Modeling of Magnetizer Target Fusion Reactor by Michael Lindstrom
Nuclear fusion is a promising source of clean energy for the future, but designing an apparatus capable of fusing plasma and yielding a net energy gain has yet to be accomplished. This talk is aimed at providing an introduction to the basic physics of fusion, and outlining the methods and results obtained in analyzing the fusion reactor design of a local Canadian fusion research company.
Quantum Field Theory (Feynman Diagrams) by Connor Behan
The discovery of quanta began a revolution on how we think about the physical world and the mathematics we use to describe it. According to quantum mechanics, a particle that appears to have three co-ordinates (x, y, z) will in fact have a position described by a vector in an infinite-dimensional Hilbert space such as L^2(R^3). Quantum field theory is an attempt to apply the same principles to a system where the number of classical degrees of freedom is already infinite. We will see that this allows the description to be compatible with many phenomena from special relativity. Because of the need for a much larger Hilbert space, calculations in quantum field theory can be difficult to carry out, even numerically. This talk will work toward a derivation of the method of Feynman diagrams including a discussion of what these famous diagrams can, and cannot do.
Nearest Neighbourhood Shifts of Finite Type by Nishant Chandgotia
Nearest neighbour shifts of Finite Type are system of constrained configurations on the Z^d lattice which arise in numerous contexts, e.g. probability, data storage, smooth dynamics and statistical mechanics. After providing some motivation, we shall try to explore how things change when we move up in dimensions.
Well Approximable Numbers by Kyle HambrookI will discuss the size of the set of real numbers x that can be well approximated by rational numbers (in the sense that |x-p/q| < 1/q^s for infinitely many rational numbers p/q) using tools from number theory, harmonic analysis, and probability theory. The talk should be accessible to all math graduate students.
The Riemann Zeta Function by Joshua NevinThe Riemann hypothesis is arguably the most important unsolved problem in mathematics. This talk will introduce the basics of analytic number theory, the connection between prime numbers and the Riemann zeta function and the importance of Riemann’s hypothesis. No background in number theory, analytic or otherwise, will be assumed.