Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

Date and Time: Tuesday, October 14, 2008, 12:15 pm

Duration: This information is not available in the database

Location: OAT S15/S16/S17

Speaker: Gabriel Katz

Tropical Centerpoints and Tverberg Points

In tropical geometry, the focus of study is the tropical semiring (\mathbb{R}, \min, +) and its semimodule \mathbb{R}^d. Notions of convexity, hyperplanes and halfspaces exist for this semimodule, but these behave differently than their classical counterparts. For instance, a tropical hyperplane splits \mathbb{R}^d into d parts.

In this talk we will look at two classical theorems, the centerpoint Theorem and Tverberg's Theorem. For both of them, we will derive a tropical equivalent. Further, for n>d, we will present an O(n^4) algorithm for finding a point that is both a tropical centerpoint and a tropical Tverberg point. In higher dimensions, this is better than in the classical setting, where the best known exact algorithms are exponential in d.

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