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Thursday, January 12, 2017 4:00 pm - 4:00 pm EST (GMT -05:00)

Graduate Student Colloquium

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.

Friday, January 13, 2017 3:30 pm - 3:30 pm EST (GMT -05:00)

Analysis Seminar

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.