Hello everybody,

This week’s talk will be given by Joachim Gudmundsson.

Title: A Generalization of Kakeya’s Problem

Abstract: The Kakeya needle problem asks whether there is a minimum area, a so-called Kakeya set, of a region in the plane, in which a needle can be turned through 360 degrees. This question was first posed, for convex regions, by Soichi Kakeya in 1917. We are interested in the following generalization of Kakeya’s problem: Given a family F of line segments, not necessarily finite, in the plane, what is the convex figure of smallest area that contains a translated copy of every s in F?

We prove that the region is a triangle and can be computed in O(n log n) time.

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Time and location: 11am-12noon SIT room 124 (boardroom)

The SACT calendar is available here: http://sact.it.usyd.edu.au/sact-index.html#%5B%5Bseminar calendar]]

Or you can subscribe to this calendar using the following URL: http://www.google.com/calendar/ical/iioj4b04743bd2nqjmeha4rm94%40group.calendar.google.com/public/basic.ics

Rgds,

Ilia

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