A "sketch" is a data structure supporting some pre-specified set of
queries and updates to a database while consuming space substantially
(often exponentially) less than the information theoretic minimum
required to store everything seen. Thus sketching can be seen as some
form of functional compression. The advantages of sketching include
reduced memory consumption, faster algorithms, and reduced bandwidth
requirements in distributed computing environments.
Sketching has been a core technique in several domains, including
processing massive data streams with low memory footprint, 'compressed
sensing' for lossy compression of signals with few linear
measurements, and dimensionality reduction or 'random projection'
methods for speedups in large-scale linear algebra algorithms, and
high-dimensional computational geometry.

This talk will provide a glimpse into some recent progress on core
problems in the theory of sketching algorithms.