Date: Tuesday, 11 Iyar 5766 (May 9, '06)

Speaker: Alex Samorodnitsky (Hebrew University)

Title: "An upper bound for permanents"

Abstract:
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A recent conjecture of Caputo, Carlen, Lieb, and Loss, and, independently,
of the speaker, states that the maximum of the permanent of a matrix whose
rows are unit vectors in l_p is attained either for the indentity matrix I
or for a constant multiple of the all-1 matrix J.

The conjecture is known to be true for p = 1 (I) and for p >= 2 (J).

We prove the conjecture for a subinterval of (1,2), and show the conjectured
upper bound to be true within a subexponential factor (in the dimension) for
all 1 < p < 2. In fact, for p bounded away from 1, the conjectured upper
bound is true within a constant factor.