Previously, I worked as a guest professor/postdoctoral fellow at the Department of Mathematics of KU Leuven (Belgium) and as senior lecturer at the Department of Mathematics and Applied Mathematics of University of Cape Town (South Africa). Below, you can find all my articles, listed in anti-chronological order.
Accepted and published papers
W. Castryck, F. Cools, J. Demeyer and A. Lemmens, Canonical syzygies of smooth curves in toric surfaces, J. Pure Appl. Algebra 224 (2020), Issue 2, 507-527 (arXiv:1609.02360)
F. Cools and A. Lemmens, Minimal polygons with fixed lattice width, Annals of Combinatorics 23 (2019), Issue 2, 285–293 (arXiv:1702.01131)
F. Cools, M. D'Adderio, D. Jensen and M. Panizzut, Brill-Noether theory of curves on P1×P1: tropical and classical approach, Algebraic Combinatorics 2 (2019), no. 3, 323-341 (arXiv:1709.07254)
W. Castryck, F. Cools, J. Demeyer and A. Lemmens, Computing graded Betti tables of toric surfaces, Trans. Amer. Math. Soc. 372 (2019), 6869-6903 (arXiv:1606.08181)
F. Cools and J. Draisma, On metric graphs with prescribed gonality, J. Comb. Theory Ser. A , Vol. 156 (2018), 1-21 (arXiv:1602.05542)
F. Cools and M. Panizzut, The gonality sequence of complete graphs, Electron. J. Comb. 24 (2017), Issue 4 (arXiv:1605.03749)
W. Castryck and F. Cools, Linear pencils encoded in the Newton polygon, Int. Math. Res. Not. 10 (2017), 2998–3049 (arXiv:1402.4651)
W. Castryck and F. Cools, Intrinsicness of the Newton polygon for smooth curves on P1×P1, Rev. Mat. Complut. 30 (2017), 233–258 (arXiv:1304.4997)
W. Castryck and F. Cools, A combinatorial interpretation for Schreyer's tetragonal invariants, Documenta Math. 20 (2015), 927-942 (arXiv:1410.1692)
W. Castryck and F. Cools, The lattice size of a lattice polygon, J. Comb. Theory Ser. A, Vol. 136 (2015), 64-95 (arXiv:1402.4652)
W. Castryck and F. Cools, A minimal set of generators for the canonical ideal of a non-degenerate curve, J. Aust. Math. Soc. Society 98 (2015), 311-323 (arXiv:1410.1698)
F. Cools and M. Coppens, Linear pencils on graphs and on real curves, Geom. Dedic. 169 (2014), 49-56 (arXiv:1006.1770)
F. Cools, Linear pencils of tropical plane curves, Discrete Comput. Geom. 48 (2012), 453-466 (arXiv:1105.1025)
W. Castryck and F. Cools, Newton polygons and curve gonalities, J. Algebr. Comb. 35 (2012), 345-366 (arXiv:1106.3762)
W. Castryck and F. Cools, Erratum to : Newton polygons and curve gonalities, J. Algebr. Comb. 35 (2012), 367-372 (arXiv:1106.3762)
F. Cools, J. Draisma, S. Payne and E. Robeva, A tropical proof of the Brill-Noether Theorem, Adv. Math. 230 (2012), 759-776 (arXiv:1001.2774)
F. Cools and M. Coppens, Singular hypersurfaces possessing infinitely many star points, P. Am. Math. Soc. 139 (2011), 3413-3422 (arXiv:0909.1727)
L. Chiantini and F. Cools, Classification of (1,2)-Grassmann secant defective threefolds, Forum Math. 23 (2011), 207-222
F. Cools and M. Coppens, Star points on smooth hypersurfaces, J. Algebra 323 (2010), 261–286 (arXiv:0903.2005)
F. Cools, On the relation between weighted trees and tropical Grassmannians, J. Symb. Comput. 44 (2009), 1079-1086 (arXiv:0903.2010)
C. Bocci and F. Cools, A tropical interpretation of m-dissimilarity maps, Appl. Math. Comput. 212 (2009), 349-356 (arXiv:0803.2184)
F. Cools, On the singular locus of Grassmann secant varieties, B. Belg. Math. Soc. Simon Stevin 16 (2009), 799-803 (link)
F. Cools and M. Coppens, Plane curves with 3 or 4 total inflection points, J. Lond. Math. Soc. 77 (2008), 149-163 (link)
C. Ciliberto and F. Cools, On Grassmann secant extremal varieties, Adv. Geom. 8 (2008), 377–386
F. Cools and M. Coppens, Some general results on plane curves with total inflection points, Arch. Math. 89 (2007), 73-80
F. Cools, On high G(k-1,k)-defective varieties, Commun. Algebra 35 (2007), 2600-2610
F. Cools, On G(k-1,k)-defectivity of smooth surfaces and threefolds, J. Pure Appl. Algebra 203 (2005), 204-219
PhD thesis
Title: Grassmann secant varieties and plane curves with total inflection points, under supervision of Marc Coppens and Willem Veys, defended on May 16th 2007