Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Thursday, December 02, 2021, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Simon Weber

Oriented Matroids and Unique Sink Orientations

In this talk I will give an overview over the connections between the Linear Complementarity Problem, Oriented Matroids, and Unique Sink Orientations. In particular I will show interesting known subclasses of each of these objects, and highlight the gap in the current state of research between combinatorially and algebraically defined classes of Unique Sink Orientations.

As a small contribution of our own, I will show a newly-discovered connection between two seemingly completely unrelated groups of objects, namely Cyclic-P-Matroids (as defined by Fukuda, Klaus and Miyata) and the realizable Matoušek orientations (as defined by Matoušek and later characterized by Gärtner).

This is in parts joint work with Bernd Gärtner.

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