Discrete Algebra and Geometry

Phenomena throughout mathematics and the natural sciences have discrete algebraic aspects, often along with analytical counterparts. While the latter are typically modelled using real numbers, differential equations, and numerical computations, describing the discrete-algebraic aspects involves objects like nite elds, graphs, polynomials, groups, algebras, and symbolic computations.

The Discrete Algebra and Geometry group at the TU/e develops the mathematics needed for such a description. It plays a leading role in algebraic graph theory, nite and incidence geometry, and discrete Lie theory. Moreover team members are active in the elds of computer algebra, interactive mathematics, and applicable algebraic geometry.

You can find more information about algebraic graph theory, coding theory, computer algebra, cardinal and ordinate numbers, but also games and puzzles, on the following websites:

Group leader: dr. Hans Cuypers

Hans Cuypers has received a MSc from Radbout University Nijmegen, and a PhD degree from Utrecht University, both in Mathematics. After spending a year at Michigan State University (USA) and another year at the University of Kiel (Germany), he joined the Eindhoven University of Technology in 1991. His research interests include Lie incidence geometry and group theory as well as the topic of interactive mathematics.

Cuypers has published over 70 research papers and (co-)authored three books. He is also leading the development of the software system MathDox for interactive mathematics. He has been involved (both as participant and as leader) in various national and international projects. Cuypers has been co-promotor of 3 PhD-students.

Key Publications

1. Arjeh M. Cohen and Gábor Ivanyos, Root ltration spaces from Lie algebras and abstract root groups, J. Algebra 300 (2006), no. 2, 433-454.

2. Hans Cuypers, Extended near hexagons and line systems, Advances in Geometry 4 (2004), 181-214.

3. Aart Blokhuis, László Lovász, Leo Storme, Tamás Szöönyi, On multiple blocking sets in Galois planes, Adv. Geom. 7 (2007), no. 1, 39-53.

4. Jan Draisma and Jochen Kuttler, On the ideals of equivariant tree models, Math. Ann. 344 (2009), no. 3, 619-644.

5. Arjeh Cohen, Hans Cuypers and Rikko Verrijzer, Mathematical Context in Interactive Documents, Mathematics in Computer Science, Volume 3, Number 3, 2010, 331-347.

Prof. dr. A.M. Cohen

Arjeh Cohen studied mathematics and theoretical computer science at Utrecht, where he obtained his Ph.D. degree in 1975. He worked at the Openbaar Lichaam Rijnmond (Rotterdam), the Technische Universiteit Twente (Enschede), CWI (Amsterdam), and at the Universiteit Utrecht, where he became a full professor in 1990.  Since 1992, he has been a full professor of Discrete Mathematics at the Technische Universiteit Eindhoven (TU/e).

He was dean of the Department of Mathematics and Computer Science at TU/e from 2009 till 2013, member of the board of the Foundation EURANDOM, chairman of the board of the Foundation CAN (from which the CANDiensten company originated), member of the Supervisory Council of the research school Beta, and member of the Advisory Council of the Eindhoven School of Education. He occupied visiting positions in Ann Arbor, Ber Sheva, Jerusalem, Kobe, Naples, Pasadena, Rome, Santa Cruz, and Sydney.

Cohen's main scientific contributions are in groups and geometries of Lie type, and in algorithms for algebras and their implementations. He is also known for his work on interactive mathematical documents. Eighteen students received a PhD. under his supervision. Currently, he is or has been on the editorial board of six research journals and the ACM book series of Springer-Verlag. 

He published 115 research papers, coauthored four books, and (co-)edited another eight.