John Duncan, Emory University
“Recent Developments in Moonshine”
Hongdi Huang, Pure Mathematics, University of Waterloo
"Morita Theory IV: The Morita Context"
If $F:\mathrm{Mod}_R \rightarrow \mathrm{Mod}_S$ is a Morita equivalence, then it preserves progenerators, so $P_S:= F(R_R)$ is a progenerator in $\mathrm{Mod}_S$. We'll see that that $P_S$ has a left $R$-module structure and $F\simeq -\otimes _RP_S$, thus giving rise to a \textit{Morita context} between $R$ and $S$. Conversely, the existence of a Morita context implies that $R$ and $S$ are Morita equivalent.
Spiro Karigiannis, Department of Pure Mathematics, University of Waterloo
“Weyl curvature, conformal geometry, and uniformization: Part II”
Stanley Xiao, Department of Pure Mathematics, University of Waterloo
“Towards the Bombieri-Vinogradov theorem”
Rahim Moosa, Pure Mathematics, University of Waterloo
"More on definable functors, and imaginaries"
Raymond Cheng, Pure Mathematics, University of Waterloo
"Donuts and Pants, then Quasiconformal Maps"
Raymond Cheng, Pure Mathematics, University of Waterloo
"Hilbert Scheme of Points on Surfaces"
Finally, we are in place to discuss the Hilbert scheme of points in a surface. We will discuss some geometric properties of this Hilbert scheme. In particular, we will attempt to explain why the Hilbert scheme of points in the affine plane is smooth and irreducible scheme. We may also give a description of this Hilbert scheme in a way suggestive for future discussions.
Henry Li, Department of Pure Mathematics, University of Waterloo
“BRST Quantization”
Jonathan Stephenson, Department of Pure Mathematics, University of Waterloo
“Bases for Randomness”
John J.C. Saunders, Department of Pure Mathematics, University of Waterloo
“Random Fibonacci Sequences”