Sheffield showed that conformally welding a γ-Liouville quantum
gravity (LQG) surface to itself gives a Schramm-Loewner evolution
(SLE) curve with parameter κ=γ2 as the interface, and
Duplantier-Miller-Sheffield proved similar stories for
I will present a somewhat novel approach to known relationships
(in works of Sheffield, Miller, and others) between SLE and GFF,
the exponential of the GFF (quantum length/area), and Minkowski
content of paths. The Neumann GFF is defined as the real...
I will explain a new construction of an Euler system for the
symmetric square of an eigenform and its connection with L-values.
The construction makes use of some simple Eisenstein cohomology
classes for Sp(4) or, equivalently, SO(3,2). This is an...
Extracting information from stochastic fields is a ubiquitous
task in science. However, from cosmology to biology, it tends to be
done either through a power spectrum analysis, which is often too
limited, or the use of convolutional neural networks...
Given a linear equation whose principal term is given by a
degenerate dispersive pseudo-differential operator, we provide a
framework for the construction of degenerating wave packet
solutions. As an application, we prove strong ill-posedness
The notion of strong stationarity was introduced by Furstenberg
and Katznelson in the early 90's in order to facilitate the proof
of the density Hales-Jewett theorem. It has recently surfaced that
this strong statistical property is shared by...
Incidence bound for points and spheres in higher dimensions
generally becomes trivial in higher dimensions due to the existence
of the Lenz example consisting of two orthogonal circles
in ℝ4, and the corresponding construction in higher
Suppose we are given matchings M1,....,MN of size t in some
r-uniform hypergraph, and let us think of each matching having a
different color. How large does N need to be (in terms of t and r)
such that we can always find a rainbow matching of size t...
Let X be a smooth projective variety over the complex numbers.
Let M be the moduli space of irreducible representations of the
topological fundamental group of X of a fixed rank r. Then M is a
finite type scheme over the spectrum of the integers Z...