We consider Laplace eigenfunctions of a metric graph satisfying
Neumann-Kirchhoff conditions on every vertex. The nodal count of a
given eigenfunction is the number of points at which it vanishes.
The nodal count of the n-th eigenfunction was shown...
This talk is about qualitative properties of the underlying
scheme of Rapoport-Zink formal moduli spaces of p-divisible groups,
resp. Shtukas. We single out those cases when the dimension of this
underlying scheme is zero, resp. those where the...
Most people interact with machine learning systems on a daily
basis. Such interactions often happen in strategic environments
where people have incentives to manipulate the learning algorithms.
As machine learning plays a more prominent role in our...
The first lecture in this series is an introduction to the
theory of asymptotic spectra. This theory describes asymptotic
behavior of basic objects in mathematics like graphs and tensors.
Example applications that we will see are the matrix...
In various applications, one is given the advice or predictions
of several classifiers of unknown reliability, over multiple
questions or queries. This scenario is different from standard
supervised learning where classifier accuracy can be
assessed...
The observation of mergers of black holes and neutron stars has
established gravitational-wave astronomy as powerful tool to
understand the Universe. After a brief introduction to
gravitational waves and how the detectors work, I will discuss
the...
In a recent result, Buckmaster and Vicol proved non-uniqueness
of weak solutions to the Navier-Stokes equations which have bounded
kinetic energy and integrable vorticity.
We discuss the existence of such solutions, which in addition
are regular...
Starting from a contact manifold and a supporting open book
decomposition, an explicit construction by Bourgeois provides a
contact structure in the product of the original manifold with the
two-torus. In this talk, we will discuss recent results...
Schur polynomials are the characters of finite-dimensional
irreducible representations of the general linear group. We will
discuss both continuous and discrete concavity property of Schur
polynomials. There will be one theorem and eight conjectures...
A sunflower with $r$ petals is a collection of $r$ sets so that
the intersection of each pair is equal to the intersection of all.
Erdos and Rado in 1960 proved the sunflower lemma: for any fixed
$r$, any family of sets of size $w$, with at least...
