Events

Anthony McCormick, Department of Pure Mathematics, University of Waterloo

"Introduction to the Spencer Complex"

We'll begin discussing the idea behind the Spencer complex associated to a linear partial differential operator between vector bundles. To do this, we'll introduce jet bundles, prolongations and the definition of the principal symbol using this machinery.

MC 5479

Jonny Stephenson, Department of Pure Mathematics, University of Waterloo

"Sets which are not the spectrum of any structure"

We continue our analysis of spectra, and show that no spectrum can be the Turing-upward closure of an F_sigma family of reals, unless that  upward closure is already an enumeration upper cone. We will see that, as in the case of the "no two cones" theorem, the key to the proof is to construct a suitably generic copy of a structure to see that it cannot possibly have the indicated spectrum.

MC 5403

Be'eri Greenfeld, Bar Ilan University

"Around and beyond the Koethe problem"

Akos Nagy, Department of Pure Mathematics, University of Waterloo

"A compactness theorem for the Seiberg–Witten equation with multiple spinors in dimension three --- Part III"

I will continue with Section 4 of the Walpuski-Haydys paper: I will introduce the frequency function, state a couple important properties of it, and give outline of how it is used in the proof of the Main Theorem. If time permits, I will talk about the proofs of the properties.

MC 5479

Shubham Dwivedi, Department of Pure Mathematics, University of Waterloo

"Simons' Inequality and consequences"

We will prove the Simons' Inequality which is satisfied by the laplacian of the normed square of the second fundamental form of any minimal hypersurface in $\mathbb{R}^n$. We will then prove various consequences of the inequality, including results of Choi and Schoen, Hopf and that of Schoen/Leon Simon/Yau.

MC 5479

Michael Deveau, Department of Pure Mathematics, University of Waterloo

"The Slaman-Wehner Family"

We introduce the Slaman-Wehner family, and use it to build a structure with an important property: it has no computable copy, but is computable in any non-computable set. In other words, this structure's degree spectrum is equal to the set of non-computable sets.

MC 5403

Anthony McCormick, Department of Pure Mathematics, University of Waterloo

"The Spencer Complex: Part 2"

Having outlined the problem we'll be studying during the previous talk, we now begin working our way towards the construction of the Spencer complex. The necessary tools such as sheaves of jets and prolongation will be developed along the way.

MC 5479

Mohammad Mahmoud, Department of Pure Mathematics, University of Waterloo

"Comparing Structures"

In Computability Theory we have tools to compare the complexities of sets of natural numbers, tools like: Turing reducibility, enumeration reducibility, many-one reducibility, etc. For structures there are also various ways. For example have Muchnik reducibility, Medvedev reducibility, effective interpretability (also known as $\Sigma$-definability), and effective bi-interpretability. We are going to talk about Muchnik and Medvedev reducibilities.

Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo

"A new construction of compact G₂~manifolds by glueing Eguchi-Hanson spaces, Part I: Overview"

Wentang Kuo, Department of Pure Mathematics, University of Waterloo

"Number Theory in Function Fields"