Seminar

Hongdi Huang, Pure Mathematics, University of Waterloo

"On *-clean group algebras"

A ring $R$ is called a $*$-ring (or a ring with involution $*$) if there exists an operation $*$: $R \rightarrow R$ such that $(x+y)^*=x^*+y^*, \,\ (xy)^*=y^*x^* \,\ $ and $(x^*)^*=x$,
for all $x, y\in R$.  An element in a ring $R$ is called $*$-clean if it is the sum of a unit and a projection ($*$-invariant idempotent). A $*$-ring is called $*$-clean if each of its elements is the sum of a unit and a projection.

Anthony McCormick, Pure Mathematics, University of Waterloo

"Algebraic Groups"

Mohammad Mahmoud, Pure Mathematics, University of Waterloo

"Existentially-atomic models"

We will talk about "Existentially atomic" and "Existentially algebraic" structures. We will give some examples and will show that being existentially algebraic implies being existentially atomic. As a particular example, we will prove a necessary and sufficient condition for a linear ordering to be existentially atomic.

Ken Dykema, Texas A & M University

"Commuting operators in finite von Neumann algebras"

We find a joint spectral distribution measure for families
of commuting elements of a finite von Neumann algebra.  This
generalizes the Brown measure for single operators.  Furthermore, we
find a lattice (based on Borel sets) consisting of hyperinvariant
projections that decompose the spectral distribution measure.  This
leads to simultaneous upper triangularization results for commuting
operators.  

Shubham Dwivedi, Pure Mathematics, University of Waterloo

"Minimal Varieties in Riemannian Manifolds - Part II"

Shubham Dwivedi, Pure Mathematics, University of Waterloo

"Minimal Varieties in Riemannian Manifolds - Part I"

Jason Bell, Pure Mathematics, University of Waterloo

"The Schafke-Singer theorem, III"

We finish (I hope) the proof of the theorem of Schafke and Singer.

Blake Madill, Pure Mathematics, University of Waterloo

"The Fundamental Theorem of Hopf Modules"

We continue our investigation of Hopf modules.

Jonny Stephenson, Pure Mathematics, University of Waterloo

"Jumps of relations"

We will show that the Kleene relation introduced last week is r.i.c.e complete, and use it to define a jump operator on relations in structures. We will check that the jump behaves as expected: if Q' is the jump of a relation Q, then Q is r.i. computable in Q', but Q' is not r.i. computable in Q.

Anthony McCormick, Pure Mathematics, University of Waterloo

"Formality of Compact Kähler Manifolds"