Chernoff's bound states that for any A⊂[N] the probability a
random k-tuple s∈([N]k) correctly `samples' A (i.e. that the
density of A in s is close to its mean) decays exponentially in the
dimension k. In 1987, Ajtai, Komlos, and Szemeredi proved...
In this talk, I'll show that the most natural low-degree test
for polynomials over finite fields is ``robust'' in the high-error
regime for linear-sized fields. This settles a long-standing open
question in the area of low-degree testing, yielding...
Although there are several ways to ''choose a compact hyperbolic
surface at random'', putting the Weil-Petersson probability measure
on the moduli space of hyperbolic surfaces of a given topology is
certainly the most natural. The work of M...
Although there are several ways to ''choose a compact hyperbolic
surface at random'', putting the Weil-Petersson probability measure
on the moduli space of hyperbolic surfaces of a given topology is
certainly the most natural. The work of M...
Chen and Ruan constructed symplectic orbifold Gromov-Witten
invariants more than 20 years ago. In ongoing work with Alex
Ritter, we show that moduli spaces of pseudo-holomorphic curves
mapping to a symplectic orbifold admit global Kuranishi
charts...
In this lecture, we will review recent works regarding
spectral statistics of the normalized adjacency
matrices of random $d$-regular graphs on $N$ vertices.
Denote their eigenvalues by $\lambda_1=d/\sqrt{d-1}\geq
\la_2\geq\la_3\cdots\geq \la_N$...
Ratner's landmark equidstribution results for unipotent flows
have had dramatic applications in many mathematical areas. Recently
there has been considerable progress in the long sought for goal of
getting effective equidistribution results for...
(Joint with Samuel Grushevsky, Gabriele Mondello, Riccardo
Salvati Manni) We determine the maximal dimension of a compact
subvariety of the moduli space of principally polarized abelian
varieties Ag for any value of g. For g<16 the dimension is g−1,
while for g≥16, it is determined by the larged dimensional compact
Shimura subvariety, which we determine. Our methods rely on
deforming the boundary using special varieties, and functional
transcendence theory.
To study the asymptotic behavior of orbits of a dynamical
system, one can look at orbit closures or invariant measures. When
the underlying system has a homogeneous structure, usually coming
from a Lie group, with appropriate assumptions a wide...
