This talk will be about a ferromagnetic spin system called the
Blume-Capel model. It was introduced in the '60s to model an exotic
multi-critical phase transition observed in the magnetisation of
uranium oxide. Mathematically speaking, the model can...
The last decade has witnessed a revolution in the circle of
problems concerned with proving sharp moment inequalities for
exponential sums on tori. This has in turn led to a better
understanding of pointwise estimates, but this topic remains...
Robust sublinear expansion represents a fairly weak notion of
graph expansion which still retains a number of useful properties
of the classical notion. The general idea behind it has been
introduced by Komlós and Szemerédi around 25 years ago and...
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
κ=16/γ2...
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...
We discuss the relation between hypersurface singularities (e.g.
ADE, E˜6,E˜7,E˜8, etc) and spectral invariants, which are
symplectic invariants coming from Floer theory.
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...
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
for...
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...
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...
