**
**

**In preparation**

- The structured Gerstenhaber problem (III), joint work with Rachel Quinlan.

**Unsubmitted preprints**

- Products of involutions of an infinite-dimensional vector space, arXiv preprint, August 2018.
- The sum and the product of two quadratic matrices, arXiv preprint, July 2017.
- Equivariant K-theory for proper actions of non-compact Lie groups, arXiv preprint, October 2010.
- A classifying space for Phillips's equivariant K-theory, arXiv preprint, October 2010.

**Submitted papers under review**

- The space of all p-th roots of a nilpotent complex matrix is path-connected, arXiv preprint, December 2018, submitted to Linear Algebra and its Applications.
- On the finite topology of a vector space and the domination problem for families of norms, arXiv preprint, January 2018, submitted to Topology proceedings.
- Products of involutions in the stable general linear group, arXiv preprint, August 2018, submitted to Journal of Algebra.
- The sum of two quadratic matrices, arXiv preprint, December 2017, submitted to Journal of Pure and Applied Algebra.

**Accepted papers awaiting publication**

- The structured Gerstenhaber problem (II), arXiv preprint, November 2018, to be published in Linear Algebra and its Applications.
- The structured Gerstenhaber problem (I), arXiv preprint, August 2018, to be published in Linear Algebra and its Applications, online final version.

**Published papers**

- On the linear preservers of Schur matrix functionals, Linear Algebra Appl.
**567**(2019), 63-117, Online final version arXiv preprint. - Continuous space-time transformations, joint work with Peter Šemrl, Adv. Geometry
**18-3**(2018), 385-393, Online final version, arXiv preprint. - From trivial spectrum subspaces to spaces of diagonalizable real matrices, Math. Proc. R. Ir. Acad.
**118A**(2018), 5-8, Online final version, arXiv preprint. - Sums of quadratic endomorphisms of an infinite-dimensional vector space, Proc. Edinburgh Math. Soc.
**61**(2018), 437-447, Online final version, arXiv preprint. - Range-compatible homomorphisms over the field with two elements, Electronic Linear Algebra
**34**(2018) 71-114, Online final version. - Sums of three quadratic endomorphisms of an infinite-dimensional vector space,
Acta Sci. Math. (Szeged)
**83**(2017) 83-111, Online final version, arXiv preprint. - A note on sums of three square-zero matrices, Linear Multilinear Algebra
**65**(2017) 787-805, Online final version, arXiv preprint. - Lines of full rank matrices in large subspaces, Oper. Matrices
**10**(2016) 985-996, Online final version, arXiv preprint. - Large spaces of symmetric or alternating matrices with bounded rank, Linear Algebra Appl.
**508**(2016) 146-189, Online final version, arXiv preprint. - Primitive spaces with upper rank two over the field with two elements, Linear Multilinear Algebra
**64**(2016) 1321-1353, Online final version, arXiv preprint. - Affine spaces of symmetric or alternating matrices with bounded rank, Linear Algebra Appl.
**504**(2016) 503-558, Online final version, arXiv preprint - Large spaces of bounded rank matrices revisited, Linear Algebra Appl.
**504**(2016) 124-189, Online final version, arXiv preprint. - Range-compatible homomorphisms on spaces of symmetric or alternating matrices, Linear Algebra Appl.
**503**(2016) 135-163. Online final version, arXiv preprint. - Quasi-range-compatible affine maps on large operator spaces, Linear Multilinear Algebra
**64**(2016) 1056-1085. Online final version, arXiv preprint - The Flanders theorem over division rings, Linear Algebra Appl.
**493**(2016) 313-322. Online final version, arXiv preprint. - The classification of large spaces of matrices with bounded rank, Israel J. Math.
**208**(2015) 219-259. Online final version, arXiv preprint. - Range-compatible homomorphisms on matrix spaces, Linear Algebra Appl.
**484**(2015) 237-289. Online final version, arXiv preprint. - 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. - Local linear dependence seen through duality I, J. Pure Appl. Algebra
**219**(2015) 2144-2188. Online final version, arXiv preprint. - LDB division algebras, J. Algebra
**423**(2015) 259-288. Online final version, arXiv preprint. - Local linear dependence seen through duality II,
Linear Algebra Appl.
**462**(2014) 133-185. Online final version, arXiv preprint. - On the minimal rank in non-reflexive operator spaces over finite fields,
Linear Algebra Appl.
**462**(2014) 126-132. Online final version, arXiv preprint. - 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. - Spaces of matrices with few eigenvalues, Linear Algebra Appl.
**449**(2014) 210-311. Online final version, arXiv preprint. - Commutators from a hyperplane of matrices, Electronic Linear Algebra
**27**(2014) 39-54. Online final version. - The geometric realization of a simplicial Hausdorff space is Hausdorff, Topology Appl.
**160-13**(2013) 1621-1632. Online final version, arXiv preprint. - 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. - Large affine spaces of non-singular matrices, Trans. Amer. Math. Soc.
**365**(2013) 2569-2596. Online final version, arXiv preprint. - On commuting matrices and exponentials, Proc. Amer. Math. Soc.
**141**(2013) 763-774. Online final version, arXiv preprint - Spaces of matrices with a sole eigenvalue,
Linear Multilinear Algebra.
**60-10**(2012) 1165-1190. Online final version. arXiv preprint. - The semigroup generated by the similarity class of a singular matrix,
Comm. Alg.
**40-9**(2012) 3414-3419. Online final version. arXiv preprint. - Large affine spaces of matrices with rank bounded below,
Linear Algebra Appl.
**437-2**(2012) 499-518. Online final version. arXiv preprint. - 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. - Sums of two triangularizable quadratic matrices over an arbitrary field.
Linear Algebra Appl.
**436-9**(2012) 3293-3302. Online final version. arXiv preprint. - 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. - 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. - 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. - On small matrix subalgebras with a trivial centralizer,
Linear Multilinear Algebra.
**59-7**(2011) 761-771. Online final version. arXiv preprint. - On the matrices of given rank in a large subspace,
Linear Algebra Appl.
**435-1**(2011) 147-151. Online final version. arXiv preprint. - The affine preservers of non-singular matrices, Arch. Math.
**95**(2010) 333-342. Online final version. arXiv preprint. - On sums of idempotent matrices over a field of positive characteristic,
Linear Algebra Appl.
**433-4**(2010) 856-866. Online final version. arXiv preprint. - On decomposing any matrix as a linear combination of three idempotents,
Linear Algebra Appl.
**433-4**(2010) 843-855. Online final version. arXiv preprint. - On linear combinations of two idempotent matrices over an arbitrary field,
Linear Algebra Appl.
**433-3**(2010) 625-636. Online final version. arXiv preprint. - 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. - The singular linear preservers of non-singular matrices, Linear Algebra Appl.
**433-2**(2010) 483-490. Online final version. arXiv preprint.

**Seminar talk slideshows**

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

**Referee activity**

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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