Hives, as defined by Knutson and Tao, are discrete concave
functions on a triangular grid on an equilateral triangle of side
n. It is known through the work of Knutson and Tao that the
probability distribution of the spectrum of the sum of two...
We consider the Schramm-Loewner evolution (SLE_{kappa}) for
kappa in (4,8), which is the regime that the curve is
self-intersecting but not space-filling. We let K be the set of
kappa in (4,8) for which the adjacency graph of connected
components of...
Weak gravitational lensing imprints a coherent distortion onto
the observed shapes of distant galaxies. At the image level, this
gravitational shear is degenerate with the intrinsic shape of
galaxies, and the weak lensing signal-to-noise from an...
We prove this bound by first using the unitary Ichino-Ikeda
formula of N. Harris to relate the central L-value to an
automorphic period integral. There is a `trivial' bound for
this integral, which turns out to correspond to the convexity bound
for...
The goal of this talk is to present new results dealing with the
asymptotic joint independence properties of commuting strongly
mixing transformations along polynomials. These results form
natural strongly mixing counterparts to various weakly and...
If f is a real polynomial and A and B are finite sets of
cardinality n, then Elekes and Ronyai proved that either f(A×B) is
much larger than n, or f has a very specific form (essentially,
f(x,y)=x+y). In the talk I will tell about an analogue of...
Given an area-preserving surface diffeomorphism, what can one
say about the topological properties of its periodic orbits? In
particular, a finite set of periodic orbits gives rise to a braid
in the mapping torus, and one can ask which isotopy...
Zeros of L-functions have been extensively studied, due to their
close connection to arithmetic problems. Despite several precise
conjectures about their behavior, our unconditional understanding
of them remains limited. In this talk we will discuss...
Several classical results in Ramsey theory (including famous
theorems of Schur, van der Waerden, Rado) deal with finding
monochromatic linear patterns in two-colourings of the
integers. Our topic will be quantitative extensions of such
results. A...
