Seminar
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| Location: | SLMath: Eisenbud Auditorium |
Keywords and Mathematics Subject Classification (MSC)
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Given a pair of convex bodies K, L, denote by N(K,L) the least number of copies of L whose union covers (or in other words contains) K. If we are allowed to linearly transform one of the bodies, can we bound both N(K,L) and N(L,K) well? Also, can the volume of the unit ball of an n-dimensional normed space and the volume of the unit ball of its dual both be very large or very small?
In this talk, after we make these questions more precise, we will discuss results (old or more recent) which give answers to them, and which also show that for most intents and purposes these answers are just restating of the same fundamental underlying property.
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