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Complexity and Condition in Algebra and Numerics

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Publications

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

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
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

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, 2/3, 2020, Page(s) 683-704, ISSN 2577-0187
Publisher: SIAM
DOI: 10.1137/19m1271178

Cotilting sheaves over weighted noncommutative regular projective curves

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

On the average condition number of tensor rank decompositions

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

The real tau‐conjecture is true on average

Author(s): Irénée Briquel, Peter Bürgisser
Published in: Random Structures & Algorithms, 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, 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, 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), 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, 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, 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, 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, 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, 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, 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, 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, 31/1, 2021, Page(s) 1049-1077, ISSN 1052-6234
Publisher: Society for Industrial and Applied Mathematics
DOI: 10.1137/20m1323527

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

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, 5/2, 2021, Page(s) 304-337, ISSN 2470-6566
Publisher: SIAM
DOI: 10.1137/20m1328932

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, 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, 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

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