I am working as a postdoc at the Laboratoire Paul Painlevé of the Université de Lille-1 (60%) and
at the Department of Electrical Engineering of KU Leuven (40%).

**→ Coordinates:**

Université de Lille-1 Sciences et Technologies

Laboratoire Painlevé, CNRS - UMR 8524

Cité Scientifique

59655 Villeneuve d'Ascq Cedex

France

wouter.castryck(at)math.univ-lille1.fr

On graded Betti tables of curves in toric surfaces, with Filip Cools, Jeroen Demeyer, and Alexander Lemmens arXiv

Computing graded Betti tables of toric surfaces, with Filip Cools, Jeroen Demeyer, and Alexander Lemmens arXiv

[ Accompanying code: see Jeroen's github ]

[ Slides: pdf (the conjecture on slide 18 turned out to be incomplete, see Conjecture 1.6 in the paper for an updated statement) ]

Point counting on curves using a gonality preserving lift, with Jan Tuitman, The Quarterly Journal of Mathematics, to appear arXiv

[ Accompanying code: see Jan's homepage ]

Faster homomorphic function evaluation using non-integral base encoding, with Charlotte Bonte, Carl Bootland, Joppe W. Bos, Ilia Iliashenko, and Frederik Vercauteren, Proceedings of CHES 2017, Lecture Notes in Computer Science10529, pp. 579-600 (2017) ePrint

Hypersurfaces in weighted projective spaces over finite fields with applications to coding theory, with Yves Aubry, Sudhir R. Ghorpade, Gilles Lachaud, Michael E. O'Sullivan, and Samrith Ram, Proceedings of Algebraic Geometry for Cryptography and Coding Theory, Association for Women in Mathematics Series9, to appear arXiv

The holomorphy conjecture for nondegenerate surface singularities, with Denis Ibadula and Ann Lemahieu, Nagoya Mathematical Journal227(3), pp. 160-188 (2017) arXiv

Linear pencils encoded in the Newton polygon, with Filip Cools, International Mathematics Research Notices2017(10), pp. 2998-3049 (2017) arXiv

[ Accompanying Magma files: basic_commands.m gonal.m neargonal.m ]

[ Erratum: pdf ]

Privacy-friendly forecasting for the smart grid using homomorphic encryption and the group method of data handling, with Joppe W. Bos, Ilia Iliashenko, and Frederik Vercauteren, Proceedings of AFRICACRYPT 2017, Lecture Notes in Computer Science10239, pp. 184-201 (2017) ePrint

Intrinsicness of the Newton polygon for smooth curves onP^{1}xP^{1}, with Filip Cools, Revista Matemática Complutense30(2), pp. 233-258 (2017) arXiv

A lower bound for the gonality conjecture, Mathematika63(2), pp. 561-563 (2017) arXiv

On error distributions in ring-based LWE, with Ilia Iliashenko and Frederik Vercauteren, Proceedings of ANTS-XII, LMS Journal of Computation and Mathematics19, Special Issue A, pp. 130-145 (2016) ePrint

Provably weak instances of Ring-LWE revisited, with Ilia Iliashenko and Frederik Vercauteren, Proceedings of EUROCRYPT 2016, Lecture Notes in Computer Science9665Part I, pp. 147-167 (2016) ePrint

[ Slides: pdf ]

A combinatorial interpretation for Schreyer's tetragonal invariants, with Filip Cools, Documenta Mathematica20, pp. 903-918 (2015) arXiv

The lattice size of a lattice polygon, with Filip Cools, Journal of Combinatorial Theory, Series A136, pp. 64-95 (2015) arXiv

A minimal set of generators for the canonical ideal of a non-degenerate curve, with Filip Cools, Journal of the Australian Mathematical Society98(3), pp. 311-323 (2015) arXiv

[ Accompanying file: canonical.m ]

New equidistribution estimates of Zhang type, with D.H.J. Polymath, Algebra & Number Theory8(9), pp. 2067-2199 (2014) arXiv

Curves in characteristic 2 with non-trivial 2-torsion, with Marco Streng and Damiano Testa, Proceedings of GEOCRYPT 2013, Advances in Mathematics of Communications8(4), pp. 479-495 (2014) arXiv

Constraints on counterexamples to the Casas-Alvero conjecture, and a verification in degree 12, with Robert Laterveer and Myriam Ounaïes, Mathematics of Computation83(290), pp. 3017-3037 (2014) arXiv

[ Accompanying files: badprimes7.txt CAbadprimes7test.m precompscenarios12.zip CAdeg12.m CAbadprimes.m ]

[ Slides: pptx ]

The distribution of the number of points modulo an integer on elliptic curves over finite fields, with Hendrik Hubrechts, The Ramanujan Journal30(2), pp. 223-242 (2013) pdf

The probability that the number of points on the Jacobian of a genus 2 curve is prime, with Amanda Folsom, Hendrik Hubrechts, and Andrew V. Sutherland, Proceedings of the London Mathematical Society104(6), pp. 1235-1270 (2012) arXiv

Newton polygons and curve gonalities, with Filip Cools, Journal of Algebraic Combinatorics35(3), pp. 345-366 (2012) + erratum, ibid., pp. 367-372 arXiv

Moving out the edges of a lattice polygon, Discrete and Computational Geometry47(3), pp. 496-518 (2012) pdf

[ Accompanying files: Polygon_commands.m readme.pdf Polygons1to30.zip ]

Toric forms of elliptic curves and their arithmetic, with Frederik Vercauteren, Journal of Symbolic Computation46(8), pp. 943-966 (2011) pdf

Nondegenerate curves of low genus over small finite fields, with John Voight, Proceedings of AGC^{2}T12, Contemporary Mathematics521, pp. 21-28 (2010) arXiv

On nondegeneracy of curves, with John Voight, Algebra & Number Theory3(3), pp. 255-281 (2009) arXiv

[ Addenda and errata: nondeg_remarks.pdf ]

Computing zeta functions in families of C, with Hendrik Hubrechts and Frederik Vercauteren, Proceedings of ANTS-VIII, Lecture Notes in Computer Science_{a,b}curves using deformation5011, pp. 296-311 (2008) pdf

[ Errata: cab_erratum.pdf ]

A shortened classical proof of the quadratic reciprocity law, American Mathematical Monthly115(6), pp. 550-551 (2008) pdf

Computing zeta functions of nondegenerate curves, with Jan Denef and Frederik Vercauteren, International Mathematics Research Papers2006, pp. 1-57 (2006) arXiv ePrint

Translating between the roots of the identity in quantum computers, with Jeroen Demeyer, Alexis De Vos, Oliver Keszocse and Mathias Soeken arXiv

La conjecture de Casas-Alvero, Les conjectures du trimestre, Images des Maths link

The "bounded gaps between primes" Polymath project - a retrospective, with D.H.J. Polymath, Newsletter of the European Mathematical Society94, pp. 13-23 (2014) arXiv

Efficient arithmetic on elliptic curves using a mixed Edwards-Montgomery representation, with Steven Galbraith and Reza Farashahi ePrint

Smooth curves in toric surfaces, Habilitation à Diriger des Recherches, under the supervision of Raf Cluckers, Université de Lille-1 (2017) pdf of extended preface

[ Facts and conjectures on Betti tables of toric surfaces: png ]

Point counting on nondegenerate curves, Ph.D. thesis, under the supervision of Jan Denef, KU Leuven (2006) pdf

[ Errata: thesis_erratum.pdf ]