Factors of Sparse Polynomials are Sparse. - Zeev Dvir; Rafael Oliveira 002 (Electron. Colloquium Comput. Complex., 2014)

Testing Equivalence of Polynomials under Shifts. - Zeev Dvir; Rafael Oliveira 002; Amir Shpilka (Electron. Colloquium Comput. Complex., 2014)

A Deterministic Polynomial Time Algorithm for Non-commutative Rational Identity Testing. - Ankit Garg; Leonid Gurvits; Rafael Mendes de Oliveira; Avi Wigderson (FOCS, 2016)

Factors of low individual degree polynomials. - Rafael Oliveira 002 (Comput. Complex., 2016)

Subexponential Size Hitting Sets for Bounded Depth Multilinear Formulas. - Rafael Oliveira 002; Amir Shpilka; Ben lee Volk (Comput. Complex., 2016)

Rank bounds for design matrices with block entries and geometric applications. - Zeev Dvir; Ankit Garg; Rafael Oliveira 002; József Solymosi (CoRR, 2016)

Algorithmic aspects of Brascamp-Lieb inequalities. - Ankit Garg; Leonid Gurvits; Rafael Mendes de Oliveira; Avi Wigderson (CoRR, 2016)

Locally testable and Locally correctable Codes Approaching the Gilbert-Varshamov Bound. - Sivakanth Gopi; Swastik Kopparty; Rafael Mendes de Oliveira; Noga Ron-Zewi; Shubhangi Saraf (Electron. Colloquium Comput. Complex., 2016)

Much Faster Algorithms for Matrix Scaling. - Zeyuan Allen-Zhu; Yuanzhi Li; Rafael Mendes de Oliveira; Avi Wigderson (FOCS, 2017)

Algorithmic and optimization aspects of Brascamp-Lieb inequalities, via operator scaling. - Ankit Garg; Leonid Gurvits; Rafael Mendes de Oliveira; Avi Wigderson (STOC, 2017)

Barriers for Rank Methods in Arithmetic Complexity. - Klim Efremenko; Ankit Garg; Rafael Mendes de Oliveira; Avi Wigderson (Electron. Colloquium Comput. Complex., 2017)

Polynomial Identity Testing: Derandomization Results and Applications to Algebraic Computation - Rafael Mendes de Oliveira (2017)

Efficient Algorithms for Tensor Scaling, Quantum Marginals, and Moment Polytopes. - Peter Bürgisser; Cole Franks; Ankit Garg; Rafael Mendes de Oliveira; Michael Walter 005; Avi Wigderson (FOCS, 2018)

Alternating Minimization, Scaling Algorithms, and the Null-Cone Problem from Invariant Theory. - Peter Bürgisser; Ankit Garg; Rafael Mendes de Oliveira; Michael Walter 005; Avi Wigderson (ITCS, 2018)

Operator scaling via geodesically convex optimization, invariant theory and polynomial identity testing. - Zeyuan Allen-Zhu; Ankit Garg; Yuanzhi Li; Rafael Mendes de Oliveira; Avi Wigderson (STOC, 2018)

Recent progress on scaling algorithms and applications. - Ankit Garg; Rafael Mendes de Oliveira (Electron. Colloquium Comput. Complex., 2018)

Towards a Theory of Non-Commutative Optimization: Geodesic 1st and 2nd Order Methods for Moment Maps and Polytopes. - Peter Bürgisser; Cole Franks; Ankit Garg; Rafael Mendes de Oliveira; Michael Walter 005; Avi Wigderson (FOCS, 2019)

More Barriers for Rank Methods, via a "numeric to Symbolic" Transfer. - Ankit Garg; Visu Makam; Rafael Mendes de Oliveira; Avi Wigderson (FOCS, 2019)

Towards a theory of non-commutative optimization: geodesic first and second order methods for moment maps and polytopes. - Peter Bürgisser; Cole Franks; Ankit Garg; Rafael Mendes de Oliveira; Michael Walter 005; Avi Wigderson (CoRR, 2019)

Search problems in algebraic complexity, GCT, and hardness of generator for invariant rings. - Ankit Garg; Visu Makam; Rafael Mendes de Oliveira; Avi Wigderson (Electron. Colloquium Comput. Complex., 2019)

Towards Optimal Depth Reductions for Syntactically Multilinear Circuits. - Mrinal Kumar 001; Rafael Mendes de Oliveira; Ramprasad Saptharishi (Electron. Colloquium Comput. Complex., 2019)

Search Problems in Algebraic Complexity, GCT, and Hardness of Generators for Invariant Rings. - Ankit Garg; Christian Ikenmeyer; Visu Makam; Rafael Mendes de Oliveira; Michael Walter 005; Avi Wigderson (CCC, 2020)

Conditional lower bounds on the spectrahedral representation of explicit hyperbolicity cones. - Rafael Oliveira 002 (ISSAC, 2020)

Operator Scaling: Theory and Applications. - Ankit Garg; Leonid Gurvits; Rafael Mendes de Oliveira; Avi Wigderson (Found. Comput. Math., 2020)

Near optimal sample complexity for matrix and tensor normal models via geodesic convexity. - Cole Franks; Rafael Mendes de Oliveira; Akshay Ramachandran; Michael Walter 005 (CoRR, 2021)

Radical Sylvester-Gallai Theorem for Cubics. - Rafael Oliveira 002; Akash Kumar Sengupta (FOCS, 2022)

Robust Radical Sylvester-Gallai Theorem for Quadratics. - Abhibhav Garg; Rafael Mendes de Oliveira; Akash Kumar Sengupta (Electron. Colloquium Comput. Complex., 2022)

Radical Sylvester-Gallai for Cubics. - Rafael Mendes de Oliveira; Akash Kumar Sengupta (Electron. Colloquium Comput. Complex., 2022)

Radical Sylvester-Gallai Theorem for Tuples of Quadratics. - Abhibhav Garg; Rafael Mendes de Oliveira; Shir Peleg; Akash Kumar Sengupta (Electron. Colloquium Comput. Complex., 2023)

Strong Algebras and Radical Sylvester-Gallai Configurations. - Rafael Oliveira 002; Akash Kumar Sengupta (STOC, 2024)

Primes via Zeros: Interactive Proofs for Testing Primality of Natural Classes of Ideals. - Abhibhav Garg; Rafael Mendes de Oliveira; Nitin Saxena 001 (Electron. Colloquium Comput. Complex., 2025)

Uniform Bounds on Product Sylvester-Gallai Configurations. - Abhibhav Garg; Rafael Mendes de Oliveira; Akash Kumar Sengupta (Electron. Colloquium Comput. Complex., 2025)

Rank Bounds and PIT for $ Sigma^3 Pi Sigma Pi^d$ circuits via a non-linear Edelstein-Kelly theorem. - Abhibhav Garg; Rafael Mendes de Oliveira; Akash Kumar Sengupta (Electron. Colloquium Comput. Complex., 2025)

Rank Bounds and PIT for Σ3 ΠΣΠd circuits via a non-linear Edelstein-Kelly theorem. - Abhibhav Garg; Rafael Oliveira 002; Akash Kumar Sengupta (CoRR, 2025)