Video of this talk is available at: https://smartech.gatech.edu/handle/1853/56062

Full collection of talk videos are available at: https://smartech.gatech.edu/handle/1853/46836**Algorithms & Randomness Center (ARC)**

**Monday, November 14, 2016**

**Klaus 1116 East - 11am**

**Title: ***Explicit Two-Source Extractors and Resilient Functions*

**Abstract**:

We explicitly construct an extractor for two independent sources on n bits, each with min-entropy at least log^C n for a large enough constant C. Our extractor outputs one bit and has error n^{-\Omega(1)}. The best previous extractor, by Bourgain, required each source to have min-entropy .499n.

A key ingredient in our construction is an explicit construction of a monotone, almost-balanced boolean function on n bits that is resilient to coalitions of size n^{1-delta}, for any delta>0. In fact, our construction is stronger in that it gives an explicit extractor for a generalization of non-oblivious bit-fixing sources on n bits, where some unknown n-q bits are chosen almost polylog(n)-wise independently, and the remaining q=n^{1-\delta} bits are chosen by an adversary as an arbitrary function of the n-q bits. The best previous construction, by Viola, achieved q=n^{1/2 - \delta}.

Our explicit two-source extractor directly implies an explicit construction of a 2^{(log log N)^{O(1)}}-Ramsey graph over N vertices, improving bounds obtained by Barak et al. and matching independent work by Cohen.

Joint work with Eshan Chattopadhyay.

**Bio: **

David Zuckerman holds an Endowed Professorship in the Computer Science Department at the University of Texas at Austin. He received an A.B. in Mathematics from Harvard University in 1987 and a Ph.D. in Computer Science from U.C. Berkeley in 1991. He was a postdoctoral fellow at MIT from 1991-1993, and at Hebrew University in the Fall of 1993. He has been with the University of Texas since then, visiting U.C. Berkeley from 1999-2000, Harvard University from 2004-2005, and the Institute for Advanced Study from 2011-12.

His research focuses primarily on pseudorandomness and the role of randomness in computing. He is best known for his work on randomness extractors and their applications. His other research interests include coding theory, distributed computing, cryptography, inapproximability, and other areas of complexity theory. His research awards include a Simons Investigator Award, a Best Paper Award at STOC 2016, ACM Fellow, a Guggenheim Fellowship, a Packard Fellowship for Science and Engineering, a Sloan Research Fellowship, and an NSF Young Investigator Award.