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Upcoming Events

Branwen Purdy at her stall during OMSI meet-a-scientist day.
Branwen Purdy prepares hands-on activities for kids at the OMSI Meet-A-Scientist Day in Portland, to share hands-on learning experiences about her research in topological data analysis.

Join us for these events hosted by the Department of Mathematics, including colloquia, seminars, graduate student defenses and outreach, or of interest to Mathematicians hosted by other groups on campus.

Access our archive of events

One-Parameter Deformations of the Bowen-Series Map Associated to Cocompact Triangle Groups

Ph.D. Defense

Speaker: Ayse Yiltekin

In 1979, for each signature for Fuchsian groups of the first kind, Bowen and Series constructed an explicit fundamental domain for one group of the signature, and from this a function on the unit circle tightly associated with this group. In general, their fundamental domain enjoys what has since been called the ‘extension property’. We determine the exact set of signatures for cocompact Fuchsian triangle groups for which this extension property can hold for any convex fundamental domain, and verify that for this restricted set, the Bowen-Series fundamental domain does have the property. To each Bowen-Series function in this corrected setting, we naturally associate four one-parameter deformation families of circle functions. We show that each of these functions is aperiodic if and only if it is surjective; and is finite Markov if and only if its natural parameter is a hyperbolic fixed point of the triangle group at hand. Furthermore, we show that the topological entropy is… Read more.

An Inner Product on Adelic Measures

Kidder 274
Ph.D. Defense

Speaker: Peter Oberly

We define an inner product on a vector space of adelic measures over a number field. When restricted to the subspace of adelic measures with total mass zero, the norm induced by our inner product agrees with the mutual energy pairing considered by Favre & Rivera-Letelier, and by Fili. We find that the norm of the canonical adelic measure associated to a rational map is commensurate with a height on the space of rational functions with fixed degree. As a consequence, a notion of dynamical distance between two rational maps is also commensurate with a height. Read more.