Salil Vadhan
| Salil Vadhan | |
|---|---|
Salil Vadhan
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| Citizenship | United States |
| Fields | Computational complexity theory, Cryptography |
| Institutions | Harvard University |
| Alma mater | Massachusetts Institute of Technology |
| Doctoral advisor | Shafi Goldwasser |
| Notable awards | Gödel Prize, 2009 |
Salil Vadhan is Vicky Joseph Professor of Computer Science and Applied Mathematics at Harvard University. He obtained his PhD in Applied Mathematics from Massachusetts Institute of Technology in 1999, where his advisor was Shafi Goldwasser. His research centers around the interface between computational complexity theory and cryptography. He focuses on the topics of pseudorandomness and zero-knowledge proofs. His work on zig-zag product, with Omer Reingold and Avi Wigderson, was awarded the 2009 Gödel Prize.
One of the main contribution of his work is a new type of graph product, called the zig-zag product.
Taking a product of a large graph with a small graph, the resulting graph inherits (roughly) its size from the large one, its degree from the small one, and its expansion properties from both. Iteration yields simple explicit constructions of constant-degree expanders of every size, starting from one constant-size expander.
Crucial to the intuition and simple analysis of the properties of the zig-zag product is the view of expanders as functions which act as “entropy wave” propagators — they transform probability distributions in which entropy is concentrated in one area to distributions where that concentration is dissipated. In these terms, the graph product affords the constructive interference of two such waves.
A variant of this product can be applied to extractors, giving the first explicit extractors whose seed length depends (poly)logarithmically on only the entropy deficiency of the source (rather than its length) and that extract almost all the entropy of high min-entropy sources. These high min-entropy extractors have several interesting applications, including the first constant-degree explicit expanders which beat the “eigenvalue bound.”
Vadhan also came up with another simplified approach to the undirected ST-connectivity problem following Reingold's breakthrough result. Also the zig-zag product was useful in Omer Reingold's proof that SL=L.
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