Samuel Kim, Pure Mathematics, University of Waterloo
"Proving the Hopkins-Levitzki Theorem"
Christopher Hawthorne, Pure Mathematics, University of Waterloo
We will work through chapter 7 of Tent and Ziegler. We will develop the notions of forking and dividing as measures of how strongly a set depends on a set of parameters. We will then introduce simple theories, an important generalization of stable theories.
Ehsaan Hossain, Pure Mathematics, University of Waterloo
"Morita theory 1: Modules"
Let $\mathrm{Mod}_R$ be the category of right $R$-modules. Two rings $R,S$ are \textit{Morita equivalent}, denoted $R\sim S$, if $\mathrm{Mod}_R$ and $\mathrm{Mod}_S$ are equivalent as categories. For example $\mathbf{C}$ is Morita equivalent to $M_2(\mathbf{C})$, because any $\mathbf{C}$-vector space can double up to become an $M_2(\mathbf{C})$-module. Many properties are Morita invariant; for instance simplicity, semisimplicity, and chain conditions.
Christopher Hawthorne, Pure Mathematics, University of Waterloo
We will work through chapter 7 of Tent and Ziegler. We will develop the notions of forking and dividing as measures of how strongly a set depends on a set of parameters. We will then introduce simple theories, an important generalization of stable theories.
Christopher Hawthorne, Pure Mathematics, University of Waterloo
We will work through chapter 7 of Tent and Ziegler. We will develop the notions of forking and dividing as measures of how strongly a set depends on a set of parameters. We will then introduce simple theories, an important generalization of stable theories.
Rahim Moosa, Pure Mathematics, University of Waterloo
"More on definable functors, and imaginaries"
Se-Jin Sam Kim, Pure Mathematics, University of Waterloo
"Crossed products and Morita equivalence"
The talk will consist of three parts. Firstly, we will establish some basic notions of crossed product $C^*$-algebras, with a focus on the irrational rotation algebras.
Adam Dor On, Pure Mathematics, University of Waterloo
"Absolute continuity and wandering vectors in Free semigroup algebras"
Thomas Parker, Michigan State University
“Paths of holomorphic curves and the GV conjecture”
Christopher Hawthorne, Pure Mathematics, University of Waterloo
We begin chapter 4 of Goldblatt. (Category theory background from chapter 3 will be assumed.) We introduce subobjects and subobject classifiers; time permitting, we will get to the definition of a topos.