**"On Dimension of Equilibrium
Measures
on Small Sets**

By

** **

** Abstract:** There are two natural measures on the classical Cantor
set : the Cantor-Lebesgue measure (that is the Hausdorff measure with dimension
log 2 / log 3), and the equilibrium measure that minimizes the logarithmic
energy. Makarov and Volberg proved in 1986 that these measures are mutually
singular. Some generalizations were obtained later for multidimensional
fractals and for Cantor repellers. We discuss the possibility to construct
Cantor-type sets for which these measures coincide or, at least, are not
mutually singular.

Tea and cookies will be served before the seminar.

**Date: ****Wednesday,
February 13, 2012**

**Time: ****14.30**

**Place: ****Mathematics
Seminar Room, SA-141**