Events

 Alberto García-Raboso, University of Toronto

"A twisted nonabelian Hodge correspondence"

The classical nonabelian Hodge correspondence establishes an equivalence between certain categories of flat bundles and Higgs bundles on smooth projective varieties. I will describe an extension of this result to twisted vector bundles. No prior knowledge of the above topics will be assumed: come one, come all! There will be pancakes too.

Alejandra Vicente Colmenares, Pure Mathematics, University of Waterloo

"Semistable rank 2 co-Higgs bundles over Hirzebruch surfaces"

Juan Felipe Carmona, Universidad Antonio Nariño

"Flatness and CM-triviality in strongly minimal theories with a predicate"

Patrick Naylor, Pure Mathematics, University of Waterloo

"Semisimplicity and the Hopkins--Levitski Theorem"

This semester we'll be meeting weekly to learn more about ring theory, mostly going through Lam's two books --- there are many interesting results in those books which will be "good to know". Starting off, we'll aim to learn the Hopkins--Levitski Theorem, one of whose (many) consequences is that the descending chain condition implies the ascending chain condition. Everyone is welcome. See you there!

MC 5403

Mohammad Mahmoud, Pure Mathematics, University of Waterloo

"Algorithmic Randomness: Introduction to Kolmogorov Complexity"

Last time we saw why the Kolmogorov complexity $K$ can be better than the plain complexity $C$ as it is subadditive and complexity doesn't dip. This time we are going to see more properties showing that $K$ matches our intuition. More precisely, (a) Incompressible (in the sense of $K$) strings have only short runs of zeros (i.e. blocks only consisting of zeros), and (b) Zeros and ones occur balancedly.

MC 5403

Samuel Kim, Pure Mathematics, University of Waterloo

"Proving the Hopkins-Levitzki Theorem"

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.

Rahim Moosa, Pure Mathematics, University of Waterloo

"More on definable functors, and imaginaries"

Omar Leon Sanchez, McMaster University

"Statement of the Main Theorem"

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.