Research works of Clément de Seguins Pazzis

My habilitation dissertation


Géométrie affine des espaces de matrices, et questions de décompositions quadratiques : HdRdSP.pdf
English version : On the affine geometry of matrix spaces, and quadratic decomposition issues : habilitationEN.pdf

Manuscripts in preparation

  1. On affine spaces of rectangular matrices with constant rank
  2. Products of involutions in symplectic groups over general fields (II)
  3. Spaces of triangularizable matrices
  4. Semilinear spaces of matrices with rank or spectral constraints

Unsubmitted preprints

  1. Equivariant K-theory for proper actions of non-compact Lie groups, arXiv preprint, October 2010.
  2. A classifying space for Phillips's equivariant K-theory, arXiv preprint, October 2010.

Submitted articles under review

  1. Products of involutions in symplectic groups over general fields (I), arXiv preprint, September 2023. Submitted to Linear Algebra and its Applications.
  2. On affine spaces of alternating matrices with constant rank. arXiv preprint, July 2023. Submitted to Linear and Multilinear Algebra.
  3. Products of unipotent elements of index 2 in orthogonal and symplectic groups. arXiv preprint, June 2023. Submitted to Linear Algebra and its Applications.
  4. On the finite topology of a vector space and the domination problem for families of norms, arXiv preprint, January 2018, submitted to Topology proceedings.

Accepted articles awaiting publication

  1. A note on bireflectional elements of an algebra, Online final version, arXiv preprint, accepted in Communications in Algebra.
  2. Sums of two square-zero selfadjoint or skew-selfadjoint endomorphisms, Online final version, arXiv preprint, accepted in Linear Algebra and its Applications.

Published articles

  1. The quadratic sum problem for symplectic pairs, Linear Algebra Appl. 683 (2024) 151-179, Online final version, arXiv preprint.
  2. Products of two involutions in orthogonal and symplectic groups, Geom. Dedic. 218-2 (2024), Online final version arXiv preprint.
  3. Locally finite cycles of linear mappings in countable dimension, Linear Algebra Appl. 669 (2023), 57-101, Online final version, arXiv preprint.
  4. Sums and products of pairs of quadratic endomorphisms of countable-dimensional vector spaces, Linear Multilinear Algebra. 70-21 (2023), 6718-6752, Online final version, arXiv preprint.
  5. The product of two invertible quadratic matrices: Exceptional cases, Linear Algebra Appl. 662 (2023), 67-109, Online final version, arXiv preprint.
  6. The sum of two quadratic matrices: Exceptional cases, Linear Algebra Appl. 653 (2022), 357-394, Online final version, arXiv preprint.
  7. The sum and the product of two quadratic matrices: regular cases, Adv. Appl. Clifford Algebras 32 (2022), Online final version, arXiv preprint.
  8. Products of involutions of an infinite-dimensional vector space, Canadian J. Math. 73 (2021), 195-220, Online final version, arXiv preprint.
  9. The structured Gerstenhaber problem III, Linear Algebra Appl. 601 (2020), 134-169, Online final version, arXiv preprint.
  10. The space of all p-th roots of a nilpotent complex matrix is path-connected, Linear Algebra Appl. 596 (2020), 106-116, Online final version, arXiv preprint.
  11. Products of involutions in the stable general linear group, J. Algebra 530 (2019), 235-289, Online final version, arXiv preprint.
  12. The structured Gerstenhaber problem (II), Linear Algebra Appl. 569 (2019), 113-145, Online final version, arXiv preprint.
  13. The structured Gerstenhaber problem (I), Linear Algebra Appl. 567 (2019), 263-298, Online final version, arXiv preprint.
  14. On the linear preservers of Schur matrix functionals, Linear Algebra Appl. 567 (2019), 63-117, Online final version, arXiv preprint.
  15. Continuous space-time transformations, joint work with Peter Šemrl, Adv. Geometry 18-3 (2018), 385-393, Online final version, arXiv preprint.
  16. From trivial spectrum subspaces to spaces of diagonalizable real matrices, Math. Proc. R. Ir. Acad. 118A (2018), 5-8, Online final version, arXiv preprint.
  17. Sums of quadratic endomorphisms of an infinite-dimensional vector space, Proc. Edinburgh Math. Soc. 61 (2018), 437-447, Online final version, arXiv preprint.
  18. Range-compatible homomorphisms over the field with two elements, Electronic Linear Algebra 34 (2018) 71-114, Online final version.
  19. Sums of three quadratic endomorphisms of an infinite-dimensional vector space, Acta Sci. Math. (Szeged) 83 (2017) 83-111, Online final version, arXiv preprint.
  20. A note on sums of three square-zero matrices, Linear Multilinear Algebra 65 (2017) 787-805, Online final version, arXiv preprint.
  21. Lines of full rank matrices in large subspaces, Oper. Matrices 10 (2016) 985-996, Online final version, arXiv preprint.
  22. Large spaces of symmetric or alternating matrices with bounded rank, Linear Algebra Appl. 508 (2016) 146-189, Online final version, arXiv preprint.
  23. Primitive spaces with upper rank two over the field with two elements, Linear Multilinear Algebra 64 (2016) 1321-1353, Online final version, arXiv preprint.
  24. Affine spaces of symmetric or alternating matrices with bounded rank, Linear Algebra Appl. 504 (2016) 503-558, Online final version, arXiv preprint
  25. Large spaces of bounded rank matrices revisited, Linear Algebra Appl. 504 (2016) 124-189, Online final version, arXiv preprint.
  26. Range-compatible homomorphisms on spaces of symmetric or alternating matrices, Linear Algebra Appl. 503 (2016) 135-163. Online final version, arXiv preprint.
  27. Quasi-range-compatible affine maps on large operator spaces, Linear Multilinear Algebra 64 (2016) 1056-1085. Online final version, arXiv preprint
  28. The Flanders theorem over division rings, Linear Algebra Appl. 493 (2016) 313-322. Online final version, arXiv preprint.
  29. The classification of large spaces of matrices with bounded rank, Israel J. Math. 208 (2015) 219-259. Online final version, arXiv preprint.
  30. Range-compatible homomorphisms on matrix spaces, Linear Algebra Appl. 484 (2015) 237-289. Online final version, arXiv preprint.
  31. Hua's fundamental theorem of geometry of rectangular matrices over EAS division rings, joint work with Peter Šemrl, J. Algebra 439 (2015) 159-187. Online final version, arXiv preprint.
  32. Local linear dependence seen through duality I, J. Pure Appl. Algebra 219 (2015) 2144-2188. Online final version, arXiv preprint.
  33. LDB division algebras, J. Algebra 423 (2015) 259-288. Online final version, arXiv preprint.
  34. Local linear dependence seen through duality II, Linear Algebra Appl. 462 (2014) 133-185. Online final version, arXiv preprint.
  35. On the minimal rank in non-reflexive operator spaces over finite fields, Linear Algebra Appl. 462 (2014) 126-132. Online final version, arXiv preprint.
  36. From primitive spaces of bounded rank matrices to a generalized Gerstenhaber theorem, Quart. J. Math. 65-2 (2014) 319-325. Online final version, arXiv preprint.
  37. Spaces of matrices with few eigenvalues, Linear Algebra Appl. 449 (2014) 210-311. Online final version, arXiv preprint.
  38. Commutators from a hyperplane of matrices, Electronic Linear Algebra 27 (2014) 39-54. Online final version.
  39. The geometric realization of a simplicial Hausdorff space is Hausdorff, Topology Appl. 160-13 (2013) 1621-1632. Online final version, arXiv preprint.
  40. On Gerstenhaber's theorem for spaces of nilpotent matrices over a skew field, Linear Algebra Appl. 438-11 (2013) 4426-4438. Online final version, arXiv preprint.
  41. Large affine spaces of non-singular matrices, Trans. Amer. Math. Soc. 365 (2013) 2569-2596. Online final version, arXiv preprint.
  42. On commuting matrices and exponentials, Proc. Amer. Math. Soc. 141 (2013) 763-774. Online final version, arXiv preprint
  43. Spaces of matrices with a sole eigenvalue, Linear Multilinear Algebra. 60-10 (2012) 1165-1190. Online final version. arXiv preprint.
  44. The semigroup generated by the similarity class of a singular matrix, Comm. Alg. 40-9 (2012) 3414-3419. Online final version. arXiv preprint.
  45. Large affine spaces of matrices with rank bounded below, Linear Algebra Appl. 437-2 (2012) 499-518. Online final version. arXiv preprint.
  46. The linear preservers of non-singularity in a large space of matrices. Linear Algebra Appl. 436-9 (2012) 3507-3530. Online final version. arXiv preprint.
  47. Sums of two triangularizable quadratic matrices over an arbitrary field. Linear Algebra Appl. 436-9 (2012) 3293-3302. Online final version. arXiv preprint.
  48. When does a linear map belong to at least one orthogonal or symplectic group? Linear Algebra Appl. 436-5 (2012) 1385-1405. Online final version. arXiv preprint.
  49. The linear preservers of real diagonalizable matrices (joint work with Bernard Randé). Linear Algebra Appl. 435-6 (2011) 1257-1266. Online final version. arXiv preprint.
  50. To what extent is a large space of matrices not closed under product? Linear Algebra Appl. 435-11 (2011) 2708-2721. Online final version. arXiv preprint.
  51. On small matrix subalgebras with a trivial centralizer, Linear Multilinear Algebra. 59-7 (2011) 761-771. Online final version. arXiv preprint.
  52. On the matrices of given rank in a large subspace, Linear Algebra Appl. 435-1 (2011) 147-151. Online final version. arXiv preprint.
  53. The affine preservers of non-singular matrices, Arch. Math. 95 (2010) 333-342. Online final version. arXiv preprint.
  54. On sums of idempotent matrices over a field of positive characteristic, Linear Algebra Appl. 433-4 (2010) 856-866. Online final version. arXiv preprint.
  55. On decomposing any matrix as a linear combination of three idempotents, Linear Algebra Appl. 433-4 (2010) 843-855. Online final version. arXiv preprint.
  56. On linear combinations of two idempotent matrices over an arbitrary field, Linear Algebra Appl. 433-3 (2010) 625-636. Online final version. arXiv preprint.
  57. Invariance of simultaneous similarity and equivalence of matrices under extension of the ground field, Linear Algebra Appl. 433-3 (2010) 618-624. Online final version. arXiv preprint.
  58. The singular linear preservers of non-singular matrices, Linear Algebra Appl. 433-2 (2010) 483-490. Online final version. arXiv preprint.

Seminar talk slideshows

  1. Affine geometry of matrix spaces, June 6th 2023, Soutenance d'Habilitation à Diriger les Recherches, UVSQ.
  2. Decomposing matrices into quadratic ones, June 22th 2022, ILAS 2022 Conference, Galway.
  3. Sums and products of quadratic matrices, 26th October 2017, UCD Mathematics Seminar, Dublin.
  4. Range-compatible homomorphisms on matrix spaces, 20th June 2017, Preservers Everywhere Conference, University of Szeged.
  5. Continuous space-time transformations, 14th July 2016, KU Leuven ILAS 2016 Conference.
  6. Range-compatible homomorphisms on matrix spaces, 16th April 2015, Ljubljana University.
  7. Spaces of matrices with rank bounded above, 20th June 2014, PolSys Seminar, Université Pierre et Marie Curie, Paris.
  8. Algèbres à division à gauche bilinéarisable, 8th March 2014, worskhop "Clifford algebras, K-theory and index theory", Université Paul Sabatier, Toulouse.
  9. Beyond Gerstenhaber: spaces of matrices with spectral conditions, 4th April 2013, Ljubljana University.
  10. Large spaces of matrices with bounded rank, 5th April 2012, Ljubljana University.
  11. Géométrie affine des espaces de matrices, 3rd May 2011, séminaire d'algèbre et géométrie, Université de Versailles-Saint-Quentin-en-Yvelines.

Referee activity

I have reviewed articles for the following journals:
Journal of Algebra, Transactions of the American Mathematical Society, Journal of the Korean Mathematical Society, Linear Algebra and its Applications, Linear and Multilinear Algebra, Electronic Journal of Linear Algebra, Special Matrices, Advances in Applied Clifford Algebras.
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