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Piercing axis-parallel boxes with axis-parallel k-flats

Series: Bangalore Theory Seminars

Speaker: Soumi Nandi,Indian Institute of Science,Bangalore

Date/Time: Sep 13 11:00:00

Location: CSA Auditorium, (Room No. 104, Ground Floor)

Abstract:
A k-flat H is said to hit or pierce a set F �?? Rd if F �?� H �?� �?? . A set T of k-flats (k-dimensional affine space) is called a k-transversal of a family F of subsets of Rd if for every F �?? F there exists a k-flat in T that pierces F. We say a family F has a k-transversal of size m (or, at most m) if there exists a k-transversal T of F and |T| = m (or, |T| �?� m ). In this talk, I will present the necessary and sufficient condition for an infinite collection of axis-parallel boxes in Rd to be pierceable by finitely many axis-parallel k-flats, where 0 �?� k < d.
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We are grateful to the Kirani family for generously supporting the theory seminar series
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Hosts: Rameesh Paul, KVN Sreenivas, Rahul Madhavan, Debajyoti Kar