Events

Jacob Tsimmerman, University of Toronto

“Bounding Torsion in Geometric Families of Abelian Varieties”

A celebrated theorem of Mazur asserts that the order of the torsion part of the Mordell-Weil group of an elliptic curve over Q is absolutely bounded; it is conjectured that the same is true for abelian varieties over number fields, though very little progress

Jason Lotay, University College London

“Hyperkaehler 4-manifolds with boundary”

An oriented hypersurface in a hyperkaehler 4-manifold naturally inherits a coclosed coframing.

Mohammad Mahmoud, Pure Mathematics, University of Waterloo

"Torsion-free groups: linear independence and computable categoricity"

We continue through Melnikov's survey paper on Computable
Abelian Groups. We use the effective analysis of linear independence
(discussed before by Sam) to characterize computable categoricity. We
go through the proof that "Every computable torsion-free

Ross Willard, Pure Mathematics, University of Waterloo

"Adding Gaussian elimination to local consistency checking - 2"

In this second of several lectures, I will present a polynomial-time consistency checking algorithm for constraint networks over a finite template having a Taylor polymorphism. I conjecture that the algorithm is complete for Maltsev templates, and in future lectures will provide evidence supporting this conjecture.

Jonas Jankauskas, Pure Mathematics, University of Waterloo

"There are no two non-real conjugates of a Pisot number with the same imaginary part"

In this talk, we will present the results from the recent arXiv paper by A. Dubickas, K. G. Hare and J. Jankauskas on the solution of three and four term linear equations in the conjugates of a Pisot number.

Jonathan Herman, Pure Mathematics, University of Waterloo

"The Curvature of Curves and Surfaces"

This talk will give an introduction to the differential geometry of curves and surfaces. In particular, I will give precise meaning to the intuitive notion of a 'curved' surface or curve. We'll see how differential geometry extends notions from calculus to more abstract spaces; for example, it allows us to do calculus on a sphere, torus, catenoid and so on.

Ruxandra Moraru, Department of Pure Mathematics, University of Waterloo

“Varieties versus schemes”

Last week, we saw the definition of a scheme. In this weeks talk, well present more examples of schemes and illustrate how, in some cases, schemes provide a better framework than varieties for studying certain geometric questions.

Francesco Sala, University of Western Ontario

“Sheaves on root stacks and Nakajima quiver varieties”

In the present talk I describe a (conjectural) relation between moduli spaces of (framed) sheaves on some two-dimensional root toric stacks and Nakajima quiver varieties of type the affine Dynkin diagram Aˆn

Matthew Wiersma, Pure Mathematics, University of Waterloo

"Intermediate $C^*$-norms"

It is known that $C^*$-algebras admit unique $C^*$-norms, but this is not true in general for dense $*$-subalgebras of $C^*$-algebras. For example, if $\Gamma$ is a discrete group, then the group ring $\mathbb C[\Gamma]$ may admit more than one $C^*$-norm.

Denis Hirschfeldt, University of Chicago

"Computable Mathematics and Reverse Mathematics"

Every mathematician knows that if 2+2=5 then Bertrand Russell is the pope. Russell is credited with having given a proof of that fact in a lecture, though from the point of view of classical logic, no such proof is needed, since a false statement implies every statement.

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