College of Liberal Arts & Sciences

# Algebra Seminar

Speaker:

Alana Huszar

Topic:

Non-commutative Rank and Stability of Quiver Representations

**Abstract: **

How would we figure out what the rank of a matrix is, when we're considering its rank over a free skew field? This non-commutative version of the "Edmonds' problem", tackled by many computer scientists, has rich connections to invariant theory and quiver representations. In this example based talk, we'll go through different formulations of non-commutative rank, and tools we can use from invariant theory, like the "nullcone", to tell us about this rank. We'll ultimately generalize non-commutative rank to any quiver representation, providing a method to measure how far from stable a representation is.

Event Date:

April 26, 2021 - 3:30pm to 4:20pm

Location:

Online

Calendar Category:

Seminar

Seminar Category:

Algebra