# On the convexity of the spectral radius of certain operators

# On the convexity of the spectral radius of certain operators

Start:

Monday, November 4, 2024 11:00 am

End:

Monday, November 4, 2024 11:50 am

Location:

STAG 161

Patrick De Leenheer

Oregon State University

Motivated by control problems arising in biology, we perform an investigation of the spectral properties of certain matrices. We conjecture that the spectral radius of De^{tA} is convex in t whenever D is diagonal with positive entries, and e^{tA} is the matrix exponential of an essentially nonnegative matrix A, provided that the right-most eigenvalue of A is nonzero. We report on some progress we made towards proving this conjecture, and will discuss some applications where extensions of this conjecture seem to appear naturally.

This is joint work with Swati Patel.

Contact:

Philipp Kunde