#### Room 327

#### COLORFUL HELLY THEOREM FOR PIERCING BOXES WITH TWO POINTS

#### Soumi Nandi

##### ISI Kolkota

*For any natural number n, a family of sets F is said to be n-pierceable if there exists an n point set S such that every set in F has non-empty intersection with S. Helly's theorem says that for any finite family F of convex sets in the d-dimensional Euclidean space, if every (d+1)-tuple from F is 1-pierceable, then the whole family F is 1-pierceable. One important generalization of Helly's theorem is Colorful Helly's Theorem. In this talk, we shall prove a colorful Helly type result for the 2-pierceability of families of axis parallel boxes.*

This work was jointly done with Sourav Chakraborty and Arijit Ghosh.

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