Dear all,
This week at the Horowitz seminar on Probability, Ergodic Theory and
Dynamical Systems at Tel Aviv University we are happy to have:
Speaker: David Ralston, Ben-Gurion University
Title: Heavy Sets: Structure and Dimension
Date: Monday, January 17
Time: 14:30
Place: Schreiber 309
Given a measure preserving transformation on a space and a function of
zero mean, the heavy set is the set of points whose ergodic sums remain
nonnegative for all (forward) time.  After discussing a few generic
results, we will turn our attention to the specific setting where the
transformation is an irrational circle rotation and the function is the
characteristic function of the interval [0,1/2].  In this setting, we
will show that the heavy set is almost-surely (with regard to the
rotation parameter) the union of a perfect Cantor set of both Hausdorff
and box dimension c, where c is some constant strictly between zero and
one, together with countably many isolated points. 
ALSO, in this week's Mathematics Colloquium, Monday from 12:15 to 13:15
in Schreiber 006, Hugo Duminil-Copin will speak on "Discrete complex
analysis and statistical physics".
Discrete harmonic and discrete holomorphic functions have been proved to
be very useful in many domains of mathematics. Recently, they have been
at the heart of the two dimensional statistical physics (for instance,
through the works of Kenyon, Schramm, Smirnov and others...). We will
present some of the connections between discrete complex analysis and
statistical physics. In particular (it is a joint work with S. Smirnov),
we will use discrete holomorphic functions to prove that the number a_n
of self-avoiding walks of length n (starting at the origin) on the
hexagonal lattice satisfies:
a_n^{1/n} ----> sqrt(2 + sqrt(2))
when n tends to infinity. This confirms a conjecture made by Nienhuis in
Best regards,
Seminar webpage:
Technion Math Net-2 (TECHMATH2)
Editor: Michael Cwikel   <> 
Announcement from: Ron Peled   <>