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| 2013 | PhD, University of California, Berkeley, CA, USA | | 2013 - 2015 | Postdoc, University of Texas, Austin, TX, USA | | since 2015 | Bonn Junior Fellow, University of Bonn | | since 2015 | Assistant Professor, University of Texas, Austin, TX, USA |
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Much of my recent research has concerned functional inequalities for Gaussian measures. As a representative example of this, I have worked on Borell's ''noise sensitivity'' inequality, which can be seen as a strengthening of the Gaussian isoperimetric inequality, or as a Gaussian version of Riesz' rearrangement inequality. From a more applied point of view, Borell's inequality and its discrete relatives played a surprising and crucial role in studying hardness of approximation in theoretical computer science. My first work on this problem concerned the rigidity and stability of Borell's inequality. Elchanan Mossel and I proved that half-spaces are the unique minimizers of noise sensitivity, and that all almost-minimizers are close to half-spaces in some sense. With Anindya De and Elchanan Mossel, I moved onto a discrete version of Borell's inequality, known as the ''majority is stablest'' theorem because of its interpretation in social choice theory. We gave a short and elementary proof of the ''majority is stablest'' theorem. Our proof was so simple that we were also able to express (an approximate version) as a constant-degree ''sum of squares'' proof, which had some implications in theoretical computer science.
Future work will address Gaussian inequalities that involve partitions of Gaussian space into three or more parts. There are many open problems involving such partitions; for example, the ''propellor'' conjecture of Khot and Naor, the Gaussian double-bubble problem, and the ''peace sign conjecture'' on the extension of Borell's inequality to three parts. (So far, I only have some negative results on this last problem with Steven Heilman and Elchanan Mossel.) Other work will involve applications of the existing results and methods. For example, a rounding technique that I helped develop in order to explore the link between Borell's inequality and the Gaussian isoperimetric inequality has implications for structural properties of Gaussian polynomials, and communication problems in computer science. This is the subject of ongoing work with Anindya De and Elchanan Mossel.
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[ 1] Elchanan Mossel, Joe Neeman, Allan Sly
Belief propagation, robust reconstruction and optimal recovery of block models
Ann. Appl. Probab. , 26: (4): 2211--2256
2016
DOI: 10.1214/15-AAP1145[ 2] Anindya De, Elchanan Mossel, Joe Neeman
Majority is stablest: discrete and SoS
Theory Comput. , 12: : Paper No. 4, 50
2016
DOI: 10.4086/toc.2016.v012a004[ 3] Steven Heilman, Elchanan Mossel, Joe Neeman
Standard simplices and pluralities are not the most noise stable
Israel J. Math. , 213: (1): 33--53
2016
DOI: 10.1007/s11856-016-1320-y[ 4] Elchanan Mossel, Joe Neeman, Allan Sly
Consistency thresholds for the planted bisection model
Electron. J. Probab. , 21: : Paper No. 21, 24
2016
DOI: 10.1214/16-EJP4185[ 5] Elchanan Mossel, Joe Neeman, Allan Sly
Reconstruction and estimation in the planted partition model
Probab. Theory Related Fields , 162: (3-4): 431--461
2015
DOI: 10.1007/s00440-014-0576-6[ 6] Elchanan Mossel, Joe Neeman
Robust dimension free isoperimetry in Gaussian space
Ann. Probab. , 43: (3): 971--991
2015
DOI: 10.1214/13-AOP860[ 7] Elchanan Mossel, Joe Neeman
Robust optimality of Gaussian noise stability
J. Eur. Math. Soc. (JEMS) , 17: (2): 433--482
2015
DOI: 10.4171/JEMS/507[ 8] Joe Neeman
Testing surface area with arbitrary accuracy
STOC'14---Proceedings of the 2014 ACM Symposium on Theory of Computing
Publisher: ACM, New York
2014[ 9] Joe Neeman
A multidimensional version of noise stability
Electron. Commun. Probab. , 19: : no. 72, 10
2014
DOI: 10.1214/ECP.v19-3005[ 10] Siu On Chan, Elchanan Mossel, Joe Neeman
On extracting common random bits from correlated sources on large alphabets
IEEE Trans. Inform. Theory , 60: (3): 1630--1637
2014
DOI: 10.1109/TIT.2014.2301155 |
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| 2018 | Alfred P. Sloan Fellowship | | 2020 | Award for best paper in information theory 2020 from IEEE for publication \"Consistency thresholds for the planted bisection model\" |
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