Welcome to the homepage of Koen Thas







Contents




Hi !

Research Interests

Upcoming Selected Lectures

Past Selected Lectures

Organization of Conferences

International Awards/Honors

Articles

Bye !




Hi !





Born on february 21, 1977, I was a Research Assistant of IWT - Flanders (Belgium) between January 1, 2000
and September 30, 2002, under the supervision of Prof. Dr. H. Van Maldeghem.
I received my Ph.D. degree on March 29, 2002. Since October 1, 2002, I am a Postdoctoral Research Fellow of the Fund for Scientific Research --- Flanders (FWO - Flanders (Belgium)).
Since October 1, 2010, I am a Professor at Ghent University.
I work at the Department of Mathematics at Ghent University.


Address:

Krijgslaan 281, S25
9000 Ghent
BELGIUM
tel ++ 32 9 264 85 47
fax ++ 32 9 264 49 93
e-mail: koen.thas@gmail.com




Research Interests

  • Incidence Geometry;
  • Groups and Geometries;
  • Quantum Physics and Quantum Information Theory;
  • Authentication Codes;
  • Finite Geometry, Algebraic Geometry and Arithmetic;
  • Group Cohomology;
  • Absolute Arithmetic. (See F_un Mathematics.)




    Upcoming and Recent Selected Lectures


  • European Congress of Mathematics (6th ECM), Mini-symposium "Absolute Arithmetic and F1-Geometry", July 2012, Krakow, Poland.
  • Main Lecture at Buekenhout Geometry, Ghent, Belgium, September 20--21, 2012.
  • Main Lecture at DIAMANT Symposium, Heeze, The Netherlands, May 30--31, 2013.
  • Main Lecture at Eighth Shanghai Conference on Combinatorics (8SHCC), Shanghai, China, May 24--28, 2014.
  • "The Berkeley Lectures on F1," three lectures (totaling 4 hours), UC Berkeley, April 2014, Berkeley, US.
  • "Special Berkeley Lectures on F1," two lectures (totaling 2+ hours), UC Berkeley, April 2015, Berkeley, US.
  • "F1-Schemes, zeta functions and automorphisms" and "Combinatorics of F1" (totaling 2 hours), Spring Noncommutative Geometry Seminar, Caltech, Pasadena, US, March 30, 2016.
  • Invited Lecture at Reinhold-Baer Colloquium, TU Berline, Berlin, GE, January 21, 2017.
  • Spring Noncommutative Geometry Seminar, Caltech, Pasadena, US, April, 2017.




    Past Selected Lectures


  • Generalized Polygons, Academy Contact Forum, Palace of the Academies, Brussels, Belgium, October 20, 2000, Invited lecture.
  • Optimalization Symposium of First Joint Meeting of the Belgian and German Mathematical Societies, BMS-DMV 2001, Universite de Liege, Belgium, June 8--10, 2001, Invited lecture.
  • Finite Geometries, Mathematisches Forschungsinstitut Oberwolfach, Oberwolfach, Germany, December 2--8, 2001, One hour lecture.
  • Geometry Day, The University of Colorado at Denver, USA, July 18, 2003, Two Main lectures.
  • Special Session ``Finite Geometries'' of the Joint Central and Western Sectional AMS Meeting at Boulder, Denver, USA, October 2--4, 2003, Main lecture.
  • Geometry Symposium of Joint Meeting of the Belgian and Dutch Mathematical Societies, The University of Utrecht, The Netherlands, April 16--17, 2004, Main lecture
  • Finite Geometries, Groups and Computation (Pingree Park), Denver, USA, September 4--9, 2004, Invited lecture.
  • Baer Colloquium, Ghent University, Ghent, Belgium, June 10, 2006, Main lecture.
  • Generalized Quadrangles, Ovals and Related Structures: A Conference in Honor of Stanley E. Payne in conjunction with Finite Geometry and Combinatorics - AMS Central Session, Oxford, Ohio, USA, March 12-18, 2007, Main lecture.
  • Buildings and Groups, Ghent University, Ghent, Belgium, May 20-26, 2007, Invited lecture.
  • 39th Southeastern International Conference on Combinatorics, Graph Theory, and Computing, Florida Atlantic University, Boca Raton, FL, USA, March 3--7, 2008, Two Plenary lectures.
  • International Conference ``Inverse Problems, Modeling and Simulation'', Fetiyeh, Turkey, May 26--30, 2008, Invited lecture.
  • Meeting of the Class of Natural Sciences, The Royal Flemish Academy of Belgium for Sciences and the Arts, March 10, 2010, Brussels, Belgium, Invited speaker.
  • Combinatorics 2010, June 27-July 3, Verbania, Italy, Plenary speaker.
  • Baer colloquium Winter 2010, 20 november, Stuttgart, Germany, Invited speaker.
  • JAMI CONFERENCE ON ``NONCOMMUTATIVE GEOMETRY AND ARITHMETIC'', Johns Hopkins University, March 22-25, 2011, US, Invited speaker.
  • 23rd British Combinatorial Conference (BCC), July 4-8, 2011, Exeter, UK, Plenary speaker.




    Organization of Conferences and Seminars


  • Incidence Geometry and Buildings (IGB), February 2012, Ghent, Belgium. (Co-organizers: B. De Bruyn, T. De Medts, J. A. Thas, H. Van Maldeghem)
  • European Congress of Mathematics (6th ECM), Mini-symposium "Absolute Arithmetic and F1-Geometry", July 2012, Krakow, Poland.
  • 50 years of Finite Geometry - A conference on the occasion of Jef Thas's 70th birthday , November 13-15, 2014, Ghent, Belgium. (Co-organizers: J. W. P. Hirschfeld, H. Van Maldeghem)
  • The F_un seminars at Ghent University , The inaugural speaker was Yuri I. Manin (Max Planck Institute for Mathematics, Bonn, GE and Northwestern University, Evanston, US). The inaugural colloquium was scheduled for Tuesday February 3, 2015, Ghent, Belgium. The second colloquium happened on December 21, 2017. The speaker was Lieven Le Bruyn.




    International Awards/Honors



    Kirkman Medal of the ICA (Institute for Combinatorics and its Applications), Canada, 2006.

    Oberwolfach Research in Pairs Fellow (joint with S. De Winter and E. E. Shult), MFO, Germany, 2007.

    Triennial Prize of the Flemish Science Foundation (Vlaamse Wetenschappelijke Stichting) for Exact Sciences, Belgium, 2009. (€ 10,000)

    Nominee, quadrennial Frans Van Cauwelaert Prize for Exact Sciences, The Royal Flemish Academy of Belgium for Science and the Arts, Belgium, 2009.

    Selected as one of 7 Research ("BOF-ZAP") Professors at Ghent University (out of more than 150 candidates), 2010. (Not filled in.)

    Oberwolfach Research in Pairs Fellow (joint with J. Schillewaert), MFO, Germany, 2010.

    Starting Grant of the Special Research Fund (BOF) --- Flanders, Belgium, 2012--2016.

    Prof. Dr. R. Mullin and myself during the ICA award ceremony




    Articles


       Books/Chapters in Books/Oberwolfach Preprints
    1. K. Thas. Automorphisms and Characterizations of Finite Generalized Quadrangles, in: Generalized Polygons (Book), Proceedings of the Academy Contact Forum ``Generalized Polygons'' 20 October, Palace of the Academies, Brussels, Belgium (2001), 111--172.
    2. K. Thas. Symmetry in Finite Generalized Quadrangles, Frontiers in Mathematics 1, Birkhauser Verlag, Basel-Boston-Berlin, 2004. ISBN: 3-7643-6158-1
    3. J. A. Thas, K. Thas and H. Van Maldeghem. Translation Generalized Quadrangles, Series in Pure Mathematics 26, World Scientific, 2006. ISBN: 981-256-951-0
    4. S. De Winter, E. E. Shult and K. Thas. Singer Quadrangles, Oberwolfach Prepint OWP 2009-07, MFO Oberwolfach, 2009.
    5. J. Schillewaert and K. Thas. Categoric Aspects of Authentication, Oberwolfach Prepint OWP 2012-05, MFO Oberwolfach, 2012.
    6. K. Thas. A Course on Elation Quadrangles, EMS Series of Lectures in Mathematics, European Math. Soc., 2012.
    7. K. Thas. The Weyl-functor - Introduction to absolute arithmetic, in: Absolute Arithmetic and F1-Geometry, EMS Publishing House, Zurich, 2016, 3--38 pp.
    8. K. Thas. The combinatorial-motivic nature of F1-schemes, in: Absolute Arithmetic and F1-Geometry, EMS Publishing House, Zurich, 2016, 83--159 pp.
    9. K. Thas. A taste of Weil theory in characteristic one, in: Absolute Arithmetic and F1-Geometry, EMS Publishing House, Zurich, 2016, 365--386 pp.
    10. K. Thas (ed.). Absolute Arithmetic and F1-Geometry, EMS Publishing House, Zurich, 2016. ISBN: 978-3-03719-157-6 HOT
    11. J. Hirschfeld, K. Thas and H. Van Maldeghem (eds.). 50 Years of Finte Geometry, Innov. Incidence Geom. 15, 2017. NEW








      Combinatorial Geometry
    12. K. Thas. Non-existence of Complete (st - t/s)-Arcs in Generalized Quadrangles of Order (s,t), I, J. Combin. Theory Ser. A 97 (2002), 394--402.
    13. K. Thas. A Theorem Concerning Nets Arising from Generalized Quadrangles with a Regular Point, Des. Codes Cryptogr. 25 (2002), 247--253.
    14. K. Thas. On Semi Quadrangles, Ars Combin. LXVII (2003), 65--87.


      Groups and Geometries (Local/Global)
    15. K. Thas. On symmetries and translation generalized quadrangles, Finite Geometries, Proceedings of the Fourth Isle of Thorns Conference, 16--21 July 2000, Edited by A. Blokhuis et al., Developments in Mathematics 3 (2001), Kluwer Academic Publishers, 333--345.
    16. K. Thas. Classification of span-symmetric generalized quadrangles of order s, Adv. Geom. 2 (2002), 189--196.
    17. K. Thas. On Generalized Quadrangles with Some Concurrent Axes of Symmetry, pages, Bull. Belgian Math. Soc. --- Simon Stevin 9 (2002), 217--243.
    18. K. Thas. The Classification of Generalized Quadrangles with Two Translation Points, Beitr"age Algebra Geom. (Contributions to Algebra and Geometry) 43 (2002), 365--398.
    19. B. De Bruyn and K. Thas. Generalized quadrangles with a spread of symmetry and near polygons, Illinois J. Math. 46 Fall (2002), 797--818.
    20. K. Thas. Finite flag-transitive projective planes: a survey and some remarks, Discrete Math. 266 (2003), 417--429.
    21. K. Thas. Symmetry in Generalized Quadrangles, Des. Codes Cryptogr. (Proceedings of the Oberwolfach 2001 Conference ``Finite Geometries'') 29 (2003), 227--245.
    22. K. Thas. A characterization of the generalized quadrangle Q(5,q), and the non-existence of certain near polygons, J. Combin. Theory Ser. A 103 (2003), 105--120.
    23. K. Thas. Translation Generalized Quadrangles for which the Translation Dual Arises from a Flock, Glasgow Math. J. 45(3) (2003), 457--474.
    24. S. E. Payne and K. Thas. Notes on Elation Generalized Quadrangles, European J. Combin. 24(8) (2003), 969--981.
    25. K. Thas. On a Conjecture of W. M. Kantor, and Strongly Irreducible Groups Acting on Generalized Quadrangles, Forum Math. 16 (2004), 671--679.
    26. A. Offer, K. Thas and H. Van Maldeghem. Generalized Quadrangles with an Ovoid that is Translation with Respect to Opposite Flags, Arch. Math. 84 (2005), 375--384.
    27. K. Thas and H. Van Maldeghem. Moufang-Like Conditions for Generalized Quadrangles and Classification of All Finite Quasi-Transitive Generalized Quadrangles, Discrete Math. (Proceedings of the 2003 Kloster Irsee Conference) 294 (2005), 203--217.
    28. K. Thas. A Lecture on Some Recent Developments and Open Problems in the Automorphism Theory of Generalized Quadrangles, Quaderni Elettronici del Seminario di Geometria Combinatoria 21E (Giugno 2005), 1--16. (Università degli Studi di Roma "La Sapienza" - Dipartimento di Matematica)
    29. K. Thas. Generalized quadrangles admitting PSL(2,q)*PSL(2,q), J. Combin. Designs 13 (2005), 425--434.
    30. K. Thas and S. E. Payne. Foundations of Elation Generalized Quadrangles, European J. Math. 27 (2006), 51--61.
    31. K. Thas. Elation Generalized Quadrangles of Order $(q,q^2)$, $q$ Even, with a Classical subGQ of Order $q$ Containing the Elation Point are Classical, Adv. Geom 6 (2006), 265--274.
    32. K. Thas. Some basic questions and conjectures on elation generalized quadrangles, and their solutions, Bull. Belgian Math. Soc. --- Simon Stevin (Proceedings of the La Roche 2004 conference `Finite Geometries') 12 (2005/2006), 909--918.
    33. S. De Winter and K. Thas. Generalized quadrangles with an abelian Singer group, Des. Codes Cryptogr. 39 (2006), 81--87.
    34. J. A. Thas and K. Thas. Translation Generalized Quadrangles in Even Characteristic, Combinatorica 26 (2006), 709--732.
    35. K. Thas. Determination of Elation Generalized Quadrangles with Distinct Elation Points, 25 pages, J. Algebraic Combin 24 (2006), 5--22.
    36. J. A. Thas and K. Thas. Translation generalized quadrangles: old results, new results, open problems, Proceedings of the Pingree Park Conference `Finite Geometries, Groups ad Computation', (2006), 223--236.
    37. K. Thas. Generalized quadrangles of order $(p,t)$ with a $2$-transitive regulus, $p$ a prime, J. Combin. Theory Ser. A 113 (2006), 1565--1571.
    38. J. A. Thas and K. Thas. Subquadrangles of order $s$ of generalized quadrangles of order $(s,s^2)$, III, J. Combin. Theory Ser. A 113 (2006), 1791-1804.
    39. K. Thas. A stabilizer lemma for translation generalized quadrangles, European J. Combin. 28 (2007), 1--16.
    40. S. De Winter and K. Thas. The automorphism group of Payne derived generalized quadrangles, Adv. Math. 214 (2007), 146--156.
    41. K. Thas. A question of Kantor on elations of translation generalized quadrangles, Adv. Geom. 7 (2007), 375--378.
    42. K. Thas. Solution of a question of Knarr, Proc. Amer. Math. Soc. 136 (2008), 1409--1418.
    43. K. Thas and H. Van Maldeghem. Geometric characterizations of finite Chevalley groups of type B_2, Trans. Amer. Math. Soc 360 (2008), 2327--2357.
    44. K. Thas. A Kantor family admitting a normal $F$-factor constitutes a $p$-group, Adv. Geom. 8 (2008), 155--159.
    45. K. Thas. Elation generalized quadrangles with extra automorphisms and trivial spans, European J. Combin. 29 (2008), 439--442.
    46. K. Thas. A generalized quadrangle of order $(s,t)$ with center of transitivity is an elation quadrangle if $s \leq t$, Designs, Codes, Cryptogr. 47 (2008), 221--224.
    47. S. De Winter and K. Thas. Generalized quadrangles admitting a sharply transitive Heisenberg group, Designs, Codes, Cryptogr. 47 (2008), 237--242.
    48. K. Thas. Note on the existence of translation nets, Designs, Codes, Cryptogr. 48 (2008), 105--107.
    49. K. Thas. Finite BN-pairs of rank 2, I, Innov. Incidence Geom. 9 (2009), 189--202.
    50. J. A. Thas and K. Thas. Subquadrangles of order $s$ of generalized quadrangles of order $(s,s^2)$, Innov. Incidence Geom. 10 (2009), 133--145.
    51. E. E. Shult and K. Thas. A theorem of Cohen on parapolar spaces, Combinatorica 30 (2010), 435--444.
    52. S. De Winter and K. Thas. Bounds on partial ovoids and spreads in classical generalized quadrangles, Innov. Incidence Geom. 11 (2010), 19--33.
    53. J. A. Thas and K. Thas. Translation Generalized Quadrangles and Translation Duals, Part I, 21 pp., Discrete Math., to appear.
    54. K. Thas. Generalized quadrangles from a local point of view, Proceedings of "Combinatorics 2010" (Vol. of plenary speakers), J. Geom. 101 (2011), 223--238.
    55. K. Thas. Isomorphisms of groups related to flocks,J. Algebraic Combin. 36 (2012), 111--121.
    56. K. Thas. Local half Moufang quadrangles, Designs Codes Cryptogr. 68 (2013), 319--324.
    57. K. Thas. Classification of skew translation generalized quadrangles, I, Discrete Math. Theoretical Computer Science 17 (2015), 89--96.
    58. J. Hirschfeld, K. Thas and H. Van Maldeghem. 50 Years of finte geometry, Innov. Incidence Geom. 15 (2017), 1--3.
    59. J. A. Thas and K. Thas. Covers for quadrangles, Glasgow Math. J. 60 (2018), 585--601.
    60. K. Thas. Central aspects of skew translation quadrangles, I, J. Algebraic Combin. 48 (2018), 429--479.
    61. K. Thas. A translation generalized quadrangle in characteristic $\ne 0$ is linear, Adv. Math. 342 (2019), 116--133.


      62. Absolute Algebraic Geometry
    62. K. Thas. Order in building theory, Surveys in Combinatorics 2011, London Math. Soc. Lecture Note Ser. 392, Cambridge University Press, 2011, pp. 235--331.
    63. K. Thas. The structure of Deitmar schemes, I, Proc. Japan Acad. Sci. Math. 90 (2014), 21--26.
    64. K. Thas. The Connes-Consani plane connection, J. Number Theory 167 (2016), 407--429.
    65. M. Merida-Angulo and K. Thas. Deitmar schemes, graphs and zeta functions, J. Geom. Physics 117 (2017), 234--266.
    66. K. Thas. Counting points and acquiring flesh, Innov. Inc. Geom. 15 (2017), 36 pp., 229--264.
    67. M. Merida-Angulo and K. Thas. The structure of Deitmar schemes, II, Zeta functions and automorphism groups, C. R. Math. Rep. Acad. Sci. Canada 39 (2017), 142--152.
    68. M. Merida-Angulo and K. Thas. Automorphisms of Deitmar schemes, I. Functoriality and trees, J. Geom. Physics 136 (2019), 68--88.
    69. K. Thas. Projective spaces over F1l, J. Combin. Des. 27 (2019), 55--74.
      70. SEE ALSO THE CHAPTER/BOOK SECTION ABOVE FOR MORE ON ABSOLUTE GEOMETRY (esp. the items 7-8-9-10).





      Finite Geometry, Algebraic Geometry and Arithmetic
    70. K. Thas. Topics in Finite and Algebraic Geometry, Atti Semin. Mat. Fis. Univ. Modena Reggio Emilia 54 (2006/2007), 1--73.
    71. Koen Thas and Don Zagier. Finite projective planes, Fermat curves and Gaussian periods, J. European Math. Soc. 10 (2008), 173--190.
    72. K. Thas. On the Number of Points of a Hypersurface in Finite Projective Space (after J.-P. Serre), Ars Combin. XCIV (2010), 183--190.


      Homological Algebra
    73. K. Thas. On the p-modular cohomology algebra of a finite p-group and a theorem of Serre, C. R. Math. Acad. Sci. Paris 344 (2007), 417-420.


      Mathematical Physics and Riemannian Geometry
    74. K. Thas. Kac's question, planar isospectral pairs and involutions in projective space, J. Phys. A: Math. Gen. 39 (23) (2006), L385-L388.
    75. K. Thas. Kac's question, planar isospectral pairs and involutions in projective space: II. Classification of generalized projective isospectral data, J. Phys. A: Math. Gen. 39 (42) (2006), 13237-13242.
    76. K. Thas. PSLn(q) as operator group of isospectral drums, J. Phys. A: Math. Gen. 39 (50) (2006), L673-L675.
    77. K. Thas. Isospectral drums in $\mathbb{R}^2$, involution graphs and Euclidean TI-domains, J. Phys. A: Math. Theor. 40 (2007), 7233--7238.
    78. K. Thas. Can one hear the shape of a Lie type geometry ?, Inverse Problems 23 (2007), 2021--2028.
    79. O. Giraud and K. Thas. Hearing the shape of drums: Physical and Mathematical aspects of isospectrality, Rev. Modern Phys. 82 (2010), 2213--2255.
    80. J. Schillewaert and K. Thas. The 2-transitive transplantable isospectral drums, Symm. Integr. Geom.: Meth. Appl. (SIGMA) 7 080 (2011), 8pp.
    81. K. Thas. Isospectral drums and simple groups, Int. J. Geom. Meth. Mod. Physics 15 (2018), 1850060, 32 pp.


      82. Quantum Information Theory and Geometry
    82. K. Thas. Pauli operators of N-qubit Hilbert spaces and the Saniga-Planat conjecture, Chaos, Solitons and Fractals, 3 pp., to appear.
    83. K. Thas. The geometry of generalized Pauli operators of N-qudit Hilbert space, and an application to MUBs, EPL (Europhysics Letters) 86 (2009) 60005.
    84. K. Thas. Unextendible mutually unbiased bases (after Mandayam, Bandyopadhyay, Grassl and Wootters), Entropy 18 (2016), 395 (15pp.).
    85. K. Thas. On the mathematical foundations of mutually unbiased bases, Quantum Inform. Proc. 17 (2018), Art. 25, 17 pp.
    86. K. Thas. Absolute Quantum Theory (after Chang, Lewis, Minic and Takeuchi), and a road to quantum deletion, Symmetry 2019, 11, 174 (13 pp.) NEW

      Authetication Codes
    87. J. Schillewaert and K. Thas. Construction and comparison of authentication codes, SIAM J. Discrete Math. 28 (2014), 474--489.


      88. Submitted
    88. K. Thas. A question of Frohardt on 2-groups, and skew translation quadrangles of even order, 10 pp. (Submitted) NEW
    89. S. De Winter and K. Thas. A criterion concerning Singer groups of generalized quadrangles, 30 pp. (Submitted) OLD
    90. K. Thas. General Quantum Theory, 19pp. (Submitted, being revised) NEW
    91. K. Thas. The geometry of drums, 14pp. (Submitted)
    92. M. Merida-Angulo and K. Thas. Graphs, F1-schemes and virtual mixed Tate motives, 8pp. (Submitted)

      Almost Finished
    93. K. Thas. Motives of synthetic geometries, I, appr. 45 pp. (In preparation) NEW
    94. J. A. Thas and K. Thas. Covers for quadrangles, 2. Kantor-Knuth covers and embedded ovoids, appr. 20 pp. (In preparation) NEW
    95. K. Thas. Infinite generalized quadrangles admitting abelian Singer groups, appr. 10 pp. (In preparation) NEW
    96. K. Thas. A question of Moorhouse on locally finite generalized quadrangles, appr. 10 pp. (In preparation) NEW
    97. K. Thas. Authentication codes, automorphisms and cohomology of local geometries, appr. 25 pp. (In preparation)
    98. K. Thas. Central aspects of skew translation quadrangles, II, appr. 40 pp. (In preparation)
    99. K. Thas. Generation of translation quadrangles. (In preparation)



      100. Preprints
    100. K. Thas. New bounds for finite field Besicovitch sets. (Preprint, NIP)
    101. K. Thas. A remark concerning union-closed families and Frankl's conjecture. (Preprint, NIP)
    102. S. De Winter, E. E. Shult and K. Thas. The Singer quadrangles amongst the known generalized quadrangles. (Preprint, NIP)
    103. K. Thas and S. Yoshiara. Translation generalized ovals and Singer quadrangles. (Preprint, NIP)
    104. K. Thas. Locally finite generalized polygons. (In preparation)
    105. K. Thas. Finite BN-pairs of rank 2, II. (Preprint)
    106. K. Thas. Mutually unbiased bases in N-qudit Hilbert space where N is a composite. (In preparation)
    107. K. Thas. Cohomology of semifields. (In preparation)
    108. K. Thas. Local Moufang conditions and a question of Knarr. (In preparation)
    109. J. A. Thas and K. Thas. Regulus Replacement Lemma, and an application to UMUBs. (In preparation)


      110.  Theses
    110. K. Thas. Symmetrieen in Eindige Veralgemeende Vierhoeken (Symmetries in Finite Generalized Quadrangles), Master Thesis, Ghent University, Ghent (1999), 186 pp.
    111. K. Thas. Automorphisms and Combinatorics of Finite Generalized Quadrangles, Ph.D. Thesis, Ghent University, Ghent (2002), xxviii + 412 pp.




    Bye !