Discrete Mathematics Days 2010, Carleton University

Main Web Page For This Event: http://www.fields.utoronto.ca/programs/scientific/09-10/discrete_math/
Directions to Carleton
Map of Carleton Campus

Friday 14 May (morning): MATH, ART AND LIFE: a morning of unusual mathematical connections
08:45-10:40	Minto Bell Theatre (note room change!)
08:45-09:00	refreshments and open remarks
09:00-09:25	Angelo Mingarelli: Leonardo da Vinci
09:25-09:50	Aaron Williams: Ringing Campanologically: New methods for Old Church Bells
09:50-10:15	Maureen Pytlik: Group Theory & Musical Composition: The Structure of Xenakis' Nomos Alpha
10:15-10:40	Lerna Pehlivan: Mathematics and Card Shuffling
10:40-11:00	move to Azrieli Theatre 101
11:00-13:00	Azrieli Theatre 101
11:00-12:00	Invited Lecture by Jason Brown: A Hard Day's Math, Connections between Mathematics and Music
12:00-13:15	Transition to HP4351 and Free Pizza Lunch
Friday 14 May (afternoon) Discrete Mathematics Days, Technical Talks Start
13:30+	Herzberg Physics 4351
13:30-14:30	Invited Lecture by Joseph Cheriyan: Some open questions on k-connected graphs
14:30-14:55	Andrew Baker: Several Ways to Approach the Maximum Number of Runs Conjecture
14:55-15:20	Feng Xie: More Colourful Simplices
15:20-15:35:	Coffee Break
15:35-16:00:	Shonda Gosselin: Paley-like uniform hypergraphs
16:00-17:00	Invited Lecture by Penny Haxell: Edge colouring multigraphs
17:00+	Dinner (catering at HP4351)
Saturday May 15
09:00-17:00	Herzberg Physics 4351
09:00-10:00	Invited Lecture by Cathy Baker: Skolem sequences: from applications to existence and back
10:00-10:25	Andrea Burgess: Cycle decompositions of complete equipartite graphs with of size 3
10:25-10:50	Jason Lobb: Using Cover Starters to Create Covering Arrays
10:50-11:05	Coffee Break
11:05-11:30	Sebatian Raaphorst: A Density-Based Algorithm for Variable Strength Covering Arrays
11:30-11:55	Robert Bailey: Generalized covering designs and clique coverings
11:55-13:55	Lunch
13:55-14:55	Invited Lecture by Richard Wilson: Proportions of graphs in graph-designs; also packings and coverings
14:55-15:20	Timothy Walsh: Enumeration of Unrooted Orientable Maps of Arbitrary Genus by Number of Edges and Vertices
15:20-15:35	Coffee Break
15:35-16:00	Masud Hasan: Equiprojective Polyhedra: Recent Advances and Future Directions
16:00-17:00	Invited Lecture by Gena Hahn: Cops and robbers on infinite graphs

Invited Speakers

• Jason Brown (Dalhousie University) with live music accompaniment.
  A HARD DAY'S MATH, Connections between Mathematics and Music
  Abstract: Mathematics and music are a match made in heaven.
  The ancient Greeks elevated both to the same level, and even the most unschooled rock musician uses more mathematics than he or she realizes. In this talk I'll survey some of the most interesting connections between mathematics and music, including:
  - trigonometric identities and tunings
  - small fractions and musical intervals
  - circular seating arrangements, scales and rhythm guitar
  - derivation of the blues and graph colourings
  - the musical art of being ambiguous (or not)
  - musical and mathematical transformations
  I'll end off the talk with a discussion of some application of mathematics I carried out on some musical mysteries surrounding The Beatles. Yeah, Yeah, Yeah.
  
  
• Joseph Cheriyan (University of Waterloo)
  Some open questions on k-connected graphs
  Abstract: The talk will address some of the open questions on k-node connected graphs; for example, connectivity augmentation, orientations, and min-cost spanning subgraphs. These questions/conjectures are analogous to similar statements for edge connectivity. Most of the statements for edge connectivity have been resolved, but the questions for node connectivity are wide open. The talk will cover some recent progress on some of these topics.
  
  
• Penny Haxell (University of Waterloo)
  Edge colouring multigraphs
  Abstract: We highlight a technique for studying edge colourings of multigraphs, due to Tashkinov. This method is a sophisticated generalisation of the method of alternating paths, and builds upon earlier work by Kierstead and Goldberg. In particular we show how to apply it to a number of edge colouring problems, including the question of whether the class of multigraphs that attain equality in Vizing's classical bound can be characterised.
  
  
• Cathy Baker (Mount Allison University)
  Skolem sequences: from applications to existence and back
  Abstract: The study of Skolem sequences arose from early work by Heffter and Skolem on constructing cyclic Steiner triple systems. Two problems that were of interest then, using Skolem sequences or equivalent structures to construct designs and finding characterizations theorems for these structures, continue to be of interest today. We consider current existence questions for Skolem-type sequences and examine the application of these sequences in design theory and beyond.
  
  
• Rick Wilson (California Institute of Technology)
  Proportions of graphs in graph-designs; also packings and coverings
  Abstract: Let $\mathcal G$ be a family of simple graphs. A $\mathcal G$-design on $n$ points is a decomposition of the edges of $K_n$ into copies of graphs in $\mathcal G$. In case that $\mathcal G$ consists of complete graphs $K_k$ with $k$ in some set $K$ of positive integers, such a $\mathcal G$-design is called a pairwise balanced design (PBD) on $n$ points with block sizes from $K$. Some applications of graph decompositions will be described. In this talk we are primarily concerned with the possible proportions of the numbers of copies of graphs $G\in \mathcal G$ that appear in decompositions for large $n$. We extend a result of Colbourn and R\"odl on PBDs to $\mathcal G$-designs, and prove that any given proportions can be achieved to any desired degree of accuracy, for $n$ sufficiently large (and such that $\mathcal G$-designs exist). A further result concerns the possible numbers of copies of $G$ in a $\mathcal G$-design containing each vertex of the complete graph $K_n$. Finally, we describe some recent work with Chee, Colbourn, and Ling on packings and coverings of complete graphs with given complete graphs.
  
  
• Gena Hahn (Universite de Montreal)
  Cops and robbers on infinite graphs
  Abstract: The game of cops-and-robbers has been studied since the 1980's. Indeed, after a hibernation of almost 20 years, interest in it was renewed by studies of variants of the game and their relation to various graph-widths. Not much has been done, however, in the case of infinite graphs, even though one of the first papers on the subject contains a characterization of graphs on which a cop is guaranteed a win. In this talk we survey what is known about the basic game of cops and robbers on infinite graphs and show how they behave rather differently from finite graphs. The talk is based on the author's work with A. Bonato, F. Laviolette, N. Sauer, C. Tardif, C. Wang, R. E. Woodrow.