Integrality gaps for sparsest cut and minimum linear arrangement problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Monotone maps, sphericity and bounded second eigenvalue
Journal of Combinatorial Theory Series B
Finite metrics in switching classes
Discrete Applied Mathematics
A geometric approach to quantum circuit lower bounds
Quantum Information & Computation
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
A PRG for lipschitz functions of polynomials with applications to sparsest cut
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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In the last several years a number of very interesting results were proved about finite metric spaces. Some of this work is motivated by practical considerations: Large data sets (coming e.g. from computational molecular biology, brain research or data mining) can be viewed as large metric spaces that should be analyzed (e.g. correctly clustered).On the other hand, these investigations connect to some classical areas of geometry - the asymptotic theory of finite-dimensional normed spaces and differential geometry. Finally, the metric theory of finite graphs has proved very useful in the study of graphs per se and the design of approximation algorithms for hard computational problems. In this talk I will try to explain some of the results and review some of the emerging new connections and the many fascinating open problems in this area.