Events - 2015

Jonny Stephenson, Pure Mathematics, University of Waterloo

"Embedding Lattices in the Computably Enumerable Degrees (continued)"

This talk is a continuation of one given August 6th.

Zack Cramer, Pure Mathematics, University of Waterloo

"Approximation of Normal Operators by Nilpotents in Purely Infinite $C^*$-algebras"

Jonny Stephenson, Pure Mathematics, University of Waterloo

"Embedding Lattices into the Computably Enumerable Degrees"

The question of which finite lattices can be embedded into the c.e.
degrees first arose with the construction of a minimal pair by Yates,
and independently by Lachlan, showing the 4 element Boolean algebra
can be embedded. This result was rapidly generalised to show any
finite distributive lattice can also be embedded. For non-distributive
lattices, the situation is more complicated.

Richard Mack, Pure Mathematics, University of Waterloo

"Dual spaces and von Neumann Algebras"

A canonical construction in Linear Algebra is that of the dual space.
In this talk, we consider two questions:
When is a Banach space a dual space?
When is there only one possible predual?

Examples will be presented illustrating that these are not trivial questions, and a major theorem (Sakai's) will be presented giving a broad class of examples for the second question.

Raymond Cheng, Pure Mathematics, University of Waterloo

"Gutting Bundles on Tori"

Shuntaro Yamagishi, Pure Mathematics, University of Waterloo

"Some additive results in $\mathbb{F}_q[t]$"

We collected several results in $\mathbb{Z}$ of additive number theory and translated to results in $\mathbb{F}_q[t]$. The results we collected are related to slim exceptional sets and the asymptotic formula in Waring's problem, diophantine approximation of polynomials over $\mathbb{Z}$ satisfying  divisibility conditions, and the problem of Sidon regarding existence of certain thin sequences.

Mohammad Mahmoud, Pure Mathematics, University of Waterloo

"A Class of Structures without a Turing Ordinal"

We continue to show that the class Kw has no Turing Ordinal. We construct a set D which is not enumeration reducible to R_\A for any structure \A in Kw. This will imply directly that if the Turing ordinal exists then it must be strictly greater than 0. On the other hand Joe Miller showed that, for our class, if the Turing Ordinal exists it must be 0. Both statements tell us that the Turing Ordinal can't exist.

Ty Ghaswala, Pure Mathematics, University of Waterloo

"If you love a group, set it free."

The existence of algebraic topology (even if you claim to know nothing about it) should be enough to convince you that doing topology without group theory is difficult, frustrating, alcoholism inducing, and above all, a disservice to topology.  In this talk I hope to convince you, at least for a moment, that thinking about groups while ignoring topology is a disservice to group theory.