Jeremy Nicholson, Pure Mathematics, University of Waterloo
"The Frobenius Problem and Combinatorics on Words"
Justin Toth, Combinatorics and Optimization
"Using Linear Algebra to do Matching Theory"
Adam Humeniuk, Pure Mathematics, University of Waterloo
"Existence of the C*-envelope"
In 1969, Arveson defined the C*-envelope of an operator algebra or operator system as a universal quotient amongst all C*-algebras which contain it. He left the existence of the C*-envelope as an open problem. In a whirlwind tour of my Master's research paper, I'll discuss the diverse tools used to prove its existence in the intervening decades.
Dennis The, The University of Tromso
"Exceptionally simple PDE"
Fan Ge, Pure Mathematics, University of Waterloo
"The number of zeros of $\zeta'(s)$
Tristan Freiberg, Pure Mathematics, University of Waterloo
"Distribution of primes in intervals"
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.