Friday May 16 12:00 to 12:50 Room C620 
Robert Benkoczi
Assistant Professor, University of Lethbridge
Ph.D. Simon Fraser University (2004)
Research interests: Wireless networks, facility location, combinatorial optimization.

On a covering problem with variable capacities.
Facility location problems arise in many real life applications, in the management of cellular networks and of the supply chain of an
enterprise to name a few. In cellular networks, for example, it is
essential for the service provider to be able to use its resources
efficiently, especially during peak periods when the number of mobile
phones used in an area may exceed the service capacity of the
provider's base station.
Very recently, researchers have quantified the dependance of capacity
on the covering range of a base station (or its transmission power).
Intuitively, in an environment where all the wireless devices transmit
at their maximum power setting, the amount of interference is
significant and this decreases capacity. A simple analogy is that of
talking to your neighbour in a room where everybody else shouts. The
communication can be difficult.
The task is now to find a way to effectively control the capacity of
the base stations of a provider's entire network in order to maximize
the number of mobile devices that can be served globally. In this talk,
which targets a broad audience, I will present our recent results on
this problem. The model we propose, that of a covering problem with
variable capacities, is new in the literature and it is interesting
from a theoretical point of view as well because it generalizes many
classical combinatorial optimization problems.
This is joint work with Daya Gaur and Shahadat Hossain.

Thursday April 17 12:05 to 12:55 Room B650 
Harald Helfgott
Senior Lecturer, University of Bristol, UK
Ph.D Princeton University (2003)
Research interests: diophantine geometry, group theory, probability theory, combinatorics and analytic number theory.
Currently: interest on the number, growth and distribution of discrete objects in algebraic structures.

Growth in SL_3.
Let $K$ be $\R$, $\C$ or a $\Z/p\Z$.
Let $G = SL_2(K)$.
Not long ago, I proved the following theorem:
for every subset $A$ of $G$ that is not contained in a proper subgroup, the set $A A A$ is much larger than $A$.
A generalisation to groups of higher rank was desired by many, but seemed hard to obtain.\\
I have obtained a generalisation to $SL_3(K)$.
The role of both linearity and the group structure of $G$ should now be clearer than they were at first.
Bourgain, Gamburd and Sarnak derived various consequences on expander graphs from my $SL_2$ result;
analogous consequences should follow in the case of $SL_3$.

Friday April 11 12:00 to 12:50 Room B650 
Klaus Denecke
Professor, University of Potsdam, Germany
Research interests: General Algebra, Category Theory and Applications in Discrete Mathematics,
Theoretical Computer Science and Mathematical Logic.

What is General Algebra?
I have frequently been asked "What is General Algebra?" I am unable to give a clear definition of this relatively new field of mathematics, but will describe some main streams and trends, influenced by my own interests and restricted knowledge. I will explain why and how classical parts of algebra like group theory and ring theory were generalized to semigroups, quasigroups, semirings and nearrings. Lattices and ordered algebraic structures and algebraic logic are also part of General Algebra, as are universal algebra and category theory. In the last ten years computer scientists have also used coalgebras to describe statebased systems, making coalgebras another important concept in General Algebra.

Friday April 04 12:00 to 12:50 Room B650 
Giuseppe Carenini
Assistant Professor, UBC, Vancouver
Ph.D University of Pittsburgh (2000)
Research interests: Computational Linguistics  Natural Language Generation, Dialog, Statistical NLP
HCI  Intelligent Interfaces, Information Visualization and Interactive Techniques
Artificial Intelligence  User Modeling, Preference Elicitation, Decision Theory, Machine Learning
Social Issues in Computing  Captology, Universal Access and Usability

Interactive multimedia summaries of evaluative documents
Many organizations are faced with the challenge of summarizing large
corpora of text data. One important application is evaluative text,
i.e. any document expressing an evaluation of an entity as either
positive or negative. For example, many websites collect large
quantities of online customer reviews of consumer electronics.
Summaries of this literature could be of great strategic value to
product designers, planners, manufacturers and consumers.
In this seminar, I will first present and compare two approaches to
the task of summarizing evaluative text. The first is a sentence
extractionbased approach, while the second is a language
generationbased approach. These approaches have been tested in a
user study. In the second part of the seminar, I will describe an
interactive multimedia interface which presents the knowledge
extracted form a corpus of evaluative documents not only as a natural
language summary but also in a hierarchical visualization mode. The
interface is interactive in that it allows the user to explore the
original dataset through intuitive visual and textual methods.
Results of a formative evaluation of our interface show general
satisfaction among users with our approach.

Friday March 28 12:00 to 12:50 Room B650 
Wendy Osborn
Ph.D. University of Calgary
Assistant Professor, University of Lethbridge
Director of the SADL
Research interests: Digital library technology,
databases that handle nonstandard data (spatial, multimedia, distributed databases).

Southern Alberta Digital Library (SADL)
The Southern Alberta Digital Library (SADL) at the University of
Lethbridge is an extension of the New Zealand Digital Library (NZDL)
project at the University of Waikato. The NZDL project manages the
development of Greenstone, a software suite for creating online digital
libraries. SADL has two primary goals: 1) to assist in the core
development of the Greenstone digital library sofware, and 2) to host
digital library collections that have ties to Southern Alberta.
For this seminar, I will present some of the core development and
applications that have taken place over the past few years. I will also
present directions, in development and applications, that SADL will take
in the near future.

Friday March 14 12:00 to 12:50 Room B650 
Matthew Greenberg
Assistant Professor, University of Calgary
Ph.D McGill University (2006)
2008 CMS Doctoral Prize
Research interests: number theory, modular forms, elliptic curves, Heegner point computations.

Analysis and Diophantine equations
A Diophantine equation is a polynomial equation in finitely many
variables with integer coefficients. A large part of number theory is
concerned with the existence of rational (or, more generally,
algebraic) solutions to particular (systems of) Diophantine equations.
Since the field of rational numbers is not complete, analytic
techniques involving successive approximation (e.g. Newton's method)
cannot be brought to bear on Diophantine equations. Even so, analysis
(both classical and $p$adic) is an invaluable tool in the study of
their properties and their solutions.

Friday February 15 12:00 to 12:50 Room D511 
John Irving
Assistant Professor Saint Mary's University, Halifax
Ph.D. University of Waterloo (2004)
Research interests: algebraic combinatorics, particularly enumerative problems underlying questions in geometry and representation theory

Minimal Transitive Factorizations of Permutations
The problem at hand is to count decompositions of a given
permutation into a product of a fixed number of transpositions of the
form (1 i). We give a simple formula for the number of such
decompositions into a minimal number of factors. Our derivation
involves an interesting relationship between factorizations of
permutations and maps on surfaces, a classical bijection between trees
and Dyck sequences, and an enumeration of such sequences via the Cycle
Lemma. Connections with algebraic geometry will be briefly discussed.

Friday January 18 12:00 to 12:50 Room D511 
Kerri Webb
University of Lethbridge
Research interests: Graph Theory, combinatorics.

A major theorem about minors
The monumental Graph Minors Project of
Robertson and Seymour ranks among the deepest
theorems in mathematics. Rota's Conjecture, regarding
an extension of these results to matroids, is arguably
the most important open problem in matroid theory.
We survey the main results and applications from the
Graph Minors Project, and describe progress towards
Rota's Conjecture.
