# Seminars and Colloquia - Spring 2009

**Dr. Adrian Vetta**Department of Mathematics & Statistics, and School of Computer Science

McGill University

Departmental Colloquium

2:00p.m., Friday, July 31, 2009

HH-3017

Paths, Viruses, and Galaxy Cutsets

A classical result of Menger states that the maximum number of disjoint paths between two nodes in a graph equals the minimum cardinality of a cut separating these nodes. In traditional applications a cut can be viewed as a static network failure occurring at a set of nodes - the failure could have either innocent or malicious causes. In many modern applications, however, network failures can spread from their initial points of “infection” in a virus-like manner. Such a process produces cutsets that we term galaxy-cutsets (a very special case being star-cutsets, objects that have been well-studied in graph theory). We examine the combinatorial and topological properties of these cutsets in planar and non-planar graphs. This leads to approximate min-max results for path packing and galaxy-cutsets. We then consider the question of how to reinforce a planar network to protect it against a single virus-like failure.

No background in these topics will be assumed.

(This is joint work with Nicolas Sonnerat.)

**Professor Chin-Cheng Lin**

National Central University, Taiwan

Colloquium

2:00p.m., Friday, June 5, 2009

HH-3017

Triebel-Lizorkin spaces of para-accretive type and a Tb theorem

In this talk we use a discrete Calderon-type reproducing formula

and Plancherel-Polya-type inequality associated to a para-accretive

function to characterize the Triebel-Lizorkin spaces of para-accretive type which reduces to the classical Triebel-Lizorkin spaces when the para-accretive function is constant. Moreover, we give a necessary and sufficient condition for boundedness of generalized singular integral operators between these spaces.

Helaman Ferguson

Sculptor & Mathematician

Public Lecture

6:00PM, Saturday, June 6, 2009

Inco Innovation Centre, Room IIC 2001

*Mathematics in Stone and Bronze*

Helaman Ferguson's mathematical sculptures in stone and bronze celebrate ancient and modern mathematical discoveries, melding the universal languages of sculpture and mathematics. Using multimedia, Helaman traces his creations from initial concept, mathematical design, computer graphics, diamond cutting and final form. Helaman's lectures have fascinated audiences worldwide, bringing together multiple disciplines and stimulating dialogue among them.

Who he is: Helaman Ferguson is both a sculptor whose work is located in institutions and collections worldwide and an internationally known mathematician whose algorithm has been listed as one of the top ten in the twentieth century.

**Cesar Polcino Milies**

Instituto de Matemática e Estatística

Universidade de São Paulo

Seminar

Friday, May 29, 2009

3:00p.m., HH-3017

Group algebras in Coding Theory

First, we shall discuss briefly some basic ideas in coding theory and then study codes that can be realized as ideals of group algebras. We shall consider some situations in which the use of group algebra methods simplifies greatly the proofs already existing in the literature about cyclic codes and are suitable to extend these results to more general codes.

The talk should be accessible to a general audience.

**Dr. Danny Dyer** Memorial University

Wednesday May 13, 2009

Colloquium

2:00p.m., HH-3017

Searching graphs efficiently

Edge searching is a long standing graph searching problem, in which "slow" cops move through a graph to capture a "fast" invisible robber. The classical version of this problem involves finding the fewest cops needed to capture the robber. Further restrictions, such as monotonicity and connectedness, have been placed on these searches to force "stronger" searches, that are in some sense more efficient, even at the cost of using more cops. This talk will discuss these ideas, and introduce two more ideas of efficiency, the first dealing with the minimum time needed to capture a robber, and the second with minimizing a more general cost function.

**Kehe Zhu**

State University of New York at Albany

Departmental Colloquium

Friday, May 8, 2009

2:00.p.m., HH-3017

Bergman spaces in the past twenty years

I will outline the function theory and operator theory developed in the past twenty years or so for Bergman spaces in the unit disk. Several open problems will be discussed as well.

Nairanjana Dasgupta

Department of Statistics

Washington State University

Departmental Colloquium

Wednesday, May 20, 2009

2:00p.m., HH-3017

Comparing Multiple Treatments to Both Positive and Negative Controls

Most comparison to control problems deal with comparing k test treatments to one control: either positive or negative. Dasgupta et al. (JSCS, 2006) enumerate situations where it is imperative to compare several test treatments to both a negative as well as a positive control simultaneously to see if the test treatments are worse than the negative control, or if they are better than the positive control when the two controls are sufficiently apart. To find critical regions for this problem, one needs to find the Least Favorable Configuration (LFC) under the composite null. In this talk I discuss how to find the LFC analytically. I will also briefly discuss a numerical technique to find LFC. I will compare our method to the logical single step alternatives: Dunnett’s (1955) or the Bonferroni correction.

## Winter 2009

Ms. Rebecca Keeping

Memorial University of Newfoundland

Combinatorics Seminar

Tuesday, April 28, 2009

3:00 p.m., HH-3017

The Watchman's Walk Problem with Time Restraints

A museum is attempting to guard each of its rooms. Rather than having guards placed at every room in a dominating set, Hartnell, Rall, and Whitehead (1998) considered having one watchman walk around the museum in such a way that the visited rooms form a dominating set; i.e., the watchman's route is a dominating walk. As the goal is to minimize the amount of time for which any room is unobserved, we are looking for a `minimum closed dominating walk' for a given graph. This talk will introduce the original problem and initial results and will then focus on a variation (from Davies, Finbow, Hartnell, Li, & Schmeisser, 2003) which considers the number of watchmen required when certain time restraints are placed on the monitoring of each room.