Online Registration (closed)
Invited Speakers
|
Keynote speaker: Title: Cybersecurity and Its Limitations Abstract: Network security is terrible, and we are constantly threatened with the prospect of imminent doom. Yet such warnings have been common for the last two decades. In spite of that, the situation has not gotten any better. On the other hand, there have not been any great disasters either. To understand this paradox, we need to consider not just the technology, but also the economics, sociology, and psychology of security. Any technology that requires care from millions of people, most very unsophisticated in technical issues, will be limited in its effectiveness by what those people are willing and able to do. The interactions of human society and human nature suggest that security will continue being applied as an afterthought. We will have to put up with the equivalent of bailing wire and chewing gum, and to live on the edge of intolerable frustration. However, that is not likely to block development and deployment of information technology, because of the non-technological protection mechanisms in our society. |
|
Invited speaker: Title: Linear Extensions of Ranked Posets, Enumerated by Descents: A Problem of Richard P. Stanley from the 1981 Banff Conference on Ordered Sets Abstract: Let P be a naturally labelled, ranked (graded) poset of rank r and cardinality n. Let Hk be the set of linear extensions of P with k descents. An explicit bijection between Hk and Hn-1-r-k is constructed for (integer) k ∈ [0, n-1-r]. A problem of Richard P. Stanley from 1981 is thereby solved. |
|
Invited speaker: Title: The Making of the 2003 Math Awareness Month Poster Abstract: This talk concerns the problem of traversing an m by n directed grid embedded on a torus so that each vertex is visited exactly once before returning to the starting position. We include an application to computer graphics that became the image on Mathematics Awareness 2003 poster. |
|
Invited speaker: Title: Spherical Codes, Fullerenes and the Structures of Solutions to the Problems of Thomson and Tammes Abstract: Spherical Codes (maximum families of non overlapping identical spherical caps on a sphere), Fullerenes (large carbon molecules) and the structures of solutions to the problems of Thomson (minimize the potential of n unit charged particles on the sphere) and Tammes (distribute n points on the sphere to maximize the minimum distance between them) all give rise to large planar graphs. This talk is about the structures of these graphs and the relationships between the graphs that arise from different problems. |
|
Invited speaker: Title: Perfect Maps and Factors Abstract: A one dimensional perfect map is a cyclic sequence in which each k-ary n-tuple appears exactly once as a consecutive subsequence. These are also called DeBruijn cycles. We will brieflypresentbasicresultsand the history of these maps and then discuss two generalizations that have been examined in recent years. For universal cycles, we have another combinatorial object which appears as the consecutive sequence. We will illustrate this with some results about Hamiltonian cycles that are used in the problem of finding a cyclic sequence in which each k permutation of an n set appears exactly once and for which the length k+1 subsequences are also permutations. Finally we will present a general framework for constructing higher dimensional perfect maps. This framework requires construction of factored versions of perfect maps. Both results and open problems for the higher dimensional problem will be given. |
|
Invited speaker: Title: Channel Assignment Problems and Graph Colorings Abstract: One of the most interesting applications of graph coloring is in channel assignments in television and radio transmission. Here we have a graph G=(V,E), with vertices representing transmitters and an edge between two transmitters representing interference. We want a channel (color) f(x) to each transmitter x so that if two transmitters interfere, they get different channels. Channel assignment has given rise to a variety of fascinating generalizations of standard coloring and we will study some of them. We will survey briefly some known results in this area and give some open problems as well. |
|
Invited speaker: Title: Tolerance Graphs Abstract: Tolerance graphs were introduced in 1982 by Golumbic and Monma as a generalization of the class of interval graphs. A graph G= (V, E) is an interval graph if each vertex v ∈ V can be assigned a real interval Iv so that xy ∈ E(G) if and only if the intersection of Ix and Iy is nonempty. Interval graphs are important both because they arise in a variety of applications and also because some well-known recognition problems that are NP-complete for general graphs can be solved in polynomial time when restricted to the class of interval graphs. In certain applications it can be useful to allow a representation of a graph using real intervals in which there can be some overlap between the intervals assigned to non-adjacent vertices. This motivates the following definition: a graph G= (V, E) is a tolerance graph if each vertex v ∈ V can be assigned a real interval Iv and a positive tolerance tv ∈ R so that xy ∈ E(G) if and only if | Ix ^ Iy | is greater than or equal to min(tx, ty). In this talk we give an overview of work done in tolerance graphs. We use hierarchy diagrams and geometric arguments as unifying themes. |