Wentang Kuo, Pure Mathematics, University of Waterloo
"On a problem of Sidon"
Christopher Hawthorne, Pure Mathematics, University of Waterloo
We begin chapter 4 of Goldblatt. (Category theory background from chapter 3 will be assumed.) We introduce subobjects and subobject classifiers; time permitting, we will get to the definition of a topos.
Satish Pandey, Pure Mathematics, University of Waterloo
"The Dinitz Problem and Five-Colouring Plane Graphs"
G. H. Hardy firmly believed that there is no permanent place for ugly Mathematics. Following his dictum, Paul Erdos liked to talk about "The Book" in which God maintains the perfect proofs for mathematical theorems. This talk is an attempt to explore Erdos' idea of perfect proofs, and the territory we choose to explore is graph theory.
Bradd Hart, University of McMaster
"Logical unification"
I will talk on preliminary work on the role of [0,1]-valued
logic in unifying the growing number of first order logics. In
particular, elementary classes in [0,1]-valued logic are CATs in the
sense of Ben Yaacov and the class of von Neumann algebras with faithful
actions on Hilbert spaces form an elementary class.
Shubham Dwivedi, Pure Mathematics, University of Waterloo
"Minimal Varieties in Riemannian Manifolds - Part I"
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.
Shubham Dwivedi, Pure Mathematics, University of Waterloo
"Minimal Varieties in Riemannian Manifolds - Part II"
Anthony McCormick, Pure Mathematics, University of Waterloo
"Algebraic Groups"
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.
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.