Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo
"A new construction of compact $G_2$ manifolds by glueing Eguchi-Hanson spaces, Part III.c: Constructing the closed pair on the Eguchi-Hanson bundle"
Sam Harris, Department of Pure Mathematics, University of Waterloo
"Sofic Groups"
Today we will give a brief introduction to Connes' embedding problem. We will then introduce invariant length groups and what it means for a countable discrete group to be sofic.
MC 5403
Ertan Elma, Department of Pure Mathematics, University of Waterloo
"The Large Sieve"
We will prove the large sieve inequality and then construct the large sieve. We will also mention some applications of this important technique in analytic number theory.
MC 5403
Sam Harris, Department of Pure Mathematics, University of Waterloo
"Hyperlinear Groups"
Today we look at the class of hyperlinear groups. We will show that every sofic group is hyperlinear, and we will summarize some of the closure properties of sofic/hyperlinear groups. If time allows, we will look at how sofic groups can address a weaker form of Connes' embedding problem.
MC 5403
Adam Morgan, Department of Applied Mathematics, University of Waterloo
"Classical Field Theory from the Hamiltonian Viewpoint"
Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo
"A new construction of compact $G_2$ manifolds by glueing Eguchi-Hanson spaces, Part IV: The Correction Theorem"
We give the details of the "correction theorem" that allow us to produce the closed pair $(\tilde \varphi, \tilde \psi)$ on the Eguchi-Hanson bundle with sufficiently small torsion. The proof involves several steps, including the Lockhart-McOwen theory of elliptic operators on weighted Sobolev spaces in the asymptotically locally Euclidean category.
MC 5479
Sam Harris, Department of Pure Mathematics, University of Waterloo
"Connes' Embedding Problem & Kirchberg's Conjecture"
Sam Harris, Department of Pure Mathematics, University of Waterloo
"Connes' Embedding Problem & Kirchberg's Conjecture (continued)"
Patrick McIntyre, Department of Pure Mathematics, University of Waterloo
"The Pisano Period"
Adam Morgan, Department of Applied Mathematics, University of Waterloo
"Geometric Aspects of Finite Element Analysis, Part 1: Lagrange Elements"