor Jaimungal Tuesday, March 16th, 2004 Sidney Smith 1072 at 4pm Stochastic Modeling for Pricing Financial Derivatives This talk will introduce students to the fundamental ideas used in the pricing of exotic financial derivative instruments. The talk will begin with a discrete time model for asset dynamics and prices of European contingent claims will be expressed in terms of discrete time Martingales. The continuous time limit will then be investigated and the role that Ito processes, Ito's lemma and partial differential equations play will be explored.    PDF Slides of Professor Jaimungal's Seminar Refreshments will be served after the talk.

Mar 01/04

Academic Seminar by Professor Edward Barbeau Friday, March 5th, 2004 Sidney Smith 2102 at 3pm Tread With Caution Mathematical reasoning has all sorts of pitfalls for the unwary. I will look at arguments that are less robust than they seem, and perhaps others that look suspect but work. Refreshments will be served after the talk.

Undergraduate Seminar by C. Emily I. Redelmeier Friday, March 5th, 2004 Sidney Smith 2115 at 5pm Tying Knots Around Knots I will look at one of the most powerful knot invariants, the knot group. This group can be seen as a description of how one can tie knots around another knot. I will briefly introduce knot theory, then describe this knot invariant, as well as the Wirtinger Presentation, a method of calculating it. I will use this invariant to demonstrate that nontrivial knots exist, and, time permitting, that there are infinitely many knots. I can cover the group theory and topology background if necessary.

Undergraduate Seminars A series of undergraduate seminars has been scheduled to take place on Fridays at 5pm in Sidney Smith 2115. Commencing this Friday the speakers will be: C. Emily I. Redelmeier - March 5 Leo Trottier - March 12 Lucy Zhang - March 19 Ben Moull - March 26 If you're interested in giving a talk please contact massu@math.utoronto.ca.