Simeon Ball

Departament de Matemàtica Aplicada IV
Universitat Politècnica de Catalunya
Jordi Girona 1-3
Mòdul C3, Campus Nord
08034 Barcelona
Espanya

simeon@ma4.upc.edu

Higher Education

University of Sussex (1991-1994)

• Completed a Doctorate of Philosophy (Ph. D.) in March 1994 under the supervision of Prof. J. W. P. Hirschfeld in the area of finite geometry. This was funded by a scholarship from the Engineering and Physical Sciences Research Council of the United Kingdom. The title of the thesis was "On sets of points in finite planes".

University of Cambridge (1986-1989)

• Completed a Bachelor of Arts degree (BA Cantab) in Mathematics (tripos) in June 1989.

Employment

Universitat Politècnica de Catalunya (2007-)

• Senior Lecturer(Profesor Agregat) at the Facultat de Matemàtiques and the Escola d'Enginyeria de Telecomunicació i Aeroespacial de Castelldefels.

Universitat Politècnica de Catalunya (2003-2007)

• A research and teaching position funded in part by the "Ministerio de Ciencia y Tecnologia" as part of the "Ramón y Cajal" program. This time included visits to

  • Eötvös Loránd University, Budapest, Hungary for research collaboration as part of the "Acción integrada" joint program between the Spanish and Hungarian governments.

University of London (2000-2003)

• Advanced Research Fellowship (ref:AF/990 480) from the Engineering and Physical Sciences Research Council of the United Kingdom started February 2000 at Queen Mary College. A full-time research position with some teaching duties. The title of the research proposal was "Ovoids, hyperovals, unitals and maximal arcs in Desarguesian Spaces". This time has included visits to

  • Universitat Politècnica de Catalunya, Barcelona, Spain to give a course entitled "Lacunary Polynomials over finite fields" and for research collaboration.
  • Universiteit Gent, Belgium (September-November 2001) for research collaboration.
  • Università di Roma, "La Sapienza", Italy (March-April 2001) to give a course entitled "The geometry of finite fields".

Technical University of Eindhoven, The Netherlands (1997-1999)

• A two year Marie Curie research Fellowship (Training and Mobility of Researchers) from the European Commission under the supervision of Prof. A. Blokhuis. This was a full-time research position.

• In the period October 1996- March 1997 I was visiting fellow at the following universities

  • Free University of Amsterdam, The Netherlands (October-December 1996) for research collaboration.
  • University of Western Australia (January-February 1997) for research collaboration.
  • University of Adelaide, Australia (March 1997) for research collaboration.

Technical University of Eindhoven (1995-1996)

• A one year full-time research position employed as a Research Fellow until May 1996 on a project on Algebraic Geometric codes supported by the European Commission.

Publications

On the size of a double blocking set in PG(2,q), Finite Fields Appl., 2 (1996) 125--137.
( with A. Blokhuis)

On the size of a triple blocking set in PG(2,q), European J. Combin., 5 (1996) 427--435.

Multiple blocking sets and arcs in finite planes, J. London Math. Soc., 54 (1996) 581--593.

Maximal arcs in Desarguesian planes of odd order do not exist, Combinatorica, 17 (1997) 31--41.
( with A. Blokhuis and F. Mazzocca)

On small complete arcs in a finite plane, Discrete Math., 174 (1997) 29--34.

Partial unitals and related structures in Desarguesian planes, Des. Codes Cryptogr., 15 (1998) 231--236.

An easier proof of the maximal arcs conjecture, Proc. Amer. Math. Soc., 126 (1998) 3377--3380.
( with A. Blokhuis)

On nuclei and blocking sets in Desarguesian spaces, J. Combin. Theory Ser. A, 85 (1999) 232--237.

On the incompleteness of (k,n)-arcs in Desarguesian planes of order q where n divides q, Geom. Dedicata, 74 (1999) 325--332.
( with A. Blokhuis)

On the number of slopes determined by a function over a finite field, J. Combin. Theory Ser. A, 86 (1999) 187--196.
( with A. Blokhuis, A. E. Brouwer, L. Storme and T. Szonyi)

Unitals with many Baer sublines, Des. Codes Cryptogr., 17 (1999) 237--252.
( with A. Blokhuis and C. M. O'Keefe)

Polynomials in finite geometries, in: Surveys in combinatorics, 1999, Lamb, J. D. (ed) et al, Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 267, 17--35, 1999.

Polynomials in finite geometry, in: Methods of Discrete Mathematics, 1999, Löwe, S. (ed) et al, Quaderni di mathematica, Napoli, volume 5, 71--101, 1999.
( with A. Blokhuis)

On intersection sets in Desarguesian affine spaces, European J. Combin., 21 (2000) 441--446.

Linear (q+1)-fold blocking sets in PG(2,q^4), Finite Fields Appl., 6 (2000) 294--301.
( with A. Blokhuis and M. Lavrauw)

On (q²+q+2,q+2)-arcs in the projective plane PG(2,q), Des. Codes Cryptogr., 24 (2001) 205--224.
( with R. Hill, I. Landjev and H. Ward)

The classification of maximal arcs in small Desarguesian planes, Bull. Belg. Math. Soc., 9 (2002) 433--445.
( with A. Blokhuis)

Commutative semifields of rank 2 over their middle nucleus, in: Finite Fields with Applications to Coding Theory, Cryptography and Related Areas, Mullen, G. L. (ed) et al, Springer-Verlag, 1--21, 2002.
( with M. Lavrauw)

On the classification of semifield flocks, Adv. Math., 180 (2003) 104--111.
( with A. Blokhuis and M. Lavrauw)

The number of directions determined by a function over a finite field, J. Combin. Theory Ser. A, 104 (2003) 341--350.

On ovoids of O(5,q), Adv. Geom., 4 (2004) 1--7.

Symplectic spreads and permutation polynomials, in: Finite Fields and Applications, Mullen, G. L. (ed) et al, Springer-Verlag, 79--88, 2004.
( with M. Zieve)

Symplectic spreads, Des. Codes Cryptogr., 32 (2004) 9--14.
( with J. Bamberg, M. Lavrauw and T. Penttila)

The six semifield planes associated with a semifield flock, Adv. Math., 189 (2004) 68--87.
( with M. Brown)

Bounds on (n,r)-arcs and their application to linear codes, Finite Fields Appl., 11 (2005) 326--336.
( with J. W. P. Hirschfeld)

On ovoids of parabolic quadrics, Des. Codes Cryptogr., 38 (2006) 131--145.
( with P. Govaerts and L. Storme)

On ovoids of PG(3,q), Adv. Geom., 6 (2006) 177--198.


How to use Redei polynomials in higher dimensional spaces, Le Matematiche (Catania), 59 (2004) 39--52 (2006).
( with M. Lavrauw)

On the graph of a function in two variables over a finite field, J. Algebraic Combin., 23 (2006) 243--253.
( with M. Lavrauw)

Introducció als polinomis de Rédei, Butl. Soc. Catalana Mat., 21 (2006) 197--211.

Functions over finite fields that determine few directions, Electr. Notes in Discrete Math., 29 (2007) 185--188.

On linear codes whose weights and length have a common divisor, Adv. Math., 211 (2007) 94--104..
( with A. Blokhuis, A. Gacs, P. Sziklai and Zs. Weiner)

Affine blocking sets, three dimensional codes and the Griesmer bound, Discrete Math., 307 (2007) 1600--1608.
( with E. Montanucci)

A geometric construction of finite semifields, J. Algebra, 311 (2007) 117--129.
(with G. Ebert and M. Lavrauw)

On the Hughes-Kleinfeld and Knuth's semifields two dimensional over a weak nucleus, Des. Codes Cryptogr., 44 (2007) 63--67.
(with M. Lavrauw)

On the graph of a function in many variables over a finite field, Des. Codes Cryptogr., 47 (2008) 159--164.

On the number of directions determined by a pair of functions over a prime field, J. Combin. Theory Ser. A, 115 (2008) 505--516.
(with A. Gacs and P. Sziklai)

On the graph of a function over a prime field whose small powers have bounded degree, European J. Combin., 30 (2009) 1575--1584.
(with A. Gacs)

Multiple blocking sets in finite projective spaces and improvements to the Griesmer bound for linear codes, Des. Codes Cryptogr., 53 (2009) 119--136.
(with S. Fancsali)

Punctured Combinatorial Nullstellensatze, Combinatorica, 29 (2009) 511--522.
(with O. Serra)

The polynomial method in Galois geometries, in Current research topics in Galois geometry, Chapter 5, Nova Sci. Publ., New York, (2012) 105--130.

On sets of vectors of a finite vector space in which every subset of basis size is a basis, J. Eur. Math. Soc., 14 (2012) 733--748.

Asymptotic improvements to the lower bound of certain bipartite Turan numbers, Combin. Probab. Comput., 21 (2012) 323--329.
(with V. Pepe)

On sets of vectors of a finite vector space in which every subset of basis size is a basis II, Des. Codes Cryptogr., 65 (2012) 5--14.
(with J. De Beule)

An alternative way to generalise the pentagon, J. Combin. Des., 21 (2013) 163--179.
(with J. Bamberg, A. Devillers and K. Stokes)

A bound for the maximum weight of a linear code, SIAM J. Discrete Math., 27 (2013) 575--583.
(with A. Blokhuis)

Lacunary polynomials over finite fields, Handbook of Finite Fields, to appear.
(with A. Blokhuis)

On the representability of the bi-uniform matroid, SIAM J. Discrete Math., to appear.
(with C. Padro, Zs. Weiner and C. Xing)

Teaching

• Linear Algebra and its Applications, Escola d'Enginyeria de Telecomunicació i Aeroespacial de Castelldefels (Universitat Politècnica de Catalunya)
  (2012/2013 Q2) Lectures and exercise classes.
• Probability and Statistics, Escola d'Enginyeria de Telecomunicació i Aeroespacial de Castelldefels (Universitat Politècnica de Catalunya)
  (2012/2013 Q1) Lectures and exercise classes. (0.5)
• Linear Algebra and its Applications, Escola d'Enginyeria de Telecomunicació i Aeroespacial de Castelldefels (Universitat Politècnica de Catalunya)
  (2012/2013 Q1) Lectures and exercise classes. (1.5)
• Codes and Cryptography, Faculty of Mathematics (Universitat Politècnica de Catalunya)
  (2012/2013 Q1) Lectures. (0.5)
• Probability and Statistics, Escola d'Enginyeria de Telecomunicació i Aeroespacial de Castelldefels (Universitat Politècnica de Catalunya)
  (2011/2012 Q2) Lectures and exercise classes. (0.3)
• Linear Algebra and its Applications, Escola d'Enginyeria de Telecomunicació i Aeroespacial de Castelldefels (Universitat Politècnica de Catalunya)
  (2011/2012 Q2) Lectures and exercise classes. (2.0)
• Codes and Cryptography, Faculty of Mathematics (Universitat Politècnica de Catalunya)
  (2011/2012 Q1) Lectures. (0.5)
• Linear Algebra, Faculty of Mathematics (Universitat Politècnica de Catalunya)
  (2011/2012 Q1) Exercise classes.
• Linear Algebra and its Applications, Escola d'Enginyeria de Telecomunicació i Aeroespacial de Castelldefels (Universitat Politècnica de Catalunya)
  (2010/2011 Q2) Lectures and exercise classes.
• Codes and Cryptography, Faculty of Mathematics (Universitat Politècnica de Catalunya)
  (2010/2011 Q1) Lectures. (0.5)
• Linear Algebra and its Applications, Escola Politècnica Superior Castelldefels (Universitat Politècnica de Catalunya)
  (2010/2011 Q1) Lectures and exercise classes.
• Linear Algebra, Faculty of Mathematics (Universitat Politècnica de Catalunya)
  (2010/2011 Q1) Exercise classes.
• Linear Algebra and its Applications, Escola Politècnica Superior Castelldefels (Universitat Politècnica de Catalunya)
  (2009/2010 Q2) Lectures and exercise classes. (0.5)
• Linear Algebra, Faculty of Mathematics (Universitat Politècnica de Catalunya)
  (2009/2010 Q1) Exercise classes.
• Linear Algebra, Escola Tècnica Superior d'Enginyeria de Telecomunicació de Barcelona (Universitat Politècnica de Catalunya)
  (2009/2010 Q1) Lectures and exercise classes.
• Probability and Statistics, Escola Politècnica Superior Castelldefels (Universitat Politècnica de Catalunya)
  (2008/2009 Q2) Lectures and exercise classes.
• Mathematical Aspects of Telecommunication, Escola Politècnica Superior Castelldefels (Universitat Politècnica de Catalunya)
  (2008/2009 Q1) Lectures and exercise classes.
• Linear Algebra, Escola Tècnica Superior d'Enginyeria de Telecomunicació de Barcelona (Universitat Politècnica de Catalunya)
  (2008/2009 Q1) Exercise classes.
• Mathematical Aspects of Telecommunication, Escola Politècnica Superior Castelldefels (Universitat Politècnica de Catalunya)
  (2007/2008 Q2) Lectures and exercise classes.
• Mathematical Aspects of Telecommunication, Escola Politècnica Superior Castelldefels (Universitat Politècnica de Catalunya)
  (2007/2008 Q1) Lectures and exercise classes.
• Probability and Statistics, Escola Politècnica Superior Castelldefels (Universitat Politècnica de Catalunya)
  (2006/2007 Q2) Lectures and exercise classes.
• Probability and Statistics, Escola Politècnica Superior Castelldefels (Universitat Politècnica de Catalunya)
  (2005/2006 Q2) Lectures and exercise classes. (0.5)
• Combinatorics, Faculty of Mathematics (Universitat Politècnica de Catalunya)
  (2005/2006 Q1) Lectures and exercise classes. (0.5)
• Linear Algebra, Escola Tècnica Superior d'Enginyeria de Telecomunicació de Barcelona (Universitat Politècnica de Catalunya)
  (2004/2005 Q2) Lectures and exercise classes.
• Linear Algebra, Escola Tècnica Superior d'Enginyeria de Telecomunicació de Barcelona (Universitat Politècnica de Catalunya)
  (2004/2005 Q1) Exercise classes using MAPLE.
• Linear Algebra, Escola Tècnica Superior d'Enginyeria de Telecomunicació de Barcelona (Universitat Politècnica de Catalunya)
  (2003/2004 Q2) Lectures and exercise classes.
• Group Theory (Queen Mary, University of London)
  (2000/2001 Q2) Exercise classes.
• Linear Algebra (Queen Mary, University of London)
  (2000/2001 Q1) Exercise classes.

• Maximum Distance Separable codes (3.5 hours).
  Universitat Rovira i Virgili, Tarragona, Febraury 2013
• Blocking sets (3 hours).
  Universita di Napoli, Naples, February 2004
• Lacunary polynomials over finite fields (4 hours).
  Universitat Politècnica de Catalunya, Barcleona, March 2002
• The geometry of finite fields (6 hours)
  "La Sapienza", Universita di Roma, Rome, February 2001

Conferences

• Invited talks
  • "The maximum weight of a linear code", Combinatorics, Perugia, Italy, September 2012.
  • "Some applications of linear algebra over finite fields", Geometric and Algebraic Combinatorics 5 , Oisterwijk, The Netherlands, August 2011.
  • "On large subsets of a finite vector space in which every subset of basis size is a basis", 4th Pythagorean conference, Corfu, Greece, June 2010.
  • "Some problems in finite geometry where algebraic curves appear", Seminario de Geomtetria Torica, Jarandilla de la Vera (Caceres), Spain, November 2008.
  • "Finite projective planes and semifields", Antalya Algebra Days, Antalya, Turkey, May 2006.
  • "How to use Redei polynomials in higher dimensional spaces", Combinatorics, Catania, Italy, July 2004.
  • "Commutative semifields of rank 2 over their nuclei", Fq6, Oaxaca, Mexico, February 2001.
  • "Multi-arcs and maximal multi-arcs", Combinatorics, Gaeta, Italy, July 2000.
  • "Polynomials in finite geometries", British Combinatorial Conference, Canterbury, United Kingdom, July 1999.


• Other talks
  • "Some applications of linear algebra to block codes", Congress of the Spanish Mathematical Society, Santiago de Compostela, January 2013.
  • "The maximum weight of a linear code", Galois Geometries and applications, Royal Flemish Academy Contact Forum, Brussels, Belgium, October 2012.
  • "An alternative way to generalise the pentagon", Reinhold-Baer-Colloquium, Magdeburg, Germany, March 2012.
  • "A proof of the MDS conjecture over prime fields", 3rd International castle meeting on coding theory and applications, Cardona, Catalonia, September 2011.
  • "Some applications of linear algebra over finite fields", Workshop on Combinatorial designs, Singapore, May/June 2011.
  • "On large subsets of a finite vector space in which every subset of basis size is a basis", Algebraic Graph Theory, Banff International Research Station, Banff, Canada, March 2011.
  • "On large subsets of a finite vector space in which every subset of basis size is a basis", 100th anniversary of the Spanish Mathematical Society, Avila, Spain, February 2011.
  • "On large subsets of a finite vector space in which every subset of basis size is a basis", 1st joint meeting of the Catalan and Swedish mathematical societies, Barcelona, September 2010.
  • "On linear codes over a prime field and the Griesmer bound", Geometric and Algebraic Combinatorics 4 , Oisterwijk, The Netherlands, August 2008.
  • "Punctured Combinatorial Nullstellensatze", Combinatorics, Lago di Garda, Italy, June 2008.
  • "Punctured Combinatorial Nullstellensatze and applications to geometry and linear codes", Algebraic Geometry, Coding and Computing (Thematic Seminar) , Segovia, Spain, October 2007.
  • "Functions over finite fields that determine few directions", EUROCOMB 2007 , Seville, Spain, September 2007.
  • "On functions over a prime field that do not determine all directions", British Combinatorial Conference, Reading, United Kingdom, July 2007.
  • "Linear combinations of permutation polynomials that are permutation polynomials", 2nd Czech-Catalan Conference in Mathematics, Barcelona, Catalonia, September 2006.
  • "The number of directions determined by a function in many variables and linear combinations of permutation polynomials", Finite Geometries, Irsee, Germany, September 2006.
  • "Linear codes whose length and weights have a common divisor", Combinatorics, Ischia, Italy, July 2006.
  • "A new approach to finite semifields", British Combinatorial Conference, Durham, United Kingdom, July 2005, and 1st Czech-Catalan Conference in Mathematics, Prague, Czech Republic, May 2005.
  • "Los polinomios de Redei y aplicaciones a la geometria finita", Primero Congreso Conjunto de Matematicas, Valencia, Spain, January 2005.
  • "Redei polynomials and some applications to finite geometry", Finite Fields, Oberwolfach, Germany, 2004.
  • "The functions over a finite field that determine few directions", EUROCOMB 2003 , Prague, Czech Republic, 2003.
  • "Conditions on the existence of ovoids", Finite Geometries , Irsee, Germany, 2003.
  • "The number of directions determined by a function over a finite field", Combinatorics , Matera, Italy, 2002.
  • "The six semifields associated to a semifield flock", Finite Geometries, Oberwolfach, Germany, 2001.
  • "Maximal arcs in small Desarguesian planes", British Combinatorial Conference, Sussex, United Kingdom, 2001.
  • "Maximal multi-arcs in finite planes", Finite Geometries, Isle of Thorns, United Kingdom, 2000.
  • "Affine blocking sets or intersection sets", 2nd Pythagorean conference, Samos, Greece, 1999.
  
  
• Organising Committee
  • Fq10 Finite Fields and Their Applications , Ghent, Belgium, July 2011.
  • Fq9 Finite Fields and Their Applications , Dublin, Ireland, July 2009.

Editorships

I am on the editorial board of the following journals.

• Designs, Codes and Cryptography (since 2002)
• Finite Fields and Their Applications (since 2000)
• Journal of Geometry (since 2009)

I have also refereed articles for the following journals.

• Combinatorica
• Discrete Mathematics
• Electronic Journal of Combinatorics
• European Journal of Combinatorics
• IEEE Transactions on Information Theory
• Journal of Algebra
• Journal of Algebraic Combinatorics
• Journal of Combinatorial Theory

References

• Prof P. J. Cameron, Professor of Mathematics

  P.J.Cameron@qmul.ac.uk
  

  School of Mathematics and Astronomy,
  Queen Mary College,
  University of London,
  E1 4NS,
  United Kingdom
  

• Prof O. Serra, Professor of Mathematics

  oserra@mat.upc.es
  

  Departament de Matemàtica Aplicada IV,
  Universitat Politècnica de Catalunya,
  Jordi Girona 1-3,
  Mòdul C3, Campus Nord,
  08034 Barcelona,
  Espanya

Updated 30 April 2013