The Kudla-Rapoport conjecture predicts a precise identity between
the arithmetic intersection number of special cycles on unitary
Rapoport-Zink spaces and the derivative of local representation
densities of hermitian forms. It is a key local...
Meta-learning (or learning to learn) studies how to use machine
learning to design machine learning methods themselves. We consider
an optimization-based formulation of meta-learning that learns to
design an optimization algorithm automatically...
A continuing mystery in understanding the empirical success of deep
neural networks has been in their ability to achieve zero training
error and yet generalize well, even when the training data is noisy
and there are many more parameters than data...
Hilbert’s 23rd Problem is the last in his famous list of problems
and is of a different character than the others. The description is
several pages, and basically says that the calculus of variations
is a subject which needs development. We will...
I'll be presenting some joint work with Ian Mertz scheduled to
appear at STOC 2020. The study of the Tree Evaluation Problem
(TEP), introduced by S. Cook et al. (TOCT 2012), is a promising
approach to separating L from P. Given a label in [k] at...
I will explain recent joint work proving that the group of
compactly supported area preserving homeomorphisms of the two-disc
is not a simple group; this answers the ”Simplicity Conjecture” in
the affirmative. Our proof uses new spectral invariants...
Let G be a real semi-simple Lie group with an irreducible unitary
representation \pi. The non-temperedness of \pi is measured by the
parameter p(\pi) which is defined as the infimum of p\geq 2 such
that \pi has matrix coefficients in L^p(G). Sarnak...
As deep learning systems become more prevalent in real-world
applications it is essential to allow users to exert more control
over the system. Exerting some structure over the learned
representations enables users to manipulate, interpret, and...
