A fundamental task in (unsupervised) analysis of data is to
detect and estimate interesting "structure" hidden in it. In low
dimensions, this task has been explored for over 100 years with
dozens of developed methods. In this talk I'll focus on...
The choiceless computation model of Blass, Gurevich and Shelah
(1999, 2002) is an algorithmic framework for computing
isomorphism-invariant properties of unordered structures. Machines
in this model have the power of parallel execution, but lack...
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...
