Homepage of the project
"Complex contact manifolds and geometry of secants" (CoCoMaGeS)
Polish title:
Zespolone rozmaitości kontaktowe i geometria siecznych
The project was realized within the
Sonata Bis (7th edition)
programme of National Science Centre, Poland.
Time span of the project:
August 1st, 2018 -- July 31st, 2024 (60 months + 12 months of extension)
Project number:
2017/26/E/ST1/00231
Main Location:
Institute of Mathematics of Polish Academy of Sciences (IMPAN), Warsaw, Poland.
Participants:
- Jarosław Buczyński, IMPAN, principal investigator
- Weronika Buczyńska, MIMUW (Math at University of Warsaw), investigator
- Maria Donten-Bury, MIMUW (Math at University of Warsaw), investigator
- Giovanni Moreno, FUW (Physics at University of Warsaw), investigator
- Aleksandra Borówka, postdoc Oct 1st, 2018 - Apr 30th, 2022,
- Francesco Galuppi, postdoc Oct 1st 2021 - Sep 30th, 2023,
- Tomasz Mańdziuk, PhD student Oct 1st, 2018 - Sep 30th, 2020,
- Filip Rupniewski, PhD student Oct 1st, 2019 - Sep 30th, 2021,
- Maciej Gałązka, PhD student Oct 1st, 2020 - Sep 30th, 2022,
- Piotr Oszer, MSc student Oct 1st, 2021 - Sep 30th, 2022,
- Robert Ĺmiech, PhD student May 1st, 2023 - Sep 30th, 2023,
Student scholarships:
The project has a possibility of funding several scholarships
for students in the Master program and PhD program:
Postdoc positions:
Two postdoctoral positions are funded jointly with the Institute of Mathematics of the Polish Academy of Sciences.
Contact manifolds are the main topic of the first position (awarded to Aleksandra Borówka).
The deadline for applications for the first position was April 30th, 2018.
Details and an official announcement are available here.
Secant varieties are the main topic of the second position (awarded to Francesco Galuppi).
The deadline for applications for the second position was May 10th, 2021.
Details and an official announcement are available here.
Articles that resulted from work supported by the grant:
Preprints:
- "Cactus varieties of sufficiently ample embeddings of projective schemes have determinantal equations"
Weronika Buczyńska, Jarosław Buczyński, Łucja Farnik
arXiv:2412.00709
- "Cactus scheme, catalecticant minors, and scheme theoretic equations"
Jarosław Buczyński, Hanieh Keneshlou
arXiv:2410.21908
- "Rank and symmetries of signature tensors"
Francesco Galuppi, Pierpaola Santarsiero
arXiv:2407.20405
- "Invariant Monge-Ampere equations on contactified para-Kähler manifolds"
Dmitri Alekseevsky, Gianni Manno, Giovanni Moreno
arXiv:2402.08315
- "Geometry of first nonempty Terracini loci"
Francesco Galuppi, Pierpaola Santarsiero, Douglas Torrance, Ettore Turatti
arXiv:2311.09067
- "Characteristic polynomials and eigenvalues of tensors"
Francesco Galuppi, Fulvio Gesmundo, Ettore Turatti, Lorenzo Venturello
arXiv:2308.10957
- "Initial values of ML-degree polynomials"
Maciej Gałązka
arXiv:2212.12588
Accepted for publication:
- "Third-order affine-invariant (systems of) PDEs in two independent variables as vanishing of the Fubini-Pick invariant"
Dmitri Alekseevsky, Gianni Manno, Giovanni Moreno
to appear in Rivista di Matematica della Universita di Parma,
arXiv:2202.09894
Published:
- "A note on dual abelian varieties"
Aleksandra Borówka, Paweł Borówka
Linear Algebra and its Applications, Volume 710, 1 April 2025, Pages 458-470
DOI: 10.1016/j.laa.2025.02.008
arXiv:2311.02718
- "Decomposing tensor spaces via path signatures"
Carlos Amendola, Francesco Galuppi, Angel Rios, Pierpaola Santarsiero, Tim Seynnaeve
Journal of Pure and Applied Algebra, Volume 229(1) (2025), pp. 1-19,
DOI: 10.1016/j.jpaa.2024.107807,
arXiv:2308.11571
- "Non-Defectivity of Segre-Veronese varieties"
Hirotachi Abo, Maria Chiara Brambilla, Francesco Galuppi, Alessandro Oneto
Proceedings of the American Mathematial Society (series B), Volume 11 (2024), pp. 589-602,
DOI: 10.1090/bproc/248,
arXiv:2406.20057
- "The moment map on the space of symplectic 3d Monge-Ampere equations"
Jan Gutt, Gianni Manno, Giovanni Moreno, Robert Śmiech
Adv. Differential Equations, 29(7/8) (2024), 575-654,
DOI: 10.57262/ade029-0708-575,
arXiv:2105.06675
- "Equations of tensor eigenschemes"
Valentina Beorchia, Francesco Galuppi, Lorenzo Venturello
Mathematics of Computations, Volume 93 (2024), pp. 589-602,
DOI: 10.1090/mcom/3882,
arXiv:2205.04413
- "Singular contact varieties"
Robert Śmiech
Manuscripta Mathematica, Volume 175 (2024), pp. 117-145,
DOI: 10.1007/s00229-024-01561-3,
arXiv:2212.07930
- "Projectively and affinely invariant PDEs on hypersurfaces"
Dmitri Alekseevsky, Gianni Manno, Giovanni Moreno
Proceedings of the Edinburgh Mathematical Society, Volume 67(3) (2024), pp. 714-739,
DOI: 10.1017/S0013091524000233,
arXiv:1907.06283
- "Toric Sarkisov links of toric Fano varieties"
Gavin Brown, Jarosław Buczyński, Alexander Kasprzyk
In: Cheltsov, I., Chen, X., Katzarkov, L., Park, J. (eds) Birational Geometry, Kähler-Einstein Metrics and Degenerations, pp 129-144 (2023)
DOI: 10.1007/978-3-031-17859-7_6,
arXiv:2207.08278
- "Distinguishing secant from cactus varieties"
Maciej Gałązka, Tomasz Mańdziuk, Filip Rupniewski
Foundations of Computational Mathematics, Volume 23 (2023), pp. 1167-1214,
DOI: 10.1007/s10208-022-09566-8,
arXiv:2007.16203
- "Generic identifiability of pairs of ternary forms"
Valentina Beorchia, Francesco Galuppi
Collectanea Mathematica, Volume 74 (2023), pp. 529-545,
DOI: 10.1007/s13348-022-00363-8,
arXiv:2106.13698
- "Spectral theory of weighted hypergraphs via tensors"
Francesco Galuppi, Raffaella Mulas, Lorenzo Venturello
Linear and Multilinear Algebra, Volume 71:3 (2023), pp. 317-347,
DOI: 10.1080/03081087.2022.2030659,
arXiv:2106.00277
- "On Rational Recursive Sequences"
Lorenzo Clemente, Maria Donten-Bury, Filip Mazowiecki, Michał Pilipczuk
40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)
Volume 254 (2023), pp. 24:1--24:21,
DOI: 10.4230/LIPIcs.STACS.2023.24,
arXiv:2210.01635
- "Secant non-defectivity via collisions of fat points"
Francesco Galuppi, Alessandro Oneto
Advances in Mathematics, 409 part B (2022),
DOI: 10.1016/j.aim.2022.108657,
arXiv:2104.02522
- "Algebraic torus actions on contact manifolds"
Jarosław Buczyński, Jarosław A. Wiśniewski, with an appendix by Andrzej Weber
J. Differential Geom. 121(2) (2022), pp. 227-289
DOI: 10.4310/jdg/1659987892,
arXiv:1802.05002
- "Identifying limits of ideals of points in the case of projective space"
Tomasz Mańdziuk
Linear Algebra and its Applications Volume 634 (2022), pp. 149-178
DOI: 10.1016/j.laa.2021.11.003,
arXiv:2011.14692
- "Apolarity, border rank and multigraded Hilbert scheme"
Weronika Buczyńska, Jarosław Buczyński
Duke Mathematical Journal, 2021, 170(16): 3659-3702,
DOI: 10.1215/00127094-2021-0048,
arXiv:1910.01944
- "Quaternion-Kähler manifolds near maximal fixed point sets of $S^1$-symmetries"
Aleksandra Borówka
Annali di Matematica Pura ed Applicata , Volume 2020, Issue 199, Pages 1243-1262,
DOI: 10.1007/s10231-019-00920-2,
arXiv:1904.08474
- "Singular curves of low degree and multifiltrations from osculating spaces"
Jarosław Buczyński, Nathan Ilten, Emanuele Ventura
International Mathematics Research Notices, Volume 2020, Issue 21, November 2020, Pages 8139-8182,
DOI:10.1093/imrn/rnaa009,
arXiv:1905.11860
Grant acknowledgements
The project support, even partial, should be explicitly acknowledged in all the publications,
including theses, produced by postdocs and PhD/MSc students during the project.
The acknowledgement should contain the keywords "National Science Centre, Poland" and the project number above, see the LaTeX templates below:
If there is only one author:
- The author is supported by the National Science Center, Poland, project ``Complex contact manifolds and geometry of secants'', 2017/26/E/ST1/00231.
If all authors are supported by the project:
- The authors are supported by the National Science Center, Poland, project ``Complex contact manifolds and geometry of secants'', 2017/26/E/ST1/00231.
- The article is a part of the project of National Science Center, Poland, ``Complex contact manifolds and geometry of secants'', 2017/26/E/ST1/00231.
- The research presented in this article is a part of the project of National Science Center, Poland, ``Complex contact manifolds and geometry of secants'', 2017/26/E/ST1/00231.
If there are more authors, and not all of them are supported by the project:
- [YourSurname] is supported by the National Science Center, Poland, project ``Complex contact manifolds and geometry of secants'', 2017/26/E/ST1/00231.
- (a footnote attached to the author using \thanks macro)
\thanks{Supported by the National Science Center, Poland, project ``Complex contact manifolds and geometry of secants'', 2017/26/E/ST1/00231.}
Or similar statements.
Related conferences and events
The following events are partially supported from the indirect costs of the grant:
Other meetings related to the topics of the project and organised by team members:
- Varieties and Group Actions, 23-29.09.2018,
- VAT mini-workshop "T-Varieties" 22-23.11.2018,
- Conference Selected Topics of Simons Semesters 16-20.12.2019,
- K3 categories and hyperkähler moduli spaces,
43rd Autumn School in Algebraic Geometry (online), 13-17.09.2021,
- Miniworkshop Tensor Days,
11-15.10.2021,
- Algebraic Geometry with Applications to TEnsors and Secants (AGATES): Simons Semester in Warsaw 12.09-16.12.2022 and its numerous workshops.
- Tensors in Applications,
Minisymposium within "2023 Hybrid SIAM Conference on Applied Algebraic Geometry (AG23)", 10-14.07.2023,