Permanent Academic Staff

Filip Cools

Since July 2014, I am working as a senior lecturer at the Department of Mathematics and Applied Mathematics of University of Cape Town (South Africa). Previously, I was a postdoctoral fellow at the Department of Mathematics of KU Leuven (Belgium).


Department of Mathematics and Applied Mathematics
University of Cape Town
Private Bag X1
7701 Rondebosch (Cape Town)
South Africa

Office: M419

Research interests

  • Research domains: algebraic geometry, combinatorics
  • Specific topics: toric and tropical geometry, linear systems, secant varieties, algebraic statistics, metric graphs

In preparation

  • W. Castryck and F. Cools, Intrinsicness of the Newton polygon for smooth curves on P1×P1
  • F. Cools and J. Draisma, On metric graphs with prescribed gonality
  • W. Castryck, F. Cools and A. Lemmens, A Kp,1 conjecture for toric surfaces


  • W. Castryck and F. Cools, A combinatorial interpretation for Schreyer's tetragonal invariants, preprint 2014 (link)
  • W. Castryck and F. Cools, Linear pencils encoded in the Newton polygon, preprint 2014 (link)
  • W. Castryck and F. Cools, A minimal set of generators for the canonical ideal of a non-degenerate curve, to appear in J. Aust. Math. Soc. (link)
  • W. Castryck and F. Cools, The lattice size of a lattice polygon, to appear in J. Comb. Theory Ser. A (link)

Published papers

  • F. Cools and M. Coppens, Linear pencils on graphs and on real curves, Geom. Dedic. 169 (2014), 49-56 (link)
  • F. Cools, Linear pencils of tropical plane curves, Discrete Comput. Geom. 48 (2012), 453-466 (link)
  • W. Castryck and F. Cools, Newton polygons and curve gonalities, J. Algebr. Comb. 35 (2012), 345-366 (link)
  • W. Castryck and F. Cools, Erratum to : Newton polygons and curve gonalities, J. Algebr. Comb. 35 (2012), 367-372 (link)
  • F. Cools, J. Draisma, S. Payne and E. Robeva, A tropical proof of the Brill-Noether Theorem, Adv. Math. 230 (2012), 759-776 (link)
  • F. Cools and M. Coppens, Singular hypersurfaces possessing infinitely many star points, P. Am. Math. Soc. 139 (2011), 3413-3422 (link)
  • 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 (link)
  • F. Cools, On the relation between weighted trees and tropical Grassmannians, J. Symb. Comput. 44 (2009), 1079-1086 (link)
  • C. Bocci and F. Cools, A tropical interpretation of m-dissimilarity maps, Appl. Math. Comput. 212 (2009), 349-356 (pdf-file)
  • F. Cools, On the singular locus of Grassmann secant varieties, B. Belg. Math. Soc. Simon Stevin 16 (2009), 799-803 (pdf-file)
  • F. Cools and M. Coppens, Plane curves with 3 or 4 total inflection points, J. Lond. Math. Soc. 77 (2008), 149-163 (pdf-file)
  • C. Ciliberto and F. Cools, On Grassmann secant extremal varieties, Adv. Geom. 8 (2008), 377–386 (pdf-file)
  • F. Cools and M. Coppens, Some general results on plane curves with total inflection points, Arch. Math. 89 (2007), 73-80 (pdf-file)
  • F. Cools, On high G(k-1,k)-defective varieties, Commun. Algebra 35 (2007), 2600-2610 (pdf-file)
  • F. Cools, On G(k-1,k)-defectivity of smooth surfaces and threefolds, J. Pure Appl. Algebra 203 (2005), 204-219 (pdf-file)

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 (pdf-file thesis, pdf-file slides)

Upcoming conferences

  • Workshop Theory and applications of syzygies on the occasion of Frank-Olaf Schreyer's 60th birthday, Universität des Saarlandes, Saarbrücken (Germany), July 1-3, 2015 (link)
  • Workshop on Algebraic Geometry, University of Nairobi (Kenya), August 10-14, 2015 (link)

Past conferences

  • AIMS-Stellenbosch University Number Theory Conference, AIMS Muizenberg, Cape Town (South Africa), January 19-23, 2015 (link, slides)
  • Workshop Specialization of Linear Series for Algebraic and Tropical Curves, Banff IRS (Canada), March 30-April 4, 2014 (link, video and slides)
  • Conference Tropical aspects in Geometry and Topology, Bonn (Germany), September 2-6, 2013
  • Workshop Syzygies in Berlin, Zuse Institute Berlin (Germany), May 27-31, 2013 (link)
  • First Joint Conference of the Belgian, Royal Spanish and Luxembourg Mathematical Societies, Liège (Belgium), June 6-8, 2012 (link)
  • Workshop for Young Researchers in Mathematics, Constanta (Romania), May 10-11, 2012 (link)
  • Workshop Tropical Geometry, ICMS Edinburgh (Scotland), April 2-6, 2012 (link, slides)
  • Tropical Geometry workshop, CIEM Castro Urdiales (Spain), December 12-16, 2011 (link)
  • Conference on tropical geometry and computational biology, Saarbrücken (Germany), September 26-30, 2011 (link, slides)
  • Workshop Number Theory, Algebraic Geometry and Model Theory in honour of Jan Denef, CIRM Luminy (France), September 12-16, 2011 (link)
  • ACAGM summer school, Leuven, July 10-23, 2011 (link)
  • Toric geometry and applications, Leuven, June 6-10, 2011 (link)
  • Bellairs Workshop Tropical and Non-Archimedean Geometry, Bellairs Research Institute (Barbados), May 6-13, 2011 (link)
  • 3rd PhD Students Conference on Tropical Geometry, Göttingen (Germany), January 28-29, 2011 (link)
  • SIAM Conference on Discrete Mathematics, Hyatt Regency Austin, Texas (USA), June 14-17, 2010 (link, slides)
  • DIAMANT/EIDMA-symposium, Lunteren (The Netherlands), November 26-27, 2009 (link)
  • Workshop Tropical Geometry in Combinatorics and Algebra, MSRI, Berkeley CA (USA), October 12-16, 2009 (link)
  • The North German Plain Goes Tropical, Göttingen (Germany), July 3, 2009 (link)
  • Phylogenetics 2009, Rényi Institute, Budapest (Hungary), June 22-25, 2009 (link)
  • MEGA 2009, Effective Methods in Algebraic Geometry, Barcelona (Spain), June 15-19, 2009 (link)
  • INdAM workshop, Geometry of Projective Varieties, Roma (Italy), September 30-October 4, 2008 (link)
  • Course on Tropical Enumerative Geometry, Barcelona (Spain), September 2-5, 2008 (link)
  • Symposium in memory of Joost van Hamel, K.U.Leuven (Belgium), June 28, 2008 (link)
  • Seminar on Algebraic Statistics, Oberwolfach (Germany), May 11-17, 2008 (link)
  • Short Course Tropical Geometry by Bernd Sturmfels, Barcelona (Spain), March 25-28, 2008 (link)
  • International Conference in honour to Pilar Pisón Casares, Commutative, Combinatorial and Computational Algebra, Sevilla (Spain), February 11-16, 2008 (link)
  • Algebraic Geometry in Higher Dimensions, Terme Levico (Italy), June 4-9, 2007
  • Linear systems and subschemes, Gent (Belgium), April 11-13, 2007
  • PRAGMATIC 2006, Extrinsic and formal geometry, Catania (Italy), September 4-23, 2006
  • Algebraic statistics, tropical geometry and computational biology, Nordfjordeid (Norway), June 17-21, 2006
  • AGaFe, Geometry of Algebraic Varieties, Ferrara (Italy), June 22-25, 2005
  • Workshop on Singularity Theory, Leuven (Belgium), June 9-11, 2005
  • International colloquium (in honour of M. Van den Bergh), Homological geometry - The mathematics behind non-commutative geometry, Brussels (Belgium), October 22-24, 2004
  • Projective varieties with unexpected properties: A conference in honour of the 150th anniversary of the birth of G. Veronese, Siena (Italy), June 8-12, 2004

Some links