Department of

Mathematics


Seminar Calendar
for events the day of Friday, April 10, 2015.

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Questions regarding events or the calendar should be directed to Tori Corkery.
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Friday, April 10, 2015

4:00 pm in 243 Altgeld Hall,Friday, April 10, 2015

Korovkin-type properties for completely positive maps and operator systems

Craig Kleski (Miami University)

Abstract: Korovkin's theorem inspired much research in approximation theory and functional analysis, and it invites a generalization to noncommutative function spaces. In this talk, we will review the classic theorem for positive maps on the continuous functions on the unit interval. We then generalize these notions to operator systems, and prove a noncommutative version of Saskin's theorem on the connection between Korovkin sets and Choquet boundaries. Finally, we discuss a conjecture of Arveson and progress towards its solution.

4:00 pm in 241 Altgeld Hall,Friday, April 10, 2015

b, Scattering, and Edge Symplectic Geometry

Melinda Lanius (UIUC Math)

Abstract: A symplectic manifold is a manifold $M$ equipped with a non-degenerate closed two form $\omega$. Symplectic manifolds are a special case of what is called a Poisson manifold. A Poisson structure gives a smooth partition of a manifold into even-dimensional symplectic submanifolds, which are not necessarily of the same dimension. These two geometries, symplectic and Poisson, each have benefits; while symplectic structures are fairly well understood, Poisson structures are much more general. We will consider the questions: can we define a generalized symplectic structure that will correspond to a mildly degenerate Poisson structure? If so, can we employ the techniques of symplectic geometry to better understand these?