# Geneseo Mathematics Colloquium Schedule

## Fall 2010

Thursday, September 23, 4:00 - 4:50pm
Newton 203
Matt Koetz, Nazareth College

### Coding Theory: Yeah, We've Got That

Coding theory is the study of transmitting information efficiently across noisy channels. It aims to reduce the number of transmission errors, detect and correct errors, and do these things as quickly and cheaply as possible. In the search for better codes, we use many branches of mathematics, including linear algebra, combinatorics, graph theory, geometry, probability, and number theory. We will explore the ways in which coding theory uses each of these fields, from its basic definitions to its most beautiful results.

Thursday, October 7, 4:00 - 4:50pm
Newton 203
Quincy Loney, Binghamton University

### The Octonions: An Alternative (Algebra) To The Reals

In this talk we will discuss some of the history and the properties of the octonions, the 8-dimensional normed division algebra, discovered by John T. Graves in 1843. We will begin with the real number system and use the Cayley-Dickson process to construct this exciting alternative algebra.

Thursday, October 21, 4:00 - 4:50pm
Newton 203
Candace Schenk, Binghamton University

### A brief overview of the conjugacy problem in Thompson's group V.

This is an introductory talk where I will define all terms used! I will explain Thompson's Group V, what the conjugacy problem is and the solution. There will be dynamics! There will be functions! There will be trees!

Thursday, November 4, 4:00 - 4:50pm
Newton 203
Brandt Kronholm, St. Mary's College of Maryland

### Integer Partitions: 1 + 1 = 2 and the Subtleties Therein

The partitions of a number are the ways of writing that number as a sum of positive integers. For example, the five partitions of 4 are 4, 3+1, 2+2, 2+1+1, and 1+1+1+1 and we write p(4) = 5. What’s the formula? It’s less than 100 years old and you wouldn’t believe it even if you saw it.

Around the same time that the formula for p(n) was formulated, it was observed that p(n) had unexpected divisibility properties:
p(5n+4)≡0 (mod5)
p(7n+5)≡0 (mod7)
p(11n + 6) ≡ 0    (mod 11)
Fifty years later one more divisibility property modulo 17 was discovered. Are there any others?

The restricted partition function p(n,m) enumerates the number of partitions of a non negative integer n into exactly m parts. For example, the two partitions of 4 into exactly 2 parts are 3 + 1 and 2+2 and we write p(4,2) = 2. p(n, m) is like a little brother function to the unrestricted partition function p(n) in that
p(n) = p(n,1)+ p(n,2) + ... + p(n,n).
This talk will introduce the theory of partitions from the ground up and segue into a discussion of recent results on divisibility properties for p(n, m). Time permitting, we will consider future research regarding p(n, m) and formulate some formulas!

Thursday, November 11, 4:00 - 4:50pm
Newton 203
Jobby Jacob, Rochester Institute of Technology

### Towers of Hanoi and Rankings of Graphs

The Towers of Hanoi is a famous puzzle that has been studied for centuries. In the Towers of Hanoi, the idea is to move a stack of disks from one pole to another without placing a larger disk on top of a smaller disk. The goal is to do this in the fewest number of moves possible. It is known that this puzzle involving k disks can be solved in 2k −1 steps. The puzzle’s optimal solution relates to some interesting mathematical problems.

An optimal solution to this puzzle is related to rankings of graphs, which are generalized vertex colorings. In this talk we will look at the relationship between rankings of graphs and an optimal solution of the Towers of Hanoi problem, as well as some properties of rankings.

Wednesday, November 17, 2:30 - 3:45pm
Newton 202
Jeff Johannes & Gary Towsley, SUNY Geneseo

### A Concise History of Calculus

A lively overview of over two thousand years of calculus history. Not only who-did-what along the way, but the cultural and sociological causes and effects of the calculus. Strongly recommended for anyone who has taken or is taking calculus.