Publications

An averagecase depth hierarchy theorem for Boolean circuits.
with Benjamin Rossman and Rocco Servedio.
FOCS 2015.
Blog posts: Computational Complexity, ShtetlOptimized, Gödel's Lost Letter and P=NP, Combinatorics and more.
Boaz Barak's lecture notes, Simons Institute research vignette.

Learning circuits with few negations.
with Eric Blais, Clément Canonne, Igor Oliveira, and Rocco Servedio.
RANDOM 2015. 
Adaptivity helps for testing juntas.
with Rocco Servedio and John Wright.
CCC 2015. [John's slides] 
Boolean monotonicity testing requires (almost) n^{1/2} nonadaptive queries.
with Xi Chen, Anindya De, and Rocco Servedio.
STOC 2015. [slides]
See also [KhotMinzerSafra] for the matching upper bound,
and Clément Canonne's open problem. 
Approximate resilience, monotonicity, and the complexity of agnostic learning.
with Dana DachmanSoled, Vitaly Feldman, Andrew Wan, and Karl Wimmer.
SODA 2015. 
New algorithms and lower bounds for monotonicity testing.
with Xi Chen and Rocco Servedio.
FOCS 2014. [video 1, video 2, scribe notes]
See also [ChenDeServedioT] for an improved lower bound. 
On DNF approximators for monotone Boolean functions.
with Eric Blais, Johan Håstad, and Rocco Servedio.
ICALP 2014. [Eric's slides]
Blog post: Process Algebra Diary. 
A composition theorem for parity kill number.
with Ryan O'Donnell, Xiaorui Sun, John Wright, and Yu Zhao.
CCC 2014. [Yu's slides] 
Hypercontractive inequalities via SOS, and the FranklRödl graph.
with Manuel Kauers, Ryan O'Donnell, and Yuan Zhou.
SODA 2014. [Yuan's slides] 
Learning sums of independent integer random variables.
with Costis Daskalakis, Ilias Diakonikolas, Ryan O'Donnell, and Rocco Servedio.
FOCS 2013. [video, slides]
Invited to Algorithmica Special Issue on Machine Learning.
Blog post: MIT Theory student blog. 
On the average sensitivity and density of kCNF formulas.
with Dominik Scheder.
RANDOM 2013. 
A composition theorem for the Fourier EntropyInfluence conjecture.

Approximating Boolean functions with depth2 circuits.

Hypercontractivity via the entropy method.
with Eric Blais.
Theory of Computing 9(29), pp. 889896, (2013).
Special issue on Analysis of Boolean Functions. 
New NPhardness results for 3Coloring and 2to1 Label Cover.
with Per Austrin, Ryan O'Donnell, and John Wright.
ACM Transactions on Computation Theory 6(1), Article 2, (2014). 
Attributeefficient learning and weightdegree tradeoffs for
PTFs.
 Bounding the average
sensitivity and noise sensitivity of PTFs.
with Ilias Diakonikolas, Prasad Raghavendra, and Rocco Servedio.
STOC 2010, merged with [HarshaKlivansMeka].
SIAM Journal on Computing 43(1), pp. 231253, (2014). 
A regularity lemma and lowweight approximators for lowdegree PTFs.
with Ilias Diakonikolas, Rocco Servedio, and Andrew Wan.
CCC 2010.
Theory of Computing 10(2), pp. 2753, (2014).  The algebra of equality proofs.
with Aaron Stump.
RTA 2005.
Other writings

Analytic Methods in Concrete Complexity.
Ph.D. Thesis.
Columbia University, 2014. 
2014 Simons Symposium on Discrete Analysis.
5day symposium on Discrete Fourier Analysis.
Guest blogger at AnalysisOfBooleanFunctions.org. 
Analysis of Boolean Functions.
10lecture minicourse by Ryan O'Donnell.
2012 Barbados workshop on Computational Complexity.
Manuscripts

Algorithmic signaling of features in auction design.
with Shaddin Dughmi, Nicole Immorlica, and Ryan O'Donnell. 
Convergence, unanimity, and disagreement in majority dynamics on unimodular graphs and random graphs.
with Itai Benjamini, Siu On Chan, Ryan O'Donnell, and Omer Tamuz. 
Discrete isoperimetry via the entropy method.
with Eric Blais and Andrew Wan. 
On the distribution of the Fourier spectrum of LTFs.
with Ilias Diakonikolas, Ragesh Jaiswal, Rocco Servedio, and Andrew Wan.