# Jerusalem Mathematics Colloquium

Thursday, 18th November 2004, 4:00 pm

Mathematics Building, Lecture Hall 2

##

Professor Shahar Mendelson

(Australian National University)

"Combinatorial dimensions, entropy and random processes"

** Abstract: **
We will explore some of the connections between three parameters that
measure the complexity of a subset of $R^n$: the covering numbers of
the set, the expectation of the supremum of the gaussian process
indexed by the set, and the combinatorial dimension of the set
(roughly speaking, the latter measures the extent coordinate
projections of the set contain ``cubic" structures).

We will then show how these parameters can be used in empirical
processes theory, and (if time permits), present some applications in
probability and geometry.

Light refreshments will be served in the faculty lounge at 3:30.

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