Abstract: Low-lying horocycles are known to equidistribute on
the modular curve. Here we consider the joint distribution of two
low-lying horocycles of different speeds in the product of two
modular curves and show equidistribution under certain...
This is a joint work with Reza Gheissari (Northwestern) and
Aukosh Jagannath (Waterloo), Outstanding paper award at NeurIPS
2022. We study the scaling limits of stochastic gradient descent
(SGD) with constant step-size in the high-dimensional regime...
Lagrangian Floer theory is a useful tool for studying the
structure of the homology of Lagrangian submanifolds. In some
cases, it can be used to detect more- we show it can detect the
framed bordism class of certain Lagrangians and in
particular...
I discuss the spectral and arithmetic side of the relative trace
formula of Kuznetsov type for congruence subgroups of SL(n, Z) with
applications to automorphic density theorems. A particular focus is
on properties of general Kloosterman sums as...
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.
