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Mathematics & Statistics

Discrete Mathematics
(Leader: Prof. Greg McColm)

Monday, April 23, 2001

Title
Speaker
Time
Place

Domination Numbers of Circulant Graphs
Vicky Wood
3:00pm-4:00pm
PHY 108

Abstract

I will define and discuss circulant graphs and some of their characteristics. Primarily, the meaning of domination number and how I used Maple to find these numbers for most graphs through \(n=2\) will be explained. Secondarily, I will touch upon connectivity, isomorphism and one technique used to eliminate isomorphic graphs from the data for better computational efficiency. In addition, I will briefly mention 2-packing numbers and explore possible application ideas for domination numbers of circulant graphs. Finally, I will wrap up the session with a challenge to others to look for patterns in the data I generated that might lead to theorems about domination number in circulant graphs.

Monday, April 16, 2001

Title
Speaker
Time
Place

Generating Caley Graphs
Daniela (Genova) Filipov
3:00pm-4:00pm
PHY 108

Abstract

Cayley graphs appear in problems related to edge-coloring, planarity, and symmetries in a graph. I will define Cayley graphs, superposition of graphs, Möbius Ladder, and twisted prismatic identification. I will discuss the structure of Cayley graphs using these concepts. This material is taken from a recent paper by Abreu and Guidici. The main goal of the paper is to give graph-theoretic descriptions of the Cayley graphs for all groups of small order.

Monday, April 9, 2001

Title
Speaker
Time
Place

More on Linear Cellular Automata
Edwin Clark
3:00pm-4:00pm
PHY 108

Abstract

This talk will be more or less independent of the talk last week. I will discuss several definitions of linear cellular automata and give a few basic results. In particular I will give a few examples and discuss implications of Fitting's Lemma for the transition diagram of global states.

Monday, April 2, 2001

Title
Speaker
Time
Place

Linear Cellular Automata and Garden-of-Eden Configurations
Edwin Clark
3:00pm-4:00pm
PHY 108

Abstract

I will discuss the definition of linear cellular automata (on graphs) and prove a few general facts concerning such automata. I will also present Sutner's proof of Sutner's Theorem: The all-ones problem has a solution in any finite graph.

The proof requires some basic facts from linear algebra over a finite field which will be reviewed prior to the presentation of the proof.

Monday, March 26, 2001

Title
Speaker
Time
Place

Cyclic Homology of Algebras, Part IV
Mohamed Elhamdadi
3:00pm-4:00pm
PHY 108

Monday, March 5, 2001

Title
Speaker
Time
Place

Cyclic Homology of Algebras, Part III
Mohamed Elhamdadi
3:00pm-4:00pm
PHY 108

Monday, February 19, 2001

Title
Speaker
Time
Place

Cyclic Homology of Algebras, Part II
Mohamed Elhamdadi
3:00pm-4:00pm
PHY 108

Monday, February 12, 2001

Title
Speaker
Time
Place

Cyclic Homology of Algebras
Mohamed Elhamdadi
3:00pm-4:00pm
PHY 108

Abstract

We will define Hochschild and Cyclic Homologies of associative Algebras, give some examples and the relationship between the two.

Monday, February 5, 2001

Title
Speaker
Time
Place

Making Bigger Quandles, Part II
Masahiko Saito
3:00pm-4:00pm
PHY 108

I will show how the 3rd cohomology groups of quandles are related to making even bigger quandles. I will also discuss relations to knots.

Monday, January 29, 2001

Title
Speaker
Time
Place

Making Bigger Quandles
Masahiko Saito
3:00pm-4:00pm
PHY 108

Abstract

A quandle is a set with a self-distributive binary operation with a few other properties. I will review some basics of quandles, and discuss a construction of bigger quandles from given smaller quandles.

Monday, January 22, 2001

Title
Time
Place

Organizational Meeting
3:00pm-4:00pm
PHY 108

Summary

This meeting will also be a special session. Natasha Jonoska has asked for volunteers to go to nearby colleges and make presentations on “How to Choose and Apply to a Math Graduate School”. She has even prepared a collection of overhead slides of volunteers to use. Masahico Saito will go over the slides. Anyone, discrete or otherwise, who is interested in volunteering is invited.