Compact Course: Theorems of the Alternative

The compact course Mathematical Complexity Reduction: Theorems of the Alternative (LSF) will be held within WS 2018 for PhD students of the Research Training Group. Interested master and PhD students, e.g., from the Faculty of Mathematics or the IMPRS, may also participate if places are available (Wahlfach).


From linear algebra to semi-algebraic geometry many areas in mathematics feature theorems of the alternative. For example, in linear algebra one has the basic fact that a linear endomorphism is either surjective, or has a nonzero vector in its kernel. This is sometimes called the Fredholm alternative. A theorem of the alternative is a theorem of the form: Either some problem is solvable, or there exists a certificate for the unsolvability which can be computed from the input data. In this compact course we take a tour of theorems of the alternative ranging from linear to non-linear and from equations to inequalities.

  • Date: March 07-March 13, 9:00-17:00, including breaks
  • Place: G03-214
  • The course will be taught in English

The course is organized and taught by Thomas Kahle and Eliana Duarte.


In order to register, show up at 9am on the first day.