Publications

Polylogarithmic Frege depth lower bounds via an expander switching lemma
with Toniann Pitassi, Benjamin Rossman, and Rocco Servedio.
STOC 2016.
Invited to STOC 2016 special issue. 
Nearoptimal smalldepth lower bounds for small distance connectivity
with Xi Chen, Igor Oliveira, and Rocco Servedio.
STOC 2016. 
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.
Stochastic Processes and their Applications 126(9), pp. 27192733, (2016). 
Algorithmic signaling of features in auction design
with Shaddin Dughmi, Nicole Immorlica, and Ryan O'Donnell.
SAGT 2015. 
An averagecase depth hierarchy theorem for Boolean circuits
with Benjamin Rossman and Rocco Servedio.
FOCS 2015.
Best Paper Award at FOCS 2015.
Invited to the Journal of the ACM.See Computational Complexity, ShtetlOptimized, Gödel's Lost Letter and P=NP, Combinatorics and more for discussions of our results. See also Boaz Barak's lecture notes, a Simons Institute research vignette, our invited article in SIGACT News, and a TCS+ talk.

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. 
Boolean monotonicity testing requires (almost) n^{1/2} nonadaptive queries
with Xi Chen, Anindya De, and Rocco Servedio.
STOC 2015.See also [KhotMinzerSafra '15] for the matching upper bound, and [BelovsBlais '16] for an n^{1/4} adaptive lower bound. 
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.Videos of talks at IAS and FOCS, and scribe notes on the lower bound. See also [ChenDeServedioT '15] for a subsequent improvement of the lower bound. 
On DNF approximators for monotone Boolean functions
with Eric Blais, Johan Håstad, and Rocco Servedio.
ICALP 2014. 
A composition theorem for parity kill number
with Ryan O'Donnell, Xiaorui Sun, John Wright, and Yu Zhao.
CCC 2014. 
Hypercontractive inequalities via SOS, and the FranklRödl graph
with Manuel Kauers, Ryan O'Donnell, and Yuan Zhou.
SODA 2014.
Discrete Analysis 2016:4. 
Learning sums of independent integer random variables
with Costis Daskalakis, Ilias Diakonikolas, Ryan O'Donnell, and Rocco Servedio.
FOCS 2013.
Invited to Algorithmica Special Issue on Machine Learning. 
On the average sensitivity and density of kCNF formulas
with Dominik Scheder.
RANDOM 2013. 
A composition theorem for the Fourier EntropyInfluence conjecture
with Ryan O'Donnell.
ICALP 2013.
See also [WanWrightWu '14] for a new proof of our composition theorem. 
Approximating Boolean functions with depth2 circuits
with Eric Blais.
CCC 2013.
SIAM Journal on Computing 44(6), pp. 15831600, (2015).See also Gödel's Lost Letter and P=NP for a discussion of this paper, and [BlaisHåstadServedioT '14] for related results. A video of my talk at the Simons Institute. 
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
with Rocco Servedio and Justin Thaler.
COLT 2012. 
Noise stable halfspaces are close to very small juntas
with Ilias Diakonikolas, Ragesh Jaiswal, Rocco Servedio, and Andrew Wan.
Chicago Journal of Theoretical Computer Science, (2015).  Bounding the average
sensitivity and noise sensitivity of PTFs
with Ilias Diakonikolas, Prasad Raghavendra, and Rocco Servedio.
STOC 2010.
Conference version 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

The Polynomial Hierarchy, Random Oracles, and Boolean Circuits
with Benjamin Rossman and Rocco Servedio.
Invited article in SIGACT News 46(4), December 2015 issue.
Overview of [RossmanServedioT '15], with an emphasis on the connections to structural complexity theory. 
Research Vignette: Hard Problems All the Way Up
with Benjamin Rossman.
UC Berkeley Simons Institute newsletter, Summer 2015 issue.

Analytic Methods in Concrete Complexity
Ph.D. Thesis.
Columbia University, 2014. 
2014 Simons Symposium on Discrete Analysis

Analysis of Boolean Functions
10lecture minicourse by Ryan O'Donnell.
2012 Barbados workshop on Computational Complexity.
Manuscripts

Improved pseudorandom generators for depthtwo circuits
with Rocco Servedio. 
What circuit classes can be learned with nontrivial savings?
with Rocco Servedio. 
Adaptivity is exponentially powerful for testing monotonicity of halfspaces
with Xi Chen, Rocco Servedio, and Erik Waingarten. 
Discrete isoperimetry via the entropy method
with Eric Blais and Andrew Wan.