Events

David R. Pitts, University of Nebraska-Lincoln

"Cartan Triples"

Cartan MASAs in von Neumann algebras have been well-studied since the pioneering work of Feldman and Moore in the 1970's. The presence of a Cartan MASA in a a given von Neumann algebra $\mathcal{M}$ is useful for understanding the structure of $\mathcal{M}$. Cartan MASAs arise when applying the group measure space construction with a countable group $\Gamma$ acting essentially freely on the measure space $(X,\mu)$.

Ellen Kirkman, Wake Forest University

"The Invariant Theory of Artin-Schelter Regular Algebras"

Ragini Singhal, Department of Pure Mathematics, University of Waterloo

"Deformations of Nearly G_2 instantons - Part 2"

In this talk we will discuss the deformation theory for instantons on  seven-manifolds with nearly parallel G_2-structure of type-I. We will see how the space of perturbations of instantons can be identified with the eigenspaces of the Dirac operatior, which can be used to prove that all the irreducible instantons with semisimple structure group are rigid.

MC 5413

Matt Satriano, Department of Pure Mathematics, University of Waterloo

"The Main Theorem"

We jump ahead and begin proving the main algebraization theorem of the Bakker-Brunebarbe-Tsimerman paper – Theorem 3.1.

MC 5479

Brad Rogers, Queen's University

"Integers in short intervals representable as sums of two squares"

Adam Fuller, Ohio University

"Describing C*-algebras in terms of topological groupoids"

Unital abelian C*-algebras are well understood. They are necessarily isomorphic to C(X), the continuous functions on a compact Hausdorff space X. Studying the topological dynamics on $X$ gives rise to the study of crossed product C*-algebras: a class of relatively well understood of non-abelian operator algebras constructed from a dynamical system.

Patrick Naylor, Department of Pure Mathematics, University of Waterloo

"Is any knot not the unknot?"

Ever wanted to learn something about knots? This is your chance! We'll talk about some basics of knot theory, including how to prove some intuitively `obvious' but mathematically tricky results. Along the way, we'll see knot coloring invariants, polynomial invariants, and more. We'll even show how to produce a knotted surface: a sphere ($S^2$) in $\mathbb{R}^4$ that is `knotted'. This talk will be very accessible and will include many cool pictures.

Yuanhang Zhang, Jilin University

"Connecting invertible analytic Toeplitz operators in $G(\mathcal{T}(\mathcal{P}^{\perp}))$"

We prove that there exists an orthonormal basis $\mathcal{F}$ for classical Hardy space $H^2$, such that each invertible analytic Toeplitz operator $T_\phi$ (i.e. $\phi$ is invertible in $H^\infty$) could be connected to the identity operator via a norm continuous path of invertible elements of the lower triangular operators with respect to $\mathcal{F}$.

Michael Deveau, Department of Pure Mathematics, University of Waterloo

"Generalizing $\omega^k$-c.e. for Relativization"

Just as the arithmetic hierarchy characterizes reductions below various Turing jumps of $\emptyset$, Anderson and Csima showed that the Ershov hierarchy -- related to the notion of $\omega^k$-c.e. -- characterizes reductions of bounded Turing jumps of $\emptyset$. We discuss how to relativize this to reductions below bounded Turing jumps of an arbitrary set.

MC 5413

Patrick Naylor, Department of Pure Mathematics, University of Waterloo

“Is any knot not the unknot?”

Ever wanted to learn something about knots? This is your chance! We'll talk about some basics of knot theory, including how to  prove some intuitively `obvious' but mathematically tricky results.  Along the way, we'll see knot coloring invariants, polynomial invariants, and more. We'll even show how to produce a knotted surface: a  sphere ($S^2$) in $\mathbb{R}^4$ that is `knotted'. This talk will be very accessible and will include many cool pictures.