Published in: LIPIcs, Volume 264, 38th Computational Complexity Conference (CCC 2023)
Abhibhav Garg, Rafael Oliveira, Shir Peleg, and Akash Kumar Sengupta. Radical Sylvester-Gallai Theorem for Tuples of Quadratics. In 38th Computational Complexity Conference (CCC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 264, pp. 20:1-20:30, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
@InProceedings{garg_et_al:LIPIcs.CCC.2023.20, author = {Garg, Abhibhav and Oliveira, Rafael and Peleg, Shir and Sengupta, Akash Kumar}, title = {{Radical Sylvester-Gallai Theorem for Tuples of Quadratics}}, booktitle = {38th Computational Complexity Conference (CCC 2023)}, pages = {20:1--20:30}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-282-2}, ISSN = {1868-8969}, year = {2023}, volume = {264}, editor = {Ta-Shma, Amnon}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2023.20}, URN = {urn:nbn:de:0030-drops-182903}, doi = {10.4230/LIPIcs.CCC.2023.20}, annote = {Keywords: Sylvester-Gallai theorem, arrangements of hypersurfaces, algebraic complexity, polynomial identity testing, algebraic geometry, commutative algebra} }
Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)
Papri Dey, Ravi Kannan, Nick Ryder, and Nikhil Srivastava. Bit Complexity of Jordan Normal Form and Polynomial Spectral Factorization. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 42:1-42:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)
@InProceedings{dey_et_al:LIPIcs.ITCS.2023.42, author = {Dey, Papri and Kannan, Ravi and Ryder, Nick and Srivastava, Nikhil}, title = {{Bit Complexity of Jordan Normal Form and Polynomial Spectral Factorization}}, booktitle = {14th Innovations in Theoretical Computer Science Conference (ITCS 2023)}, pages = {42:1--42:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-263-1}, ISSN = {1868-8969}, year = {2023}, volume = {251}, editor = {Tauman Kalai, Yael}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.42}, URN = {urn:nbn:de:0030-drops-175450}, doi = {10.4230/LIPIcs.ITCS.2023.42}, annote = {Keywords: Symbolic algorithms, numerical algorithms, linear algebra} }
Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)
Abhibhav Garg, Rafael Oliveira, and Akash Kumar Sengupta. Robust Radical Sylvester-Gallai Theorem for Quadratics. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 42:1-42:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)
@InProceedings{garg_et_al:LIPIcs.SoCG.2022.42, author = {Garg, Abhibhav and Oliveira, Rafael and Sengupta, Akash Kumar}, title = {{Robust Radical Sylvester-Gallai Theorem for Quadratics}}, booktitle = {38th International Symposium on Computational Geometry (SoCG 2022)}, pages = {42:1--42:13}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-227-3}, ISSN = {1868-8969}, year = {2022}, volume = {224}, editor = {Goaoc, Xavier and Kerber, Michael}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.42}, URN = {urn:nbn:de:0030-drops-160505}, doi = {10.4230/LIPIcs.SoCG.2022.42}, annote = {Keywords: Sylvester-Gallai theorem, arrangements of hypersurfaces, locally correctable codes, algebraic complexity, polynomial identity testing, algebraic geometry, commutative algebra} }
Published in: LIPIcs, Volume 187, 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)
Peter Bürgisser. Optimization, Complexity and Invariant Theory (Invited Talk). In 38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 187, pp. 1:1-1:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
@InProceedings{burgisser:LIPIcs.STACS.2021.1, author = {B\"{u}rgisser, Peter}, title = {{Optimization, Complexity and Invariant Theory}}, booktitle = {38th International Symposium on Theoretical Aspects of Computer Science (STACS 2021)}, pages = {1:1--1:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-180-1}, ISSN = {1868-8969}, year = {2021}, volume = {187}, editor = {Bl\"{a}ser, Markus and Monmege, Benjamin}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2021.1}, URN = {urn:nbn:de:0030-drops-136460}, doi = {10.4230/LIPIcs.STACS.2021.1}, annote = {Keywords: geometric invariant theory, geodesic optimization, non-commutative optimization, null cone, operator scaling, moment polytope, orbit closure intersection, geometric programming} }
Published in: LIPIcs, Volume 169, 35th Computational Complexity Conference (CCC 2020)
Ankit Garg, Christian Ikenmeyer, Visu Makam, Rafael Oliveira, Michael Walter, and Avi Wigderson. Search Problems in Algebraic Complexity, GCT, and Hardness of Generators for Invariant Rings. In 35th Computational Complexity Conference (CCC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 169, pp. 12:1-12:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)
@InProceedings{garg_et_al:LIPIcs.CCC.2020.12, author = {Garg, Ankit and Ikenmeyer, Christian and Makam, Visu and Oliveira, Rafael and Walter, Michael and Wigderson, Avi}, title = {{Search Problems in Algebraic Complexity, GCT, and Hardness of Generators for Invariant Rings}}, booktitle = {35th Computational Complexity Conference (CCC 2020)}, pages = {12:1--12:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-156-6}, ISSN = {1868-8969}, year = {2020}, volume = {169}, editor = {Saraf, Shubhangi}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2020.12}, URN = {urn:nbn:de:0030-drops-125645}, doi = {10.4230/LIPIcs.CCC.2020.12}, annote = {Keywords: generators for invariant rings, succinct encodings} }
Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)
Mrinal Kumar, Rafael Oliveira, and Ramprasad Saptharishi. Towards Optimal Depth Reductions for Syntactically Multilinear Circuits. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 78:1-78:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)
@InProceedings{kumar_et_al:LIPIcs.ICALP.2019.78, author = {Kumar, Mrinal and Oliveira, Rafael and Saptharishi, Ramprasad}, title = {{Towards Optimal Depth Reductions for Syntactically Multilinear Circuits}}, booktitle = {46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)}, pages = {78:1--78:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-109-2}, ISSN = {1868-8969}, year = {2019}, volume = {132}, editor = {Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.78}, URN = {urn:nbn:de:0030-drops-106548}, doi = {10.4230/LIPIcs.ICALP.2019.78}, annote = {Keywords: arithmetic circuits, multilinear circuits, depth reduction, lower bounds} }
Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)
Klim Efremenko, Ankit Garg, Rafael Oliveira, and Avi Wigderson. Barriers for Rank Methods in Arithmetic Complexity. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 1:1-1:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
@InProceedings{efremenko_et_al:LIPIcs.ITCS.2018.1, author = {Efremenko, Klim and Garg, Ankit and Oliveira, Rafael and Wigderson, Avi}, title = {{Barriers for Rank Methods in Arithmetic Complexity}}, booktitle = {9th Innovations in Theoretical Computer Science Conference (ITCS 2018)}, pages = {1:1--1:19}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-060-6}, ISSN = {1868-8969}, year = {2018}, volume = {94}, editor = {Karlin, Anna R.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.1}, URN = {urn:nbn:de:0030-drops-83506}, doi = {10.4230/LIPIcs.ITCS.2018.1}, annote = {Keywords: Lower Bounds, Barriers, Partial Derivatives, Flattenings, Algebraic Complexity} }
Published in: LIPIcs, Volume 94, 9th Innovations in Theoretical Computer Science Conference (ITCS 2018)
Peter Bürgisser, Ankit Garg, Rafael Oliveira, Michael Walter, and Avi Wigderson. Alternating Minimization, Scaling Algorithms, and the Null-Cone Problem from Invariant Theory. In 9th Innovations in Theoretical Computer Science Conference (ITCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 94, pp. 24:1-24:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
@InProceedings{burgisser_et_al:LIPIcs.ITCS.2018.24, author = {B\"{u}rgisser, Peter and Garg, Ankit and Oliveira, Rafael and Walter, Michael and Wigderson, Avi}, title = {{Alternating Minimization, Scaling Algorithms, and the Null-Cone Problem from Invariant Theory}}, booktitle = {9th Innovations in Theoretical Computer Science Conference (ITCS 2018)}, pages = {24:1--24:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-060-6}, ISSN = {1868-8969}, year = {2018}, volume = {94}, editor = {Karlin, Anna R.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2018.24}, URN = {urn:nbn:de:0030-drops-83510}, doi = {10.4230/LIPIcs.ITCS.2018.24}, annote = {Keywords: alternating minimization, tensors, scaling, quantum marginal problem, null cone, invariant theory, geometric complexity theory} }
Published in: LIPIcs, Volume 33, 30th Conference on Computational Complexity (CCC 2015)
Rafael Oliveira. Factors of Low Individual Degree Polynomials. In 30th Conference on Computational Complexity (CCC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 33, pp. 198-216, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
@InProceedings{oliveira:LIPIcs.CCC.2015.198, author = {Oliveira, Rafael}, title = {{Factors of Low Individual Degree Polynomials}}, booktitle = {30th Conference on Computational Complexity (CCC 2015)}, pages = {198--216}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-81-1}, ISSN = {1868-8969}, year = {2015}, volume = {33}, editor = {Zuckerman, David}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2015.198}, URN = {urn:nbn:de:0030-drops-50594}, doi = {10.4230/LIPIcs.CCC.2015.198}, annote = {Keywords: Arithmetic Circuits, Factoring, Algebraic Complexity} }
Published in: LIPIcs, Volume 33, 30th Conference on Computational Complexity (CCC 2015)
Rafael Oliveira, Amir Shpilka, and Ben Lee Volk. Subexponential Size Hitting Sets for Bounded Depth Multilinear Formulas. In 30th Conference on Computational Complexity (CCC 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 33, pp. 304-322, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)
@InProceedings{oliveira_et_al:LIPIcs.CCC.2015.304, author = {Oliveira, Rafael and Shpilka, Amir and Volk, Ben Lee}, title = {{Subexponential Size Hitting Sets for Bounded Depth Multilinear Formulas}}, booktitle = {30th Conference on Computational Complexity (CCC 2015)}, pages = {304--322}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-81-1}, ISSN = {1868-8969}, year = {2015}, volume = {33}, editor = {Zuckerman, David}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CCC.2015.304}, URN = {urn:nbn:de:0030-drops-50548}, doi = {10.4230/LIPIcs.CCC.2015.304}, annote = {Keywords: Arithmetic Circuits, Derandomization, Polynomial Identity Testing} }
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