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Changho Han, Department of Pure Mathematics, University of Waterloo

"Inverse and Direct Images of D-modules"

In this talk, I will pick up from the last time and define the general definition of the Inverse Image of D-modules, and then provide examples for closed immersions and smooth morphisms. If time remains, then I will give a "naive" definition of the direct image of D-modules, with an example of closed embedding.

MC 5403

Larissa Kroell, Department of Pure Mathematics, University of Waterloo

"Boundaries and C*-simplicity of discrete groups and (maybe) more"

We are going to discuss the connection between the action of a discrete group on its Furstenberg boundary and C*-simplicity. To do so we will be looking at the papers by Kalantar & Kennedy (Boundaries of reduced C*-algebras of discrete groups) and Breuillard et al (C*-simplicity and the unique trace property for discrete groups).

MC 5479

Leo Jimenez, Department of Pure Mathematics, University of Waterloo

"Restricted Zilber Trichotomy"

We continue to read Ben Castle’s paper.

MC 5479

Andy Zucker, Department of Pure Mathematics, University of Waterloo

"Reverse Math VIII"

We continue our discussion of the reverse math theoretic aspects of Devlin's theorem.

MC 5403

Talk #1 (1:00pm - 2:15pm)

Jacques van Wyk, Department of Pure Mathematics, University of Waterloo

"Fundamentals of Elliptic Partial Differential Operators"

Yash Singh, Department of Pure Mathematics, University of Waterloo

"Sheaves of Modules on Schemes"

We introduce sheaves of modules associated to schemes and in particular study the theory of coherent sheaves, quasi-coherent sheaves, and vector bundles.

MC 5403

Marcelo Laca, University of Victoria

"On the Matter of Numbers"

Erik Seguin, Department of Pure Mathematics, University of Waterloo

"Haagerup's noncommutative Grothendieck inequality (cont. cont. cont.)"

We will continue^3 to prove things related to and on the subject of the NCG theorem. Possibly we will finish the proof of the theorem this week, and possibly not; we conjecture that no third option exists, but we are unable to prove this claim at present. Time permitting, we may attempt to prove this rigorously; this attempt is unlikely to be successful, veracity of the claim notwithstanding.

Andrew Zucker, Department of Pure Mathematics, University of Waterloo

"Reverse Math VII"

We discuss some results and open problems related to the reverse mathematics of results in structural Ramsey theory.

MC 5403

Daniel Han, Department of Pure Mathematics, Univesity of Waterloo 

"Derived functors and (co)homology theories"

We will give an overview of derived functors and their use to form homological invariants for objects in abelian categories. Using this abstract machinery, we will give rise to group cohomology, sheaf cohomology, and others. Lastly, the Eilenberg-Watts theorem will be presented to give a loose explanation as to why many of these cohomology groups are presented as Ext groups.

MC 5479