

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 


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 halfspaces are the unique minimizers of noise sensitivity, and that all almostminimizers are close to halfspaces 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 constantdegree ''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 doublebubble 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.


[ 1] Elchanan Mossel, Joe Neeman, Allan Sly
Belief propagation, robust reconstruction and optimal recovery of block models Ann. Appl. Probab. , 26: (4): 22112256 2016 DOI: 10.1214/15AAP1145[ 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): 3353 2016 DOI: 10.1007/s118560161320y[ 4] Elchanan Mossel, Joe Neeman, Allan Sly
Consistency thresholds for the planted bisection model Electron. J. Probab. , 21: : Paper No. 21, 24 2016 DOI: 10.1214/16EJP4185[ 5] Elchanan Mossel, Joe Neeman, Allan Sly
Reconstruction and estimation in the planted partition model Probab. Theory Related Fields , 162: (34): 431461 2015 DOI: 10.1007/s0044001405766[ 6] Elchanan Mossel, Joe Neeman
Robust dimension free isoperimetry in Gaussian space Ann. Probab. , 43: (3): 971991 2015 DOI: 10.1214/13AOP860[ 7] Elchanan Mossel, Joe Neeman
Robust optimality of Gaussian noise stability J. Eur. Math. Soc. (JEMS) , 17: (2): 433482 2015 DOI: 10.4171/JEMS/507[ 8] Joe Neeman
Testing surface area with arbitrary accuracy STOC'14Proceedings 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.v193005[ 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): 16301637 2014 DOI: 10.1109/TIT.2014.2301155



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