Time: 5:30 p.m. Place: Jeffery Hall 118
Speaker: Jamie Mingo (Queen's University)
Title: Paradoxical Probabilities.
Abstract: Since the early days of probability theory there have been paradoxical statements, usually the result of implicit assumptions. The best known example is the Monty Hall problem. In this talk I discuss several examples, in particular the "bigger number paradox".
Time: 5:30 p.m. Place: Jeffery Hall 118
Speaker: Tianyuan Xu (Queen's University)
Title: Knot Invariants by Pulling Strings.
Abstract: A knot is a smooth closed curve in the 3-dimensional space, and two knots are equivalent if they can be distorted into each other without cutting or gluing. How can we tell whether two knots are equivalent? For example, is the trefoil equivalent to its mirror image? This turns out to be a highly non-trivial problem, and one approach to solving it is to study so-called knot invariants, quantities associated to knots that remain unchanged under equivalences.
We will discuss a knot invariant called the Kauffman bracket of knots. While knots are inherently 3-dimensional objects, in developing this invariant we will simplify their study to the study of 2-dimensional objects called non-crossing pairings. To achieve this, we will need to literally "pull some strings"!
Time: 5:30 p.m. Place: Jeffery Hall 118
Speaker: Greg Smith (Queen's University)
Title: Realistic Expectations.
Abstract: How many real roots should we expect a real polynomial to have? In this talk, we will convert this vague question into a well-posed mathematical problem. With the help of geometry, we will also provide the surprisingly beautiful solution.
