#### Event Title

Invariant Subspaces and Their Invariants

#### Description

Subspaces of vector spaces that are invariant under the action of a linear operator have garnered a lot of interest since the late 19th Century. In the Jordan Normal Form Theorem, vector spaces are decomposed as a direct sum of cyclic invariant subspaces. In case the base field is finite, the invariant subspaces can be counted; one can try to classify them up to isomorphy, or study their projective variety.

In this talk, Schmidmeier will discuss combinatorial isomorphism invariants that are based on partitions. The Klein tableaux play a particular role as they link the counting problem, the classification up to isomorphy, and the geometric approach.

#### Date of Event

April 28, 2010 12 - 1:00 PM

#### Location

Mailman-Hollywood Building, Room 309, 3301 College Ave., Fort Lauderdale (main campus)

#### NSU News Release Link

http://nsunews.nova.edu/dont-final-mathematics-colloquium-series-talk-semester-invariant-subspaces-invariants-apr-28/

Invariant Subspaces and Their Invariants

Mailman-Hollywood Building, Room 309, 3301 College Ave., Fort Lauderdale (main campus)

Subspaces of vector spaces that are invariant under the action of a linear operator have garnered a lot of interest since the late 19th Century. In the Jordan Normal Form Theorem, vector spaces are decomposed as a direct sum of cyclic invariant subspaces. In case the base field is finite, the invariant subspaces can be counted; one can try to classify them up to isomorphy, or study their projective variety.

In this talk, Schmidmeier will discuss combinatorial isomorphism invariants that are based on partitions. The Klein tableaux play a particular role as they link the counting problem, the classification up to isomorphy, and the geometric approach.

https://nsuworks.nova.edu/mathematics_colloquium/ay_2009-2010/events/1

## Presenter Bio

Markus Schmideier has a Ph.D. and is an Associate Professor at Florida Atlantic University