In the talk we demonstrate many different constructions which are

analogous to constructions of irrational numbers from rationals. We

show, following Il.Molchanov, that the solutions of "quadratic"

equations like Z^o = Z + K always exists (where Z^o is the polar

body of Z ; Z and K are convex compact bodies containing 0 in the

interior). Then we show how the geometric mean may be defined for any

convex compact bodies K and T (containing 0 into their interior).

We also construct K^a for any centrally symmetric K and 0 < a < 1, and also

Log K for K containing the euclidean ball D (and K = -K).

Note, the power a cannot be above 1 in the definition of power !

All these constructions may be considered also for the infinite

dimensional setting, but this is outside the subject of the talk.

The talk will be well understood by any graduate student.

These results are joint with Liran Rotem.

# "Irrational" Convexity

Date:

Tuesday, August 22, 2017 - 3:30pm

Location:

STRICK 209

Speaker:

Vitali Milman (University of Tel Aviv)

Event Type: