Papers
o
Quasilinear time list-decodable codes for
space bounded channels
with Ronen Shaltiel
and Jad Silbak
o
DEEP-FRI: Sampling outside the box improves soundness
with Eli Ben-Sasson,
Lior Goldberg and Shubhangi
Saraf
o
On multilinear forms: bias, correlation and
tensor rank
with Abhishek Bhrushundi,
Prahladh Harsha, Pooya Hatami and Mrinal Kumar
o
On list recovery of high rate tensor codes
with Nicolas Resch, Noga Ron-Zewi, Shubhangi Saraf and Shashwat Silas
o
Improved decoding of folded Reed-Solomon and
multiplicity codes
with Noga
Ron-Zewi, Shubhangi Saraf and Mary Wootters
o
Worst case to average case reductions for the distance to a
code
with Eli Ben-Sasson
and Shubhangi Saraf
o
Syndrome decoding of Reed-Muller codes and tensor
decomposition over finite fields
with Aditya Potukuchi
o
Near-optimal approximation algorithm for simultaneous
MAXCUT
with Amey Bhangale, Subhash Khot, Sushant Sachdeva and Deva Thiruvenkatachari
o
Maximally recoverable codes for grid-like topologies
with Parikshit
Gopalan, Guangda Hu, Shubhangi Saraf, Carol Wang and
Sergey Yekhanin
o
Local testing and decoding of high-rate
error-correcting codes (a survey)
with Shubhangi
Saraf
o
Robust Positioning Patterns
with Ross Berkowitz
o
Locally-testable and locally-correctable codes
approaching the Gilbert-Varshamov bound
with Sivakanth
Gopi, Rafael Oliveira, Noga
Ron-Zewi and Shubhangi Saraf
o
On strictly nonzero integer-valued charges
with K.P.S. Bhaskara
Rao
o
Decoding Reed-Muller codes on product
sets
with John Kim
o
A Cauchy-Davenport theorem for linear maps
with Simao Herdade and John Kim
o
High rate locally-testable codes with quasipolylogarithmic query complexity
with Or Meir, Noga
Ron-Zewi and Shubhangi Saraf
o
High rate locally-correctable codes and locally-testable
codes with subpolynomial query complexity
with Or Meir, Noga
Ron-Zewi and Shubhangi
Saraf
o
Indexing necklaces and irreducible polynomials over
finite fields
with Mrinal
Kumar and Mike Saks
(video)
o
The complexity of computing the minimum rank of a sign
pattern matrix
with Amey Bhangale
o
A local central limit theorem for triangles in a random
graph
with Justin Gilmer
o
List-decoding algorithms for lifted codes
with Alan Guo
o
Simultaneous approximation of constraint satisfaction
problems
with Amey Bhangale and Sushant Sachdeva
o Efficient indexing of necklaces and irreducible
polynomials over finite fields
with Mrinal Kumar and Mike Saks
o
Some remarks on multiplicity codes
(a survey)
o
Equivalence of polynomial identity testing and
multivariate polynomial factorization
with Shubhangi
Saraf and Amir Shpilka
o
Roots and coefficients of polynomials over finite
fields
with Qiang
Wang
o
Constant rate PCPs for Circuit-SAT with sublinear query
complexity
with Eli Ben-Sasson,
Yohay Kaplan, Or Meir and Henning Stichtenoth
(video)
o
Explicit subspace designs
with Venkatesan
Guruswami
(video)
o
New affine-invariant codes from lifting
with Alan Guo
and Madhu Sudan
o
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
o
Certifying polynomials for AC0(Parity),
with applications
with Srikanth Srinivasan
(video)
o
List-decoding Multiplicity Codes
(video)
o
On the complexity of powering in finite fields
(video 1, video 2)
o
High-rate codes with sublinear-time decoding
with Shubhangi Saraf and Sergey Yekhanin
(video 1, video
2)
o
On the List-Decodability
of Random Linear Codes
with Venkatesan Guruswami and Johan Håstad
o
Local List-Decoding and Testing of Sparse Random Linear
Codes from High-Error
with Shubhangi Saraf
o
Optimal Testing of Reed-Muller Codes
with Arnab Bhattacharyya, Grant Schoenebeck, Madhu Sudan and
David Zuckerman
o
Affine Dispersers from Subspace Polynomials
with Eli Ben-Sasson
(video)
o
Random Graphs and the Parity Quantifier
with Phokion Kolaitis
o
Kakeya-type sets in finite
vector spaces
with Vsevolod
Lev, Shubhangi Saraf and
Madhu Sudan
o
Extensions to the Method of Multiplicities, with
applications to Kakeya Sets and Mergers
with Zeev Dvir, Shubhangi Saraf and Madhu Sudan
o
Tolerant Linearity Testing and Locally Testable Codes
with Shubhangi Saraf
o
On the Communication
Complexity of Read-Once AC0 formulae
with T.S. Jayram
and Prasad Raghavendra
o
The Universal Capacity of of
Channels with Given Rate-Distortion in the absence of Common Randomness
with Mukul
Agarwal and Sanjoy Mitter
o
The Homomorphism Domination Exponent
with Benjamin Rossman
o
Detecting Rational Points on Hypersurfaces over Finite
Fields
with Sergey Yekhanin
o
Decodability of Group Homomorphisms
beyond the Johnson Bound
with Irit Dinur, Elena Grigorescu and
Madhu Sudan
o
The Minimum Rank Problem: a
counterexample
with K.P.S. Bhaskara
Rao
o
Local Decoding and Testing of Group Homomorphisms
with Elena Grigorescu
and Madhu Sudan
o
Subspace Polynomials and List Decoding of Reed-Solomon Codes
with Eli Ben-Sasson
and Jaikumar Radhakrishnan
|
Local links
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Ph.D. Students
Current: Abhishek
Bhrushundi, Vishvajeet
Nagargoje, Aditya Potukuchi,
Justin Semonsen
Graduated: Brian Garnett (2016), John
Kim (2016), Ross Berkowitz (2017), Amey Bhangale (2017), Mrinal
Kumar (2017), Danny Scheinerman (2018)
Courses
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
Some
open problems about codes (Intractability center)
Error-correcting
codes (IAS “mathematical conversation”)
|
Swastik Kopparty