Hi, I'm Avishay, an Assistant Professor at the Department of Electrical Engineering and Computer Sciences at UC Berkeley. I am honored to be part of Berkeley's Theory Group.
I received my Ph.D. in 2015 from the Weizmann Institute of Science, under the guidance of Ran Raz. Prior to that, I was an M.Sc. student at the Technion under the guidance of Amir Shpilka. I feel very fortunate to have had both Amir and Ran as my mentors.
I held postdoctoral appointments at the Institute for Advanced Study (hosted by Avi Wigderson), Simons Institute (as part of the Lower Bounds in Computational Complexity program), and Stanford University (hosted by Omer Reingold).
Main Research Interests:
Analysis of Boolean Functions,
Circuit and Formula Lower Bounds,
Computational Learning Theory,
Connections between Algorithms and Lower Bounds.
Motivating questions that guide my research:
What is the power and limitations of parallel computation?
What is the role of randomness in computation?
What is the role of memory in learning?
For which tasks do quantum algorithms outperform classical algorithms?
635 Soda Hall
Department of Electrical Engineering and Computer Sciences
University of California, Berkeley
Berkeley, CA, 94720
E-mail: atal "at" berkeley.edu
Workshop on Derandomizing Space-Bounded Computation (Part of STOC 2020)
Advances in Boolean Function Analysis Lecture Series @ The Simons Institute
CS 294-92 - Analysis of Boolean Functions - Spring 2020
CS 170 - Efficient Algorithms and Intractable Problems - Fall 2020
CS 278 - Computational Complexity Theory - Spring 2021
CS 294-202 - Pseudorandomness - Fall 2021
CS 172 - Spring 2022
Fourier Growth of Parity Decision Trees
joint with Uma Girish and Kewen Wu.
Pseudorandom Generators for Read-Once Monotone Branching Programs
joint with Dean Doron, Raghu Meka, Omer Reingold, and Salil Vadhan.
Fooling Constant-Depth Threshold Circuits
joint with Pooya Hatami, William Hoza, and Roei Tell.
Junta Distance Approximation with Sub-Exponential Queries
joint with Vishnu Iyer and Michael Whitmeyer.
Shrinkage under Random Projections, and Cubic Formula Lower Bounds for AC0
joint with Yuval Filmus and Or Meir.
Degree vs. Approximate Degree and Quantum Implications of Huang's Sensitivity Theorem
joint with Scott Aaronson, Shalev Ben-David, Robin Kothari, and Shravas Rao.
(Subsumes an earlier version named "Quantum Implications of Huang's Sensitivity Theorem")
To be presented at QIP 2021 as a short plenary talk.
Rigid Matrices From Rectangular PCPs
joint with Amey Bhangale, Prahladh Harsha, and Orr Paradise.
Towards Optimal Separations between Quantum and Randomized Query Complexities
Quantum versus Randomized Communication Complexity, with Efficient Players
joint with Uma Girish and Ran Raz.
Presented at the 23rd Annual Conference on Quantum Information Processing (QIP 2020).
On the Computational Power of Radio Channels
joint with Mark Braverman, Gillat Kol, and Rotem Oshman.
Time-Space Lower Bounds for Two-Pass Learning
joint with Sumegha Garg and Ran Raz.
AC0[p] Lower Bounds against MCSP via the Coin Problem
joint with Alexander Golovnev, Rahul Ilango, Russell Impagliazzo, Valentine Kabanets, and Antonina Kolokolova.
Oracle Separation of BQP and PH
joint with Ran Raz.
STOC, 2019. (Best Paper Award)
Presented at the 22nd Annual Conference on Quantum Information Processing (QIP 2019) as a plenary talk.
Exponential separation between shallow quantum circuits and unbounded fan-in shallow classical circuits
joint with Adam Bene Watts, Robin Kothari, and Luke Schaeffer.
Presented at the 22nd Annual Conference on Quantum Information Processing (QIP 2019).
Pseudorandom Generators for Width-3 Branching Programs
joint with Raghu Meka and Omer Reingold.
Pseudorandom generators from the second Fourier level and applications to AC0 with parity gates
joint with Eshan Chattopadhyay, Pooya Hatami, and Shachar Lovett.
Cubic Formula Size Lower Bounds Based on Compositions with Majority
joint with Anna Gal and Adrian Trejo Nuñez.
Improved Pseudorandomness for Unordered Branching Programs through Local Monotonicity
joint with Eshan Chattopadhyay, Pooya Hatami and Omer Reingold.
Extractor-Based Time-Space Lower Bounds for Learning
joint with Sumegha Garg and Ran Raz.
On Constant-Depth Canonical Boolean Circuits for Computing Multilinear Functions
joint with Oded Goldreich.
The Choice and Agreement Problems of a Random Function
joint with Or Meir.
Information Processing Letters, Volume 133, 2018.
Pseudorandom Generators for Low Sensitivity Functions
joint with Pooya Hatami.
joint with Shachar Lovett and Jiapeng Zhang.
Lower Bounds for 2-Query LCCs over Large Alphabet
joint with Arnab Bhattacharyya and Sivakanth Gopi.
Tight Bounds on The Fourier Spectrum of AC0
The Bipartite Formula Complexity of Inner-Product is Quadratic
STOC, 2017 (merged with "Computing Requires Larger Formulas than Approximating").
Computing Requires Larger Formulas than Approximating
STOC, 2017 (merged with "The Bipartite Formula Complexity of Inner-Product is Quadratic").
Time-Space Hardness of Learning Sparse Parities
joint with Gillat Kol and Ran Raz.
Low-Sensitivity Functions from Unambiguous Certificates
joint with Shalev Ben-David and Pooya Hatami.
Degree and Sensitivity: Tails of Two Distributions
joint with Parikshit Gopalan, Rocco Servedio, and Avi Wigderson.
(a preliminary version of this paper by Gopalan, Servedio, and Wigderson appeared in CCC, 2016).
On the Sensitivity Conjecture
#SAT Algorithms from Shrinkage
Matrix Rigidity of Random Toeplitz Matrices
joint with Oded Goldreich.
Computational Complexity, 2016 (preliminary version in STOC, 2016).
Shrinkage of De Morgan Formulae by Spectral Techniques
On Fractional Block Sensitivity
joint with Raghav Kulkarni.
Two Structural Results for Low Degree Polynomials and Applications
joint with Gil Cohen.
An implementation of the algorithm suggested in Theorem 4.1.
On the Structure of Boolean Functions with Small Spectral Norm
joint with Amir Shpilka and Ben lee Volk.
Computational Complexity, 2015 (preliminary version in ITCS, 2014).
Improved Average-Case Lower Bounds for De Morgan Formula Size
joint with Ilan Komargodski and Ran Raz.
SICOMP, 2017 (preliminary version in FOCS, 2013).
Properties and Applications of Boolean Function Composition
ITCS, 2013. (Best Student Paper)
On the Degree of Univariate Polynomials Over the Integers
joint with Gil Cohen and Amir Shpilka.
Combinatorica, 2016 (preliminary version in ITCS, 2012).
On The Minimal Fourier Degree of Symmetric Boolean Functions
joint with Amir Shpilka.
Combinatorica, 2014 (preliminary version in CCC, 2011).