Events

Joey Lakerdas-Gayle, University of Waterloo

Fundamentals of Computability Theory 1

This semester in the Computablility Theory Learning Seminar, we will be learning general Computability Theory following Robert Soare's textbook. This week, we will prove some of the fundamental theorems about Turing machines in Chapter 1 and 2.

MC 5403

Aleksandar Milivojevic, University of Waterloo

Formality in rational homotopy theory

I will introduce the notion of formality of a manifold and will discuss some topological implications of this property, together with a computable obstruction to formality called the triple Massey product. I will then survey a conjecture relating formality and the existence of special holonomy metrics.

MC 5479

Robert Haslhofer, University of Toronto, University of Wisconsin Madison

Mean curvature flow through singularities

A family of surfaces moves by mean curvature flow if the velocity at each point is given by the mean curvature vector. Mean curvature flow first arose as a model of evolving interfaces in material science and has been extensively studied over the last 40 years. In this talk, I will give an introduction and overview for a general mathematical audience. To gain some intuition we will first consider the one-dimensional case of evolving curves. We will then discuss Huisken's classical result that the flow of convex surfaces always converges to a round point. On the other hand, if the initial surface is not convex we will see that the flow typically encounters singularities. Getting a hold of these singularities is crucial for most striking applications in geometry, topology and physics. In particular, we will see that flow through conical singularities is nonunique, but flow through neck singularities is unique. Finally, I will report on recent work with various collaborators on the classification of noncollapsed singularities in R^4.

MC 5501

Gregory G. Smith, Queen's University

Sums of Squares and Projective Geometry

A multivariate real polynomial is nonnegative if its value at any real point is greater than or equal to zero.  These special polynomials play a central role in many branches of mathematics including algebraic geometry, optimization theory, and dynamical systems.  However, it is very difficult, in general, to decide whether a given polynomial is nonnegative.  In this talk, we will review some classical methods for certifying that a polynomial is nonnegative.  We will then present novel certificates in some important cases. This talk is based on joint work with Grigoriy Blekherman, Rainer Sinn, and Mauricio Velasco.

MC 5501