Swastik Kopparty
Department of Mathematics and
Department of Computer Science
University of Toronto
swastik.kopparty@utoronto.ca
Research Interests: Theoretical Computer Science, Discrete Mathematics, Error-Correcting Codes, Complexity Theory, Probabilistic and Interactive Proofs, Finite Fields, Randomness and Pseudorandomness.
Previously, I had been a faculty member at Rutgers University for 10 years.
Before that, I did my postdoc at the Institute for Advanced Study, my PhD at MIT, and my undergrad at the University of California, Riverside.
I am a Scientific Advisor to StarkWare.
Papers
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Elliptic Curve Fast Fourier Transform (ECFFT) Part II: Scalable and Transparent Proofs over All Large Fields
with Eli Ben-Sasson, Dan Carmon and David Levit
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Elliptic Curve Fast Fourier Transform (ECFFT) Part I: Fast Polynomial Algorithms over all Finite Fields
with Eli Ben-Sasson, Dan Carmon and David Levit
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Proximity gaps for Reed-Solomon codes
with Eli Ben-Sasson, Dan Carmon, Yuval Ishai and Shubhangi Saraf
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Geometric rank of tensors and subrank of matrix multiplication
with Guy Moshkovitz and Jeroen Zuiddam
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Quasilinear time list-decodable codes for space bounded channels
with Ronen Shaltiel and Jad Silbak
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DEEP-FRI: Sampling outside the box improves soundness
with Eli Ben-Sasson, Lior Goldberg and Shubhangi Saraf
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On multilinear forms: bias, correlation and tensor rank
with Abhishek Bhrushundi, Prahladh Harsha, Pooya Hatami and Mrinal Kumar
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On list recovery of high rate tensor codes
with Nicolas Resch, Noga Ron-Zewi, Shubhangi Saraf and Shashwat Silas
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Improved decoding of folded Reed-Solomon and multiplicity codes
with Noga Ron-Zewi, Shubhangi Saraf and Mary Wootters
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Worst case to average case reductions for the distance to a code
with Eli Ben-Sasson and Shubhangi Saraf
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Syndrome decoding of Reed-Muller codes and tensor decomposition over finite fields
with Aditya Potukuchi
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Near-optimal approximation algorithm for simultaneous MAXCUT
with Amey Bhangale, Subhash Khot, Sushant Sachdeva and Deva Thiruvenkatachari
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Maximally recoverable codes for grid-like topologies
with Parikshit Gopalan, Guangda Hu, Shubhangi Saraf, Carol Wang and Sergey Yekhanin
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Local testing and decoding of high-rate error-correcting codes (a survey)
with Shubhangi Saraf
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Robust Positioning Patterns
with Ross Berkowitz
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Locally-testable and locally-correctable codes approaching the Gilbert-Varshamov bound
with Sivakanth Gopi, Rafael Oliveira, Noga Ron-Zewi and Shubhangi Saraf
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On strictly nonzero integer-valued charges
with K.P.S. Bhaskara Rao
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Decoding Reed-Muller codes on product sets
with John Kim
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A Cauchy-Davenport theorem for linear maps
with Simao Herdade and John Kim
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High rate locally-correctable codes and locally-testable codes with subpolynomial query complexity
with Or Meir, Noga Ron-Zewi and Shubhangi Saraf
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Indexing necklaces and irreducible polynomials over finite fields
with Mrinal Kumar and Mike Saks
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The complexity of computing the minimum rank of a sign pattern matrix
with Amey Bhangale
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A local central limit theorem for triangles in a random graph
with Justin Gilmer
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List-decoding algorithms for lifted codes
with Alan Guo
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Simultaneous approximation of constraint satisfaction problems
with Amey Bhangale and Sushant Sachdeva
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Some remarks on multiplicity codes (a survey)
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Equivalence of polynomial identity testing and multivariate polynomial factorization
with Shubhangi Saraf and Amir Shpilka
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Roots and coefficients of polynomials over finite fields
with Qiang Wang
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Constant rate PCPs for Circuit-SAT with sublinear query complexity
with Eli Ben-Sasson, Yohay Kaplan, Or Meir and Henning Stichtenoth
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Explicit subspace designs
with Venkatesan Guruswami
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New affine-invariant codes from lifting
with Alan Guo and Madhu Sudan
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A new family of locally correctable codes based on degree-lifted algebraic geometry codes
with Eli Ben-Sasson, Ariel Gabizon, Yohay Kaplan and Shubhangi Saraf
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Certifying polynomials for AC0(Parity), with applications
with Srikanth Srinivasan
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List-decoding Multiplicity Codes
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On the complexity of powering in finite fields
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High-rate codes with sublinear-time decoding
with Shubhangi Saraf and Sergey Yekhanin
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On the List-Decodability of Random Linear Codes
with Venkatesan Guruswami and Johan Håstad
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Local List-Decoding and Testing of Sparse Random Linear Codes from High-Error
with Shubhangi Saraf
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Optimal Testing of Reed-Muller Codes
with Arnab Bhattacharyya, Grant Schoenebeck, Madhu Sudan and David Zuckerman
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Affine Dispersers from Subspace Polynomials
with Eli Ben-Sasson
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Random Graphs and the Parity Quantifier
with Phokion Kolaitis
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Kakeya-type sets in finite vector spaces
with Vsevolod Lev, Shubhangi Saraf and Madhu Sudan
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Extensions to the Method of Multiplicities, with applications to Kakeya Sets and Mergers
with Zeev Dvir, Shubhangi Saraf and Madhu Sudan
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Tolerant Linearity Testing and Locally Testable Codes
with Shubhangi Saraf
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On the Communication Complexity of Read-Once AC0 formulae
with T.S. Jayram and Prasad Raghavendra
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The Universal Capacity of of Channels with Given Rate-Distortion in the absence of Common Randomness
with Mukul Agarwal and Sanjoy Mitter
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The Homomorphism Domination Exponent
with Benjamin Rossman
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Detecting Rational Points on Hypersurfaces over Finite Fields
with Sergey Yekhanin
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Decodability of Group Homomorphisms beyond the Johnson Bound
with Irit Dinur, Elena Grigorescu and Madhu Sudan
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The Minimum Rank Problem: a counterexample
with K.P.S. Bhaskara Rao
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Local Decoding and Testing of Group Homomorphisms
with Elena Grigorescu and Madhu Sudan
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Subspace Polynomials and List Decoding of Reed-Solomon Codes
with Eli Ben-Sasson and Jaikumar Radhakrishnan
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Local links
theory events
PhD Students
Current: Harry Sha, Gal Gross
Graduated: Brian Garnett (2016), John Kim (2016), Ross Berkowitz (2017), Amey Bhangale (2017), Mrinal Kumar (2017), Danny Scheinerman (2018), Abhishek Bhrushundi (2020), Aditya Potukuchi (2020), Justin Semonsen (2020), Vishvajeet N (2022)
Courses
Courses at Rutgers (links coming soon)
Intro to Discrete Structures (Spring 2021, Undergrad)
Algorithmic Number Theory (Fall 2020, Grad)
Calculus I – Math 151:22-24 (Fall 2020, Undergrad)
Topics in Algorithms and Complexity Theory (Spring 2020, Grad)
Topics in Finite Fields (Fall 2019, Grad)
Graph Theory (Fall 2019, Undergrad)
Topics in Complexity and Pseudorandomness (Spring 2018, Grad)
Formal Languages and Automata (Spring 2018, Undergrad)
Combinatorics I (Fall 2017, Grad)
Honors Abstract Algebra (Fall 2017, Undergrad)
Problem Solving Seminar (Fall 2017, Undergrad)
Topics in Complexity and Pseudorandomness (Spring 2017, Grad)
Arithmetic Combinatorics (Fall 2016, Grad)
Problem Solving Seminar (Fall 2016, Undergrad)
Error-Correcting Codes (Spring 2016, Grad)
Intro to Discrete Structures I (Spring 2015, Undergrad)
Algorithmic Number Theory (Fall 2014, Grad)
Theory of Numbers (Fall 2014, Undergrad)
Algorithms (Spring 2014, Grad)
Topics in Finite Fields (Fall 2013, Grad)
Problem Solving Seminar (Fall 2013, Undergrad)
Topics in Complexity and Pseudorandomness (Spring 2013, Grad)
Combinatorics I (Fall 2012, Grad)
Problem Solving Seminar (Fall 2012, Undergrad)
Algorithms (Spring 2012, Grad)
Graph Theory (Fall 2011, Grad)
Problem Solving Seminar (Fall 2011, Undergrad)
Videos of miscellaneous talks
Error-correcting codes (IAS “mathematical conversation”)
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