Events

Julius Frizzell, University of Waterloo

Szemerédi's Theorem and Multiple Recurrence

We will cover Szemerédi's Theorem and its equivalence to Furstenberg's multiple recurrence theorem, we will then begin to look at weak-mixing transformations in more detail.

MC 5417

Boris Li, University of Waterloo, Pure Mathematics

On the physics of bells

We shall discuss the acoustics and resonance of bells from the perspective of physics. After a short review ofnormal modes in musical instruments, we shall compare bells with one-dimensional systems such as strings andwinds. In contrast to these systems, bells exhibit strongly inharmonic partials due to its curved geometry. Wediscuss some consequences of this structure, including some prominent partials and the psychoacousticphenomenon of the strike note. Time permitting, we shall examine how bell geometry and thickness profilesaffect tuning.

Refreshments at 3:30pm. Talk starts at 4:00pm.

MC 5403

Spencer Kelly, University of Waterloo

Sobolev Spaces Over Compact Manifolds

The space of smooth sections of a vector bundle over a manifold is an infinite dimensional Fréchet Space, and thus many of the tools used in finite-dimensional geometry are rendered useless on this space. However, taking the completion of this space with respect to the Sobolev norm, we obtain a Banach space. What's even better is that in the $L^2$ case we obtain a Hilbert space. In this talk we will walk through different constructions of the$L^2$-Sobolev spaces of sections of a vector bundle over a compact manifold, and discuss the Sobolev embedding theorem. We will also work through some of the properties of differential operators on this space and, time permitting, we will finish with the Berger-Ebin decomposition for differential operators with injective symbol.

MC 5417

Barbara Csima, University of Waterloo

Priority Arguments in Computability Theory

This term, Computability Learning Seminar will focus on Priority Arguments. Priority Arguments are a common proof technique used in Computability Theory. A theorem is broken down to being equivalent to a list of requirements. These requirements are given a priority order, and a strategy is devised to meet all the requirements, making use of the priority order. In the early days of the subject, a big question (Post’s Problem -1944) was whether there were any non-computable computably enumerable (c.e.) sets that were not Turing equivalent to the halting set. The solution, from Friedberg (1957) and Muchnik (1956), was to construct a pair of Turing incomparable c.e. sets, using a finite injury priority argument. In this first talk, we will begin our examination of priority arguments by going through the proof of this theorem, introducing definitions and reviewing notions from Computability Theory as needed along the way.

MC 5403