### Optimization and Systems Theory Seminar

Wednesday, April 5, 2000, 11.00-12.00, Room 3733, Lindstedtsv. 25

**Professor Joachim
Rosenthal**

Department of Mathematics

University of Notre Dame

Notre Dame, Indiana

USA

and

Department of Communication Systems

Ecole Polytechnique Fédérale de Lausanne - EPFL

Lausanne

Switzerland

E-mail: Joachim.J.Rosenthal.1@nd.edu

####
Pole placement problems, inverse eigenvalue problems
and Schubert calculus

Several prominent problems originating in linear algebra and in
control theory are through their nature actually problems in
algebraic geometry. Examples include a large class of so called
*matrix extension problems* studied in the linear algebra
literature as well as most *pole placement problems* studied
in the linear systems theory literature.
In this talk we will explain those different links and we will
report on several recent results obtained by geometric
techniques. We will show how many of those problems have an
interpretation in terms of Schubert calculus and that some of the
more prominent problems require computations in the quantum ring
of the Grassmannian.

The presented results represent joint work with Bill Helton,
Meeyoung Kim, M.S. Ravi, Frank Sottile and Alex Wang.

Calendar of seminars

*Last update: March 28, 2000 by
Anders Forsgren,
anders.forsgren@math.kth.se.
*