**Dr. Damien Roy**

**Institution**: The University of Ottawa

**About**: Dr. Roy is a distinguished professor of Number Theory at the University of Ottawa where he has been named Researcher of the Year. Professor Roy is a leading number theorist who received his Ph.D. from l’universit ́e Laval. He has made substantial, original and lasting contributions, including progress on conjectures that have stood for decades. His research has taken on an incredible momentum, with stunning breakthroughs on a variety of long-standing problems in just the past few years.

**Title: **On the values of the exponential function

**Abstract**: We know that e, π and eπ are transcendental numbers, meaning that they are not the roots of nonzero polynomials with integer coefficients, but what about e+π? In this talk, we present results and conjectures about the (algebraic independence of the) values of the exponential function and discuss recent advances on the topic.

**Dr. Kevin Cheung, **

**Institution**: Carleton unviversity

**About**: Kevin Cheung is an Associate Professor at Carleton University in the School of Mathematics and Statistics. After completing his Ph.D. at the University of Waterloo in the Department of Com- binatorics and Optimization under the supervision of William H. Cunningham in 2003,he spent two years at the Massachusetts Institute of Technology as an NSERC Postdoctoral Fellow under the men- torship of Michel X. Goemans. In addition to discrete optimization, his current academic interests include designing and developing teaching tools and exploiting technology to help students attain mastery.

**Title: **How much do you trust computed results?

**Abstract**: Mathematical software is used by mathematicians and non-mathematicians alike. Computations are used in practical applications as well as in establishing theoretical results. An example of the latter is the Four Colour Theorem. When one delegates a large chunk of mathematical derivations to a computer, a natural question arises: How much can one trust the results? Establishing correctness of computations is an active area of research. There are two complementary points of view that one can take: one is to develop provably correct software. The other, which is the focus of this talk, is to obtain ways to verify computed answers. A brief overview of some of the ideas involved in previous work will be given. A recent effort in verifying mixed-integer linear programming results will be described. Some future research directions will be discussed.

**Dr. Mayer Alvo, **

**Institution**: University of Ottawa

**About**: Dr. Mayer Alvo is a professor of statistics at the University of Ottawa. He received his Ph. D from Columbia University where he worked with Herbert Robins. Dr. Alvo was named a fellow of the Fields Institute in recognition of his outstanding contributions to the Canadian Mathematical Society and Fields activities. Dr. Alvo was the driving force which led to the University of Ottawa becoming a Principal Sponsoring University of the Fields Institute in 2002, a sponsorship which directly benefits our department, through the funding of postdoctoral fellows and of several research workshops and conferences each year.

**Title: **The Many Facets of Correlation

**Abstract**: The popular Pearson correlation coefficient is used to measure the linear dependence between two random variables. Its interpretation in practice depends upon the underlying distribution of the data. In this talk, we revisit the concept of correlation and define it through the use of the ranks of the data. This avoids the reliance on the underlying distribution. We then extend the notion of rank correlation to situations where the data is partially missing. We do this by introducing the concept of compatibility. In another direction we extend rank correlation to deal with angular data. We provide some examples to illustrate the concepts.