Events - 2018

Sascha Troscheit, Department of Pure Mathematics, University of Waterloo

"Quasi self-similarity and the dimension drop conjecture for self-conformal sets"

Andrej Vukovic, Department of Pure Mathematics, University of Waterloo

"Fundamental Group of the Circle and Other Highlights"

Today we construct the circle type and show that its fundamental group is Z, using synthetic homotopy theory. As requested at the last meeting, we also show that function extensionality implies weak function extensionality.

MC 5413

Aasaimani Thamizhazhagan, Department of Pure Mathematics, University of Waterloo

"Uncertainty Principles and Fourier Analysis"

The uncertainty principle is partly a description of a characteristic feature of quantum mechanical systems, partly a statement about the limitations of one's ability to perform measurements on a system without disturbing, and partly a meta-theorem in harmonic analysis that can be summed up as follows:

MC 5501

Ananth Shankar, MIT

"Exceptional splitting of abelian surfaces over global function fields"

Hanci Chi, McMaster University

"Invariant Einstein Metrics of Cohomogeneity One with Principal Orbits as Wallach Spaces"

Daniel Perales, Department of Pure Mathematics, University of Waterloo

"Random matrices, interlacing families of polynomials, and the expected characteristic polynomial"

In this session we will begin by ;reviewing the notion of real stability and some of its basic properties. Then we continue with the study of operators that preserve real stability. For this, we will look into the proof of the Gauss-Lucas Theorem, which asserts that for any complex polynomial f, the roots of its derivative, f', are contained in the convex hull of the roots of f.

Ross Willard, Department of Pure Mathematics, University of Waterloo

"Dualizing the finite level"

Last week, Justin proved the Duality Compactness Theorem, which reduces the task of proving a duality to proving it “at the finite level,” that is, for the finite algebras in the quasi-variety ISP(M), at least for alter egos with a finite signature. This week I will present a characterization of when an alter ego dualizes the finite algebras in ISP(M). The characterization is especially useful when the term operations of M are understood.

MC 5403

Jesse Madnick, McMaster University

"Nearly-Kahler 6-Manifolds of Cohomogeneity-Two"

Justin Laverdure, Pure Math Department

"Duality Compactness Part 2"

We'll prove the DCT itself, after having seen several supporting lemmas.

MC 5403

Jerry Wang, Department of Pure Mathematics, University of Waterloo

"The number of elliptic curves ordered by conductor"