The Department of Mathematics and Computer Science provides undergraduate and MSc programs in Industrial and Applied Mathematics and in Computer Science. The Department has research collaborations with other Departments at the Technische Universiteit Eindhoven as well as with a large number of other universities and companies, both at home and abroad. The Department has approximately 350 employees and more than 700 students.
The Discrete Mathematics group focuses on discrete mathematics, algebra, geometry and computer mathematics. These areas represent a number of subjects, from applied to more fundamental: (Lie) algebras & representation theory, groups of Lie type and their geometries, combinatorics, and interactive mathematics and computer algebra.
This exciting Ph.D. project should be seen as part of a rapidly intensifying, world-wide focus on “applicable algebraic geometry”, with good job prospects afterwards. The student will learn the basics of the subject from Draisma and his (local and global) collaborators, and will quickly be led to the point where s/he can make valuable own contributions.
Ultimately, the project should lead to a solid foundation for highly symmetric systems of polynomial equations in infinitely many variables, analogous to Hilbert's groundbreaking work for finitely many variables at the turn of the century, as well as to computational tools analogous to Groebner basis algorithms. Apart from research, the student will be required to help out with teaching (typically one exercise class per semester, except in the first and last semesters).
The prospective should have successfully concluded undergraduate studies in mathematics, including basic abstract algebra (fields, rings, groups, etc.) Ideally, the student should already have learned some of the basics of (computational) algebraic geometry or commutative algebra, such as Groebner bases, algebraic groups, etc---but this is not strictly necessary.
“Ph.D. student” in the Netherlands is a full-fledged, four-year job. It comes with a good salary, climbing from approximately 2040 euros (gross) in the first year to 2600 euros (gross) in the fourth and last year. Discrete mathematics at TU/e comprises renowned mathematicians in areas ranging from algebra and geometry (which hosts this project) and optimisation to coding theory and cryptology. Depending on the direction the project takes, there will also be contact with further top-rank mathematicians in statistics & stochastics. TU/e has an attractive campus with excellent sports facilities, help in finding housing, child care facilities, etc.
PhD student Infinite - dimensional polynomial systems of equations with symmetry
