I will describe how basic ergodic theory can be used to prove
that certain amenable groups are stable. I will demonstrate our
method by showing that lamplighter groups are stable. Another
uncountably infinite family to which our method applies are...
A polynomial with nonnegative coefficients is strongly
log-concave if it and all of its derivatives are log-concave as
functions on the positive orthant. This rich class of polynomials
includes many interesting examples, such as homogeneous real...
We will discuss the geometry behind the horizon of various
asymptotically AdS black holes when the boundary CFT is deformed by
a scalar operator. The dynamics of classical GR in the region
inside the black hole turns out to be rather intricate, with...
We consider systems of NN particles interacting
through a repulsive potential in the Gross-Pitaevskii regime. We
prove complete Bose-Einstein condensation and we determine the form
of the low-energy spectrum, in the limit of large NN. Our
results...
The celebrated Brunn-Minkowski inequality states that for
compact
subsets XX and YY of ℝdRd, m(X+Y)1/d≥m(X)1/d+m(Y)1/dm(X+Y)1/d≥m(X)1/d+m(Y)1/d where m(⋅)m(⋅) is
the Lebesgue measure. We will introduce a conjecture generalizing
this inequality to...
"Games against Nature" [Papadimitriou '85] are two-player games
of perfect information, in which one player's moves are made
randomly. Estimating the value of such games (i.e., winning
probability under optimal play by the strategic player) is
an...
