Complexity and Condition in Algebra and Numerics

Optimization, complexity and invariant theory

Author(s): Peter Bürgisser
Published in: Proc. 38th International Symposium on Theoretical Aspects of Computer Science, 2021
Publisher: Leibniz-Zentrum für Informatik
DOI: 10.4230/lipics.stacs.2021.1

Generalised cone complexes and tropical moduli in polymake

Author(s): Dominic Bunnett, Michael Joswig, Julian Pfeifle
Published in: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation, 2024, Page(s) 100-106
Publisher: ACM
DOI: 10.1145/3597066.3597093

Complexity of Robust Orbit Problems for Torus Actions and the abc-conjecture

Author(s): Bürgisser, Peter; Doğan, Mahmut Levent; Makam, Visu; Walter, Michael;Wigderson, Avi
Published in: Proceedings 39th Computational Complexity Conference, LIPIcs. Leibniz Int. Proc. Inform., 300, 2024
Publisher: Schloss Dagstuhl. Leibniz-Zentrum für Informatik, Wadern, 2024
DOI: 10.4230/lipics.ccc.2024.14

Solving Sparse Polynomial Systems using Gröbner Bases and Resultants

Author(s): Matías R. Bender
Published in: Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, 2023, Page(s) 21-30
Publisher: ACM
DOI: 10.1145/3476446.3535498

Gröbner Basis over Semigroup Algebras - Algorithms and Applications for Sparse Polynomial Systems

Author(s): Matías R. Bender, Jean-Charles Faugère, Elias Tsigaridas
Published in: Proceedings of the 2019 on International Symposium on Symbolic and Algebraic Computation, 2019, Page(s) 42-49, ISBN 9781450360845
Publisher: ACM
DOI: 10.1145/3326229.3326248

Polynomial time algorithms in invariant theory for torus actions

Author(s): Peter Bürgisser, Levent Dogan, Visu Makam, Michael Walter, Avi Wigderson
Published in: Proc. 36th Computational Complexity Conference, 2021, 2021
Publisher: Leibniz-Zentrum für Informatik
DOI: 10.4230/lipics.ccc.2021.32

Barriers for recent methods in geodesic optimization

Author(s): Cole Franks, Philipp Reichenbach
Published in: Proc. 36th Computational Complexity Conference, 2021, 2021
Publisher: Leibniz-Zentrum für Informatik
DOI: 10.4230/lipics.ccc.2021.13

Real zeros of mixed random fewnomial systems

Author(s): Peter Burgisser
Published in: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation, 2024, Page(s) 107-115
Publisher: ACM
DOI: 10.1145/3597066.3597105

On the Order of Power Series and the Sum of Square Roots Problem

Author(s): Gorav Jindal, Louis Gaillard
Published in: Proceedings of the 2023 International Symposium on Symbolic and Algebraic Computation, 2024, Page(s) 354-362
Publisher: ACM
DOI: 10.1145/3597066.3597079

Towards a Theory of Non-Commutative Optimization: Geodesic 1st and 2nd Order Methods for Moment Maps and Polytopes

Author(s): Peter Burgisser, Cole Franks, Ankit Garg, Rafael Oliveira, Michael Walter, Avi Wigderson
Published in: 2019 IEEE 60th Annual Symposium on Foundations of Computer Science (FOCS), 2019, Page(s) 845-861, ISBN 978-1-7281-4952-3
Publisher: IEEE
DOI: 10.1109/focs.2019.00055

Random Points on an Algebraic Manifold

Author(s): Paul Breiding, Orlando Marigliano
Published in: SIAM Journal on Mathematics of Data Science, Issue 2/3, 2020, Page(s) 683-704, ISSN 2577-0187
Publisher: SIAM
DOI: 10.1137/19m1271178

Algebraic compressed sensing

Author(s): Paul Breiding; Fulvio Gesmundo; Mateusz Michałe; Nick Vannieuwenhoven
Published in: Applied and Computational Harmonic Analysis, Issue Volume 65, 2023, Page(s) 374-406, ISSN 1063-5203
Publisher: Academic Press
DOI: 10.1016/j.acha.2023.03.006

A Bridge between Invariant Theory and Maximum Likelihood Estimation

Author(s): Carlos Améndola, Kathlén Kohn, Philipp Reichenbach, Anna Seigal
Published in: SIAM Review, Issue 66, 2024, Page(s) 721-747, ISSN 0036-1445
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/24m1661753

On the moduli of hypersurfaces in toric orbifolds

Author(s): Dominic Bunnett
Published in: Proceedings of the Edinburgh Mathematical Society, Issue 67, 2024, Page(s) 577-616, ISSN 0013-0915
Publisher: Cambridge University Press
DOI: 10.1017/s0013091524000166

Certifying Zeros of Polynomial Systems Using Interval Arithmetic

Author(s): Paul Breiding; Kemal Rose; Sascha Timme
Published in: ACM Transactions on Mathematical Software, Issue Volume 49, Issue 121, 2023, Page(s) 1–14, ISSN 0098-3500
Publisher: Association for Computing Machinary, Inc.
DOI: 10.1145/3580277

Dimension results for extremal-generic polynomial systems over complete toric varieties

Author(s): Matías Bender, Pierre-Jean Spaenlehauer
Published in: Journal of Algebra, Issue 646, 2024, Page(s) 156-182, ISSN 0021-8693
Publisher: Academic Press
DOI: 10.1016/j.jalgebra.2024.01.029

Cotilting sheaves over weighted noncommutative regular projective curves

Author(s): Dirk Kussin, Rosanna Laking
Published in: Doc. Math. 25, Issue 25, 2020, Page(s) 1029–1077, ISSN 1431-0643
Publisher: DMV
DOI: 10.25537/dm.2020v25.1029-1077

The Complexity of Factors of Multivariate Polynomials

Author(s): Peter Bürgisser
Published in: Foundations of Computational Mathematics, Issue 4, 2020, Page(s) 369-396, ISSN 1615-3375
Publisher: Springer Verlag
DOI: 10.1007/s10208-002-0059-5

The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite

Author(s): Carlos Beltran; Paul Breiding; Nick Vannieuwenhoven
Published in: Foundations of Computational Mathematics, Issue 23, pages, 2023, Page(s) 433–491, ISSN 1615-3375
Publisher: Springer Verlag
DOI: 10.1007/s10208-022-09551-1

Toric invariant theory for maximum likelihood estimation in log-linear models

Author(s): Carlos Améndola, Kathlén Kohn, Philipp Reichenbach, Anna Seigal
Published in: Algebraic Statistics, Issue 12, 2024, Page(s) 187-211, ISSN 2693-3004
Publisher: New York Business Global
DOI: 10.2140/astat.2021.12.187

Equations for GL Invariant Families of Polynomials

Author(s): Paul Breiding, Reuven Hodges, Christian Ikenmeyer, Mateusz Michałek
Published in: Vietnam Journal of Mathematics, Issue 50, 2022, Page(s) 545-556, ISSN 2305-221X
Publisher: Springer Science + Business Media
DOI: 10.1007/s10013-022-00549-4

Symmetries in directed Gaussian graphical models

Author(s): Visu Makam, Philipp Reichenbach, Anna Seigal
Published in: Electronic Journal of Statistics, Issue 17, 2023, Page(s) 2397-2429,, ISSN 1935-7524
Publisher: Institute of Mathematical Statistics
DOI: 10.1214/23-ejs2192

Koszul-Type Determinantal Formulas for Families of Mixed Multilinear Systems

Author(s): Matías R. Bender, Jean-Charles Faugère, Angelos Mantzaflaris, Elias Tsigaridas
Published in: SIAM Journal on Applied Algebra and Geometry, Issue 5, 2021, Page(s) 589-619, ISSN 2470-6566
Publisher: SIAM
DOI: 10.1137/20m1332190

Rigid continuation paths II. structured polynomial systems

Author(s): Peter Bürgisser, Felipe Cucker, Pierre Lairez
Published in: Forum of Mathematics, Pi, Issue 11, 2023, ISSN 2050-5086
Publisher: Cambridge University Press
DOI: 10.1017/fmp.2023.7

Corrigendum: Invariant Theory and Scaling Algorithms for Maximum Likelihood Estimation

Author(s): Carlos Améndola, Kathlén Kohn, Philipp Reichenbach, Anna Seigal
Published in: SIAM Journal on Applied Algebra and Geometry, Issue 8, 2024, Page(s) 460-463, ISSN 2470-6566
Publisher: SIAM
DOI: 10.1137/23m1588317

Sensitivity of low-rank matrix recovery

Author(s): Paul Breiding; Nick Vannieuwenhoven
Published in: Numerische Mathematik, Issue volume 152, 2022, Page(s) 725–759, ISSN 0945-3245
Publisher: Springer Verlag
DOI: 10.1007/s00211-022-01327-7

On the average condition number of tensor rank decompositions

Author(s): Paul Breiding, Nick Vannieuwenhoven
Published in: IMA Journal of Numerical Analysis, Issue 40/3, 2019, Page(s) 1908-1936, ISSN 0272-4979
Publisher: Oxford University Press
DOI: 10.1093/imanum/drz026

The zonoid algebra, generalized mixed volumes, and random determinants

Author(s): Paul Breiding, Peter Bürgisser, Antonio Lerario, Léo Mathis
Published in: Advances in Mathematics, Issue 402, 2022, Page(s) 108361, ISSN 0001-8708
Publisher: Academic Press
DOI: 10.1016/j.aim.2022.108361

On the Complexity of Chow and Hurwitz Forms

Author(s): M. Levent Dogan, Alperen A. Ergür, Elias Tsigaridas
Published in: ACM Communications in Computer Algebra, Issue 57, 2024, Page(s) 167-199, ISSN 1932-2240
Publisher: ACM
DOI: 10.1145/3653002.3653003

The real tau‐conjecture is true on average

Author(s): Irénée Briquel, Peter Bürgisser
Published in: Random Structures & Algorithms, Issue 57/2, 2020, Page(s) 279-303, ISSN 1042-9832
Publisher: John Wiley & Sons Inc.
DOI: 10.1002/rsa.20926

How many eigenvalues of a random symmetric tensor are real?

Author(s): Paul Breiding
Published in: Transactions of the American Mathematical Society, Issue 372/11, 2019, Page(s) 7857-7887, ISSN 0002-9947
Publisher: American Mathematical Society
DOI: 10.1090/tran/7910

Random Spectrahedra

Author(s): Paul Breiding, Khazhgali Kozhasov, Antonio Lerario
Published in: SIAM Journal on Optimization, Issue 29/4, 2019, Page(s) 2608-2624, ISSN 1052-6234
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/18m1208812

Probabilistic Schubert calculus

Author(s): Peter Bürgisser, Antonio Lerario
Published in: Journal für die reine und angewandte Mathematik (Crelles Journal), Issue 2020/760, 2020, Page(s) 1-58, ISSN 0075-4102
Publisher: Walter de Gruyter GmbH & Co. KG
DOI: 10.1515/crelle-2018-0009

On the Number of Real Zeros of Random Fewnomials

Author(s): Peter Bürgisser, Alperen A. Ergür, Josué Tonelli-Cueto
Published in: SIAM Journal on Applied Algebra and Geometry, Issue 3/4, 2019, Page(s) 721-732, ISSN 2470-6566
Publisher: SIAM
DOI: 10.1137/18m1228682

3264 Conics in a Second

Author(s): Sascha Timme, Paul Breiding, Bernd Sturmfels
Published in: Notices of the American Mathematical Society, Issue 67/01, 2020, Page(s) 1, ISSN 0002-9920
Publisher: Mathematical Association of America
DOI: 10.1090/noti2010

An Algebraic Geometric Perspective on Topological Data Analysis

Author(s): Paul Breiding
Published in: SIAM News, Issue 53(1), 2020, ISSN 0003-1224
Publisher: SAGE Publications

Computing the Homology of Semialgebraic Sets. I: Lax Formulas

Author(s): Peter Bürgisser, Felipe Cucker, Josué Tonelli-Cueto
Published in: Foundations of Computational Mathematics, Issue 20/1, 2020, Page(s) 71-118, ISSN 1615-3375
Publisher: Springer Verlag
DOI: 10.1007/s10208-019-09418-y

No occurrence obstructions in geometric complexity theory

Author(s): Peter Bürgisser, Christian Ikenmeyer, Greta Panova
Published in: Journal of the American Mathematical Society, Issue 32/1, 2019, Page(s) 163-193, ISSN 0894-0347
Publisher: American Mathematical Society
DOI: 10.1090/jams/908

Pencil-Based Algorithms for Tensor Rank Decomposition are not Stable

Author(s): Carlos Beltrán, Paul Breiding, Nick Vannieuwenhoven
Published in: SIAM Journal on Matrix Analysis and Applications, Issue 40/2, 2019, Page(s) 739-773, ISSN 0895-4798
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/18m1200531

Computing the Homology of Basic Semialgebraic Sets in Weak Exponential Time

Author(s): Peter Bürgisser, Felipe Cucker, Pierre Lairez
Published in: Journal of the ACM, Issue 66/1, 2019, Page(s) 1-30, ISSN 0004-5411
Publisher: Association for Computing Machinary, Inc.
DOI: 10.1145/3275242

Computing the Homology of Semialgebraic Sets. II: General Formulas

Author(s): Peter Bürgisser, Felipe Cucker, Josué Tonelli-Cueto
Published in: Foundations of Computational Mathematics, 2021, ISSN 1615-3375
Publisher: Springer Verlag
DOI: 10.1007/s10208-020-09483-8

The Condition Number of Riemannian Approximation Problems

Author(s): Paul Breiding, Nick Vannieuwenhoven
Published in: SIAM Journal on Optimization, Issue 31/1, 2021, Page(s) 1049-1077, ISSN 1052-6234
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/20m1323527

Toric eigenvalue methods for solving sparse polynomial systems

Author(s): Matías Bender, Simon Telen
Published in: Mathematics of Computation, Issue 91, 2022, Page(s) 2397-2429, ISSN 0025-5718
Publisher: American Mathematical Society
DOI: 10.1090/mcom/3744

Quantitative Singularity Theory for Random Polynomials

Author(s): Paul Breiding, Hanieh Keneshlou, Antonio Lerario
Published in: International Mathematics Research Notices, 2020, ISSN 1073-7928
Publisher: Oxford University Press
DOI: 10.1093/imrn/rnaa274

Euclidean distance degree and mixed volume

Author(s): Paul Breiding; Frank Sottile; James Woodcock
Published in: Foundations of Computational Mathematics, Issue 22, 2022, Page(s) 1743–1765, ISSN 1615-3383
Publisher: Springer Verlag
DOI: 10.1007/s10208-021-09534-8

Invariant Theory and Scaling Algorithms for Maximum Likelihood Estimation

Author(s): Carlos Améndola, Kathlén Kohn, Philipp Reichenbach, Anna Seigal
Published in: SIAM Journal on Applied Algebra and Geometry, Issue 5/2, 2021, Page(s) 304-337, ISSN 2470-6566
Publisher: SIAM
DOI: 10.1137/20m1328932

The Multivariate Schwartz--Zippel Lemma

Author(s): M. Levent Doğan, Alperen A. Ergür, Jake D. Mundo, Elias Tsigaridas
Published in: SIAM Journal on Discrete Mathematics, Issue 36, 2022, Page(s) 888-910, ISSN 0895-4801
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/20m1333869

A nearly optimal algorithm to decompose binary forms

Author(s): Matías R. Bender, Jean-Charles Faugère, Ludovic Perret, Elias Tsigaridas
Published in: Journal of Symbolic Computation, Issue 105, 2021, Page(s) 71-96, ISSN 0747-7171
Publisher: Academic Press
DOI: 10.1016/j.jsc.2020.06.002

Classifier Construction in Boolean Networks Using Algebraic Methods

Author(s): Robert Schwieger, Matías R. Bender, Heike Siebert, Christian Haase
Published in: Computational Methods in Systems Biology - 18th International Conference, CMSB 2020, Konstanz, Germany, September 23–25, 2020, Proceedings, Issue 12314, 2020, Page(s) 210-233, ISBN 978-3-030-60326-7
Publisher: Springer International Publishing
DOI: 10.1007/978-3-030-60327-4_12

On the Hardness of PosSLP

Author(s): Peter Bürgisser, Gorav Jindal
Published in: Proceedings of the 2024 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 2024, Page(s) 1872-1886
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/1.9781611977912.75

Mathematical Software – ICMS 2018 - 6th International Conference, South Bend, IN, USA, July 24-27, 2018, Proceedings

Author(s): Paul Breiding, Sascha Timme
Published in: 2018, ISBN 978-3-319-96418-8
Publisher: Springer
DOI: 10.1007/978-3-319-96418-8

Complexity Theory

Author(s): Peter Bürgisser, Irit Dinur, Salil Vadhan
Published in: Oberwolfach Reports, Issue 21, 2024, Page(s) 1517-1562, ISSN 1660-8933
Publisher: EMS Press
DOI: 10.4171/owr/2024/27

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