Tuesday, March 23, 2010

An Evening with Leonhard Euler

We have no live presentation in the Pizza Seminar this week, but you can watch and enjoy a nice lecture on several aspects of Euler's work here: An Evening with Leonhard Euler.

Friday, March 12, 2010

Pizza Seminar: Remote Coin Tossing

Department of Mathematics Pizza Seminar

Speaker: Ajneet Dhillon (Western)

Title: Remote Coin Tossing

Time and Place: Tuesday, March 16, 5 PM, MC 107; All are welcome!

Abstract: Judy and Andrew are going through a bitter divorce. They live thousands of miles apart. They wish to toss a coin over the phone to see who will keep the car. How can they do this without anyone cheating? Here you can download a pdf file of this talk.

Pizza Seminar: The mathematics of music from the wave equation to equal temperament

Department of Mathematics Pizza Seminar

Speaker: Rasul Shafikov (Western)

Title: The mathematics of music: from the wave equation to equal temperament.

Time: 17:30 PM, Tuesday, March 9; Room: MC 107

In this talk I will explain how the solution of the wave equation can be used to explain music scales, temperament (i.e., music tuning) and harmony. We will also do a few experiments on a guitar.

Wallpaper groups

Pizza Seminar

Speaker: Zack Wolske (Western)

Title: Wallpaper groups

Time: 17:30 PM, Tuesday March 2; Room: MC 107

A planar tiling is a repeating symmetric pattern in the plane. Because of their common everyday appearances such patterns are called "wallpaper groups." We follow Conway's orbifold notation, which describes the 17 wallpaper groups as certain topological spaces: quotients of the plane by some finite group. Completeness is given by computing the Euler characteristic of such spaces. No knowledge of groups, topology, orbifolds, or how to hang wallpaper required.

What if we had infinitely many fingers to count on

Pizza Seminar

Speaker: Serge Randriambololona (Western)

Title: What if we had infinitely many fingers to count on ?

Time: 17:30 PM, Tuesday February 9; Room: MC 107

Natural numbers encompasses at least two way of counting. The first one tells how many objects a collection has: there are 84 students in the class, 4 apples in my lunch box or 223,647,852 inhabitants in Indonesia. In the second way of counting, we care for the position of an event in a sequence of events: the final exam will be the 106th day of the academic year, "trois" is the name of the numeral that comes after "deux" in French and the 8,000,000,000th human birth has already happened. As far as we only consider finite collections, these two notions of counting lead to the same arithmetic. But when we try to generalize them to infinite collections, surprising phenomena appear.

Circular Billiards

Pizza Seminar

Speaker: Siyavus Acar (Western)

Title: Circular Billiards

Time: 17:00 PM, Tuesday January 26, 2010; Room: MC 107

There is an old question in optics that has been called Alhazen's Problem. The name Alhazen honours an Arab scholar Ibn-al-Haytham who flourished 1000 years ago. The problem itself can be traced further back, at least to Ptolemy's Optics written around AD 150. The problem - while considered one of the 100 great problems of elementary mathematics - is very easy to state: Given two arbitrary balls on a circular billiard table, how does one aim the object ball so that it hits the target ball after one bounce off the rim. In this talk we introduce various methods of approach that has been studied, but mainly focus on the number of solutions and their distribution on the table.

What does the spectral theorem say

Pizza Seminar

Speaker: Farzad Fathizadeh (Western)

What does the spectral theorem say?

Time: 17:00 PM, Tuesday January 19, 2010; Room: MC 107

The Spectral Theorem, and the closely related Spectral Multiplicity Theory is a gem of modern mathematics. It is about the structure, and complete classification, up to unitary equivalence, of normal operators on a Hilbert space. This theorem is the generalization of the theorem in linear algebra which says that every normal, in particular selfadjoint, matrix is unitarily equivalent to a diagonal matrix; or, in simple terms, is diagonalizable in an orthonormal basis. The extension of this result to infinite dimensions is by no means obvious and involves many new subtle phenomena that have no analogue in finite dimensions. The final result has many applications to pure and applied mathematics, mathematical physics, and quantum mechanics. In this talk, a proof of the spectral theorem for Hermitian operators on a Hilbert space will be outlined and some applications will be discussed. This talk should be accessible to undergraduate students.

An elementary introduction to elliptic curves

Pizza Seminar

Speaker: Emre Coskun (Western)

Title: An elementary introduction to elliptic curves

Time: 17:00 PM, Tuesday December 8 2009; Room: MC 108

The theory of elliptic curves is a fascinating field with many connections to algebraic geometry, number theory, complex analysis and even computational problems. In this talk, we introduce these objects in a very elementary manner, describe some of their properties and as an application, we show how they can be used to prove special cases of Fermat's Last Theorem.

Oppositions and Paradoxes in Mathematics and Philosophy

Pizza Seminar

Speaker: John Bell (Western)

Title: Oppositions and Paradoxes in Mathematics and philosophy

Time: 17:00 PM, Tuesday, October 27, 2009; Room: MC 108

From antiquity mathematics and philosophy has been beset by a number of oppositions, such as the Continuous and the Discrete, the One and the Many, the Finite and the Infinite, the Whole and the Part, and the Constant and the Variable. These oppositions have on occasion crystallized into paradox and they continue to haunt fundamental thinking to this day. In my talk I'll analyze some of these and describe their impact on the development of mathematics and philosophy.

Solving Rubik's cube using group theory

Pizza Seminar

Speaker: Sheldon Joyner (Western)

Title: Solving Rubik's cube using group theory

Time: 17:00 PM, Tuesday, September 2009, Room: 108

Group theory is the mathematical language of symmetry, and as such has many real world applications, ranging from the study of crystals to fundamental ideas about the workings of the universe. In this talk, we will introduce group theory and see how it is used to create a wonderful algorithm to solve Rubik's cube.