Michel Lavrauw Faculty of Engineering and Natural Sciences Sabancı University, Istanbul, Turkey

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My research is focussed on the areas of combinatorics, algebra, Galois geometry, finite geometry, incidence geometry, finite fields and coding theory. More specifically, arcs in projective spaces, finite semifields (non-associative division algebras), projective planes, Segre varieties, Veronese varieties, geometry of tensor product spaces, translation generalised quadrangles (equivalent to the theory of eggs in projective spaces), polynomial techniques in finite geometry, field reduction techniques, linear sets, MDS codes, MRD codes, and the links between incidence geometry and coding theory.

Check out our FinInG package for computation in Finite Incidence Geometry.

`Publications`

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Preprints are available for most of my published research articles. These preprints may differ from the published version (for which I have signed a copyright agreement). In case you want a reprint of a published article (e.g. for references), you can download the publication from the journal website, or contact me.
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Details about my publications can also be found on MathSciNet, Scopus, or zbMATH.

- The symmetric representation of lines in PG(F^3\otimes F^3) (with T. Popiel) preprint.
- Planar arcs (with S. Ball) preprint.
- Classification of 8-dimensional rank two commutative semifields (with M. Rodgers) preprint.
- The BEL-rank of finite semifields (with J. Sheekey) preprint.
- Scattered Spaces in Galois Geometry preprint.
- Classification of subspaces in F^2 \otimes F^3 and orbits in F^2\otimes F^3 \otimes F^r (with J. Sheekey) preprint.
- Canonical forms of 2x3x3 tensors over the real field, algebraically closed fields, and finite fields (with J. Sheekey) preprint.
- Subspaces intersecting each element of a regulus in one point, André-Bruck-Bose representation and clubs (with C. Zanella) preprint.
- On BEL-configurations and finite semifields (with J. Sheekey). To appear in Des. Codes Cryptogr. preprint.
- Subgeometries and linear sets on a projective line (with C. Zanella). To appear in Finite Fields Appl. preprint.
- Field reduction and linear sets in finite geometry (with G. Van de Voorde). To appear in AMS Contemporary Math. preprint.
- The isotopism problem of a class of 6-dimensional rank 2 semifields and its solution (with G. Marino, O. Polverino and R. Trombetti). To appear in Finite Fields Appl. preprint.
- Geometry of the inversion in a finite field and partitions of PG(2^k-1,q) in normal rational curves (with C. Zanella).
*Journal of Geometry*, preprint. - Orbits of the stabiliser group of the Segre variety product of three projective lines (with J. Sheekey).
*Finite Fields and Their Applications*, preprint. - Constant rank-distance sets of hermitian matrices and partial spreads in hermitian polar spaces (with R. Gow, J. Sheekey and F. Vanhove).
*Electronic Journal of Combinatorics*, preprint. - On embeddings of minimum dimension of PG(n,q)xPG(n,q) (with J. Sheekey and C. Zanella).
*Des. Codes Cryptogr.*Available online. - Aspects of tensor products over finite fields and Galois geometries (with J. Sheekey). Proceedings of the Academy Contact Forum {\em Galois Geometries and Applications} at the {\em Royal Flemish Academy of Belgium for Science and the Arts} (October 5, 2012), (2014), S. Nikova, B. Preneel and L. Storme, Eds., pp. 95--102.
- Solution to an isotopism question conerning rank 2 semifields (with G. Marino, O. Polverino and R. Trombetti).
*Journal of Combinatorial Designs*. preprint on arXiv. - Segre embeddings and finite semifields (with C. Zanella).
*Finite Fields Appl.*preprint. - Scattered linear sets and pseudoreguli (with G. Van de Voorde).
*Electronic Journal of Combinatorics.*preprint - On the rank of 3x3x3-tensors (with A. Pavan and C. Zanella).
*Linear Multilinear Algebra*(2012). preprint - Finite semifields and nonsingular tensors.
*Des. Codes Cryptogr.*preprint - Semifields from skew polynomial rings (with J. Sheekey).
*Adv. Geom.*preprint - F_q-pseudoreguli of PG(3,q^3) and scattered semifields of order q^6 (with G. Marino, O. Polverino and R. Trombetti).
*Finite Fields Appl.*(2011). preprint - Linear codes from projective spaces (with G. Van de Voorde en L. Storme).
*Proceedings of the Conference on Error-Correcting Codes, Cryptography and Finite Geometries, AMS book seriess*(2010). preprint - Finite semifields with a large nucleus and higher secant varieties to Segre varieties.
*Adv. Geom. (2011). preprint* - On linear sets on a projective line (with G. Van de Voorde).
*Des. Codes Cryptogr.*(2010). preprint - A proof of the linearity conjecture for k-blockings sets in PG(n,q^3), q prime (with L. Storme and G. Van de Voorde).
*J. Combin. Theory Ser. A*(2011). preprint - An empty interval in the spectrum of small weight codewords in the code from points and k-spaces of PG(n,q).
*J. Combin. Theory Ser. A*(available online 29 January 2009) (with L. Storme, P. Sziklai and G. Van de Voorde). preprint - On the isotopism classes of finite semifields.
*Finite Fields Appl.*14 (2008) 897--910. preprint - On the code generated by the incidence matrix of points and k-spaces in PG(n, q) and its dual.
*Finite Fields and Appl.*14 (2008) 1020--1038 (with L. Storme and G. Van de Voorde). preprint - On the Hughes-Kleinfeld and Knuth's semifields two dimensional over a weak nucleus.
*Des. Codes Cryp togr.*44 (2007), no. 1-3, 63--67 (with S. Ball). preprint - A geometric construction of finite semifields.
*J. Algebra*311 (2007), no. 1, 117--129 (with G. Ebert and S. Ball). preprint - How to use Redei polynomials in higher dimensional spaces, with S. Ball,
*Le Matematiche*(Catani a), 59 (2004), 39--52 (2006). preprint - On the graph of a function in two variables over a finite field, with S. Ball,
*J. Algebraic Combin.*23 (2006) 243--253. preprint - Sublines of prime order contained in the set of internal points of a conic.
*Des. Codes Cryptogr.*38 (2006), no. 1, 113--123. preprint - The two sets of three semifields associated with a semifield flock.
*Innov. Incidence Geom.*2 (2 005), 101--107. preprint - Characterizations and properties of good eggs in PG(
*4n-1,q*),*q*odd,*Discrete Math.*301, (2005), 106--116. preprint - BLT-sets admitting the symmetric group S_4, with M. Law,
*Australasian J. Combinatorics*, 33 (200 5), 307--316. preprint - Semifield flocks, eggs, and ovoids of Q(4,q),
*Adv. Geom.*5 (2005), no. 3, 333--345. preprint - Good Eggs and Veronese Varieties, with G. Lunardon,
*Discrete Math.*294 (2005), no. 1-2, 119--12 2. preprint - Eggs in PG(4n-1,q), q even, containing a pseudo pointed conic, with M. R. Brown,
*European J. Combin .*26 (2005), no.1, 117--128. preprint - Good Eggs and Veronese Varieties, with G. Lunardon,
*Discrete Math.*294 (2005), no. 1-2, 119--12 - Eggs in PG(4n-1,q), q even, containing a pseudo-conic, with M. R. Brown,
*Bull. London Math. Soc.*36 (2004), no. 5, 633--639. preprint - Symplectic Spreads, with S. Ball, J. Bamberg and T. Penttila,
*Des. Codes Cryptogr.*33 (2004) 9- -14. preprint - On the classification of semifield flocks, with Simeon Ball and Aart Blokhuis,
*Adv. Math.*180 ( 2003) 104--111. preprint - Commutative semifields of rank 2 over their middle nucleus, with Simeon Ball, Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, Mullen, G. L. (ed) et al, Springer-Verlag, 1--21, 2002. preprint
- On eggs and translation generalised quadrangles, with Tim Penttila,
*J. Combin. Theory Ser. A*96 (2001), no. 2, 303--315. preprint - Linear (
*q*+1)-fold blocking sets in*PG*(2,*q*^{4}), with Simeon Ball and Aart Blokhuis,*Finite Fields Appl.*6 (2000), no. 4, 294--301. preprint - Scattered spaces with respect to a spread in
*PG(n,q)*, with Aart Blokhuis,*Geom. Dedicata*81 (2000), no. 1-3, 231--243. preprint

- Special issue on finite geometries in honor of Frank de Clerck. Edited by J. Bamberg, J. De Beule, N. Durante, M. Lavrauw. Des. Codes Cryptogr. (2014)

- Theory and applications of finite fields. Proceedings of the 10th International Conference on Finite Fields and Their Applications (Fq 10) held in Ghent, July 11-15, 2011. Edited by Michel Lavrauw, Gary L. Mullen, Svetla Nikova, Daniel Panario and Leo Storme. Contemporary Mathematics, 579. American Mathematical Society, Providence, RI, 2012. viii+204 pp. ISBN: 978-0-8218-5298-9. Available from the AMS bookstore.

- Scattered Spaces and Eggs in Finite Projective Spaces, Topics in Finite Geometry

*VDM Verlag Dr. Muller Aktiengesellschaft & Co. KG*(2008) ISBN-10: 363906397X, ISBN-13: 978-3 639063974 (Available from amazon)

- Finite Semifields (with Olga Polverino) preprint

Chapter to appear in*Current Research Topics in Galois Geometries*(NOVA collected works, Eds. Jan De Beule and L. Storme) (2011) website

- Scattered spaces with respect to spreads and eggs in finite projective spaces. (2001) pdf

Technische Universiteit Eindhoven, The Netherlands. Advisors: Aart Blokhuis and Andries Brouwer.