2012-2013 Colloquium

Speaker:  Dr. Eugeniu Spinu, Postdoctoral Fellow of Department of Mathematical Sciences at Lakehead University
Title:  Ideals of Operators Acting on $C^*$-Algebras.
Time:  Monday, March 18, 2013, 3:45 pm - 4:45 pmRoom:  RB 3046

We will consider the inclusion relation between classical operator ideals such as ideals of (finitely) strictly singular, (weakly) compact, and inessential operators acting on $C^*$-algebras. In particular, we will present a generalization of Pelczynski-Milman's characterization of strictly singular operators on $C^*$-algebras. This is a joint work with Timur Oikhberg from the University of Illinois at Urbana-Champaign.

Augustine O'Keefe, University of Kentucky Postdoctoral Fellow
Time:  Tuesday, March 12, 2013, 2:45 pm - 3:45 pm
Room:  RB 2026
Title:   An Introduction to Toric Ideals

Abstract:  As an algebraic object toric ideals are a topic of interest as they behave "nicely" and have a multitude of associated combinatorial objects.  If one thinks of monomial ideals as the simplest case, then toric ideals can be thought of as the next simplest as they are generated by homogeneous binomials.  In this talk we will go over the construction of a toric ideal in general.  We will then turn our attention to two examples.  The first will be toric ideals arising from finite graphs for which you can read the generators of the ideal directly from the graph.  The second will be the toric ideal associated to the independence model of random variables.  This will be an introductory talk and we will define terms as we go.



Speaker:  Dr. Xikui Wang, Professor and Chair of Department of Statistics at University of Manitoba
Title:  Response Adaptive Design of Clinical Trials
Time:  Friday, February 15, 2013, 2:30 pm - 3:30 pm
Room:  RB 1047

Abstract:  Clinical trials are regarded as the most reliable and efficient way to evaluate the efficacy of new medical interventions. This practice has taken a prominent role in modern clinical research. Clinical experimentation on human subjects requires a careful balancing act between the benefits of the collective and the benefits of the individual. Response adaptive designs represent a major advancement in clinical trial methodology that helps balance these ethical issues and improve efficiency without undermining the validity and integrity of the clinical research. Such designs are particularly desirable in desperate medical situations in which individual ethics is often jeopardized for the collective good. Response adaptive designs use information so far accumulated from the trial to modify the randomization procedure and deliberately bias treatment allocation in order to assign more patients to the potentially better treatment. In this talk, we examine some important issues and methods of response adaptive designs and anticipate future developments.


Speaker:  Dr. Howard E. Bell, Professor Emeritus of Mathematics at Brock University
Title:  On Factorization in Arbitrary Rings
  Wednesday, October 03, 2012, 12:30 pm - 1:30 pm
Room:  RB 2042

Abstract:  We study factorization in arbitrary rings, not just in integral domains. Define a ring R to be an F-ring if every nonzero element has a 2-factorization - i.e. can be expressed as a product of two (not necessarily distinct) elements of R. We give some examples and basic properties of F-rings, we investigate existence of 1 in F-rings, and we discuss conditions for an F-ring to be finite. Defining M(R) to be the maximum number of 2-factorizations for elements of a finite F-ring R, we discuss several questions concerning M(R).

Speaker: Craig Kainulainen (MSc Student)
Title: Average Distance Results in Geometric Figures
Time:  Wednesday, September 26, 2012, 3:00 pm - 3:30 pm
Room:  Ryan Building 1045, Lakehead University

Abstract: Consider choosing two points at random (independently with uniform distribution) from within a given region. If the distance between these two points is measured and the process is continued repeatedly, the expected average distance between any two randomly selected points can be expressed in terms of the diameter of the region. We investigate some different techniques used to calculate this value.

Speaker: Aaron Pearson (MSc Student)
Title: Fractal Dimensions of Cantor Sets
Time:  Wednesday, September 26, 2012, 3:30 pm - 4:00 pm
Room:  Ryan Building 1045, Lakehead University

Abstract: A Cantor set is any compact, perfect, totally disconnected subset of the real line: this definition covers a large and diverse family of fractals. Each of these, however, is uniquely defined by a summable sequence of real numbers. Hausdorff dimension generalizes the intuitive notion of dimension in a rigorous
way that is appropriate for fractals as well as more familiar geometrical objects.Until the last decade, for large classes of Cantor sets, precise estimates of the Hausdorff dimension could not be found. This presentation reviews these concepts, and explores some current research that is finding tight bounds for the dimensions of general Cantor sets.