Publications

Strong Algebras and Radical Sylvester-Gallai Configurations
Rafael Oliveira, Akash K Sengupta
56th ACM Symposium on Theory of Computing, STOC 2024 (to appear)
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Radical Sylvester-Gallai Theorem for Tuples of Quadratics
Abhibhav Garg, Rafael Oliveira, Shir Peleg, Akash K Sengupta
38th Computational Complexity Conference, CCC 2023
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Radical Sylvester-Gallai Theorem for Cubics
Rafael Oliveira, Akash K Sengupta
63rd IEEE Symposium on Foundations of Computer Science, FOCS 2022
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Robust Radical Sylvester-Gallai Theorem for Quadratics
Abhibhav Garg, Rafael Oliveira, Akash K Sengupta
38th International Symposium on Computational Geometry, SoCG 2022
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Scaling problems, algorithms and applications to computer science and statistics
Rafael Oliveira, Akshay Ramachandran
Survey, 33o Coloquio Brasileiro de Matematica
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Near-Optimal Sample Complexity for Matrix and Tensor Normal Models via Geodesic Convexity
Cole Franks, Rafael Oliveira, Akshay Ramachandran, Michael Walter
Submitted, 2021
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Conditional Lower Bounds on the Spectrahedral Representation of Explicit Hyperbolicity Cones
Rafael Oliveira
45th International Symposium on Symbolic and Algebraic Computation, ISSAC 2020
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Search problems in algebraic complexity, GCT, and hardness of generator for invariant rings
Ankit Garg, Christian Ikenmeyer, Visu Makam, Rafael Oliveira, Michael Walter, Avi Wigderson
Computational Complexity Conference, CCC 2020
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Towards a theory of non-commutative optimization: geodesic first and second order methods for moment maps and moment polytopes
Peter Buergisser, Cole Franks, Ankit Garg, Rafael Oliveira, Michael Walter, Avi Wigderson
60th Annual Symposium on Foundations of Computer Science, FOCS 2019
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More barriers for rank methods, via a "numeric to symbolic"" transfer
Ankit Garg, Visu Makam, Rafael Oliveira, Avi Wigderson
60th Annual Symposium on Foundations of Computer Science, FOCS 2019
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Towards optimal depth reductions for syntactically multilinear circuits
Mrinal Kumar, Rafael Oliveira, Ramprasad Saptharishi
46th International Colloquium on Automata, Languages, and Programming, ICALP 2019
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Operator scaling: theory and applications
Ankit Garg, Leonid Gurvits, Rafael Oliveira, Avi Wigderson
Foundations of Computational Mathematics, FoCM 2019
A previous version of this paper appeared at FOCS 2016 and at QIP 2017
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Efficient Algorithms for Tensor Scaling, Quantum Marginals and Moment Polytopes
Peter Buergisser, Cole Franks, Ankit Garg, Rafael Oliveira, Michael Walter, Avi Wigderson
59th Annual Symposium on Foundations of Computer Science, FOCS 2018
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Recent Progress on Scaling Algorithms and Applications
Ankit Garg, Rafael Oliveira
Invited Survey, Bulletin of EATCS 2018
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Algorithmic Aspects of Brascamp-Lieb Inequalities, via operator scaling.
Ankit Garg, Leonid Gurvits, Rafael Oliveira, Avi Wigderson
Geometric and Functional Analysis, GAFA 2018
Conference version appeared at STOC 2017
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Rank Bounds for Design Matrices with Block Entries and Geometric Applications
Zeev Dvir, Ankit Garg, Rafael Oliveira, Jozsef Solymosi
Discrete Analysis 2018
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Operator Scaling via Geodesically Convex Optimization, Invariant Theory and Polynomial Identity Testing
Zeyuan Allen-Zhu, Yuanzhi Li, Ankit Garg, Rafael Oliveira, Avi Wigderson
50th Annual ACM SIGACT Symposium on Theory of Computing, STOC 2018
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Barriers for Rank Methods in Arithmetic Complexity
Klim Efremenko, Ankit Garg, Rafael Oliveira, Avi Wigderson
9th Innovations in Theoretical Computer Science Conference, ITCS 2018
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Alternating minimization, scaling algorithms, and the null-cone problem from invariant theory
Peter Buergisser, Ankit Garg, Rafael Oliveira, Michael Walter, Avi Wigderson
9th Innovations in Theoretical Computer Science Conference, ITCS 2018
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Locally Testable and Locally Correctable Codes Approaching the Gilbert-Varshamov Bound
Sivakanth Gopi, Swastik Kopparty, Rafael Oliveira, Noga Ron-Zewi, Shubhangi Saraf
IEEE Transactions on Information Theory 2018
Conference version appeared at SODA 2017
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Much Faster Algorithms for Matrix Scaling
Zeyuan Allen-Zhu, Yuanzhi Li, Rafael Oliveira, Avi Wigderson
58th Annual Symposium on Foundations of Computer Science, FOCS 2017
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Factors of low individual degree polynomials
Rafael Oliveira
Computational Complexity 2016
Best Student Paper at CCC 2015
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Subexponential Size Hitting Sets for Bounded Depth Multilinear Formulas
Rafael Oliveira, Amir Shpilka, Ben Lee Volk
Computational Complexity 2016
Conference version appeared at CCC 2015
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Testing Equivalences of Polynomials under Shifts
Zeev Dvir, Rafael Oliveira, Amir Shpilka
International Colloquium on Automata, Languages, and Programming, ICALP 2014
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