Let F be a CM field. Scholze constructed Galois representations
associated to classes in the cohomology of locally symmetric spaces
for GL_n/F with p-torsion coefficients. These Galois
representations are expected to satisfy local-global...
Flows of vector fields: classical and modern Consider a (possibly
time-dependent) vector field v on the Euclidean space. The
classical Cauchy-Lipschitz (also named Picard-Lindel\"of) Theorem
states that, if the vector field v is Lipschitz in space...
There are significant gaps between legal and technical thinking
around data privacy. Technical standards such as k-anonymity and
differential privacy are described using mathematical language
whereas legal standards are not rigorous from a...
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...
