Research
Consider the fractional Brownian motions on the real line. What should we expect if we replace the real line by a manifold M? We will provide an answer to this question, extending work begun by…
In joint work with Soumik Pal, we study natural mixing processes where cards (or dominoes or mahjong tiles) are ‘smushed’ around on a table with two hands. How long should mixing continue. If things are…
Given n uniform points on the surface of a two-dimensional sphere, how can we partition the sphere fairly among them? “Fairly” means that each region has the same area. It turns out that if the…
Modern data often consists of feature vectors with a large number of features. High-dimensional geometry and Linear Algebra (Singular Value Decomposition) are two of the crucial areas which form the mathematical foundations of Data Science.…
Economics and computer science (EconCS) is at the core of Microsoft Research New England, an interdisciplinary lab of thirty full-time researchers and postdocs working in machine learning, statistics, computational biology, theoretical computer science, algorithmic game…
A secure multiparty computation protocol allows a set of mutually distrusting parties to compute a joint function of their private inputs without leaking anything apart from the output of the functionality. Ever since the initial…
All computer systems, be it a standalone device, a datacenter, the internet, an advertising platform, deep neural networks or the internet of things rely on sound algorithmic ideas at their foundations.
Modern data often consists of feature vectors with a large number of features. High-dimensional geometry and Linear Algebra (Singular Value Decomposition) are two of the crucial areas which form the mathematical foundations of Data Science.…
Microsoft is a silver sponsor of LISA17, the annual vendor-neutral meeting place for the wider system administration community. The program will address the overlap and differences between traditional and modern IT operations and engineering, curated…
Modern data often consists of feature vectors with a large number of features. High-dimensional geometry and Linear Algebra (Singular Value Decomposition) are two of the crucial areas which form the mathematical foundations of Data Science.…
