Carlos Valero, Department of Pure Mathematics, University of Waterloo
"Why we Caré about the Poincaré Conjecture?"
In an effort to maintain geometry’s hegemony over the PMATH grad colloquium, this week we’ll discuss the Poincaré conjecture, which at the time of writing remains the only solved Millennium Prize Problem. In this colloquium, we’ll look at the history of the Poincaré conjecture, give a qualitative overview of its proof, and try to understand why it has become such a huge meme among mathematicians. Only an intuitive understanding of geometry will be necessary, as the focus will be less on definitions and more on the big ideas involved.