**Avishay Tal**

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:**

Computational Complexity,

Analysis of Boolean Functions,

Circuit and Formula Lower Bounds,

Query Complexity,

Pseudorandomness,

Computational Learning Theory,

Quantum Computing,

Combinatorics, and

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?

**Contact Information**

**Address:**

635 Soda Hall

Department of Electrical Engineering and Computer Sciences

University of California, Berkeley

Berkeley, CA, 94720

**E-mail: **atal "at" berkeley.edu

**Events**

Workshop on Derandomizing Space-Bounded Computation (Part of STOC 2020)

Advances in Boolean Function Analysis Lecture Series @ The Simons Institute

**Teaching**

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

**Program Committees**

FOCS 2019, SODA 2020, CCC 2020, RANDOM 2020, ITCS 2021, STOC 2021

**Publications**

**Fourier Growth of Parity Decision Trees**

joint with Uma Girish and Kewen Wu.

CCC, 2021.

**Pseudorandom Generators for Read-Once Monotone Branching Programs**

joint with Dean Doron, Raghu Meka, Omer Reingold, and Salil Vadhan.

RANDOM, 2021.

**Fooling Constant-Depth Threshold Circuits**

joint with Pooya Hatami, William Hoza, and Roei Tell.

FOCS, 2021.

**Junta Distance Approximation with Sub-Exponential Queries**

joint with Vishnu Iyer and Michael Whitmeyer.

CCC, 2021.

**Shrinkage under Random Projections, and Cubic Formula Lower Bounds for AC0**

joint with Yuval Filmus and Or Meir.

ITCS, 2021.

**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.

STOC, 2021.

**Rigid Matrices From Rectangular PCPs**

joint with Amey Bhangale, Prahladh Harsha, and Orr Paradise.

FOCS, 2020.

**Towards Optimal Separations between Quantum and Randomized Query Complexities**

FOCS, 2020.

**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).

ITCS, 2021.

**On the Computational Power of Radio Channels**

joint with Mark Braverman, Gillat Kol, and Rotem Oshman.

DISC, 2019.

**Time-Space Lower Bounds for Two-Pass Learning**

joint with Sumegha Garg and Ran Raz.

CCC, 2019.

**AC0[p] Lower Bounds against MCSP via the Coin Problem**

joint with Alexander Golovnev, Rahul Ilango, Russell Impagliazzo, Valentine Kabanets, and Antonina Kolokolova.

ICALP, 2019.

**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.

[Computational Complexity Blog] [Shtetl-Optimized] [Windows on Theory]

[New Scientist] [Quanta] [The Hindu] [CACM] [Nature]

Video (CMO Oaxaca) Video (IAS)

**Exponential separation between shallow quantum circuits and unbounded fan-in shallow classical circuits**

joint with Adam Bene Watts, Robin Kothari, and Luke Schaeffer.

STOC, 2019.

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.

STOC, 2019.

**Pseudorandom generators from the second Fourier level and applications to AC0 with parity gates**

joint with Eshan Chattopadhyay, Pooya Hatami, and Shachar Lovett.

ITCS, 2019.

**Cubic Formula Size Lower Bounds Based on Compositions with Majority**

joint with Anna Gal and Adrian Trejo NuĂ±ez.

ITCS, 2019.

**Improved Pseudorandomness for Unordered Branching Programs through Local Monotonicity**

joint with Eshan Chattopadhyay, Pooya Hatami and Omer Reingold.

STOC, 2018.

**Extractor-Based Time-Space Lower Bounds for Learning**

joint with Sumegha Garg and Ran Raz.

STOC, 2018.

**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.

ITCS, 2018.

**Robust Sensitivity**

joint with Shachar Lovett and Jiapeng Zhang.

SODA, 2018.

**Lower Bounds for 2-Query LCCs over Large Alphabet**

joint with Arnab Bhattacharyya and Sivakanth Gopi.

RANDOM, 2017.

**Tight Bounds on The Fourier Spectrum of AC0**

CCC, 2017.

**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.

STOC, 2017.

**Low-Sensitivity Functions from Unambiguous Certificates**

joint with Shalev Ben-David and Pooya Hatami.

ITCS, 2017.

**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**

ICALP, 2016.

**#SAT Algorithms from Shrinkage**

**Matrix Rigidity of Random Toeplitz Matrices**

PDF Journal-version Slides (STOC) Slides (longer version)

joint with Oded Goldreich.

Computational Complexity, 2016 (preliminary version in STOC, 2016).

**Shrinkage of De Morgan Formulae by Spectral Techniques**

FOCS, 2014.

**On Fractional Block Sensitivity**

joint with Raghav Kulkarni.

CJTCS, 2016.

**Two Structural Results for Low Degree Polynomials and Applications**

PDF Video (IAS) Slides (RANDOM)

joint with Gil Cohen.

RANDOM, 2015.

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**

PDF Journal-version Slides Amir@MSR

joint with Amir Shpilka.

Combinatorica, 2014 (preliminary version in CCC, 2011).