Events - March 2019

Tobias Fritz, Perimeter Institute for Theoretical Physics

"Real algebra, random walks, and information theory"

Michael Deveau, Department of Pure Mathematics, University of Waterloo

"Generalizing $\omega^k$-c.e. for Relativization - Part 2"

We finish the proof of a characterization of $A \leq_{bT} B^b$ that we started last time. We then use this to motivate a more general characterization, namely when $A \leq{bT} B^{nb}$. Finally, we begin the proof of a weak non-collapse theorem which uses this expanded characterization.

MC 5413

Ben Webster, Department of Pure Mathematics, University of Waterloo

"Coulomb, Galois, Gelfand-Tsetlin"

In the grand tradition of naming objects after mathematicians who knew nothing about them, I'll talk a bit about Galois orders, their Gelfand-Tsetlin modules, and how most important examples are Coulomb branches.

Remi Jaoui, Department of Pure Mathematics, University of Waterloo

"Failure of essential surjectivity"

We consider Example 3.2 of the Bakker-Brunebarbe-Tsimerman paper, of an analytic line bundle on G_m that does not definably trivialise.

MC 5479

Rahim Moosa, Department of Pure Mathematics, University of Waterloo

"Pseudo-finite dimensions IX"

I will discuss the description of approximate subgroups of simple algebraic groups in Udi's "Stable groups and approximate subgroups".

MC 5403

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 $\mathcal{F}$.

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.

Brad Rogers, Queen's University

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

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

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 $(X,\mu)$.

Brett Nasserden, Department of Pure Mathematics, University of Waterloo

"Quotient singularities"

Singularities of algebraic varieties which are quotients of a vector space by a finite group provide interesting connections between algebraic geometry, representation theory, and group theory.  I will discuss this circle of ideas with a focus on applications to algebraic geometry.

MC 5403

Ragini Singhal, Department of Pure Mathematics, University of Waterloo

"Deformations of Nearly G₂ Instantons"

In this talk we will discuss the deformation theory for instantons on  seven-manifolds with nearly parallel G₂-structure of type-I. We will see how the space of perturbations of instantons can be identified with the eigenspaces of the Dirac operator, which can be used to prove that all the irreducible instantons with semisimple structure group are rigid.

MC 5413