Three versions of the same topic: Spectral theory of reducible nonnegative matrices in classical and max linear algebra.

Moscow and ILAS Shanghai, July 2007

ILAS Cancun, June 2008

Vienna, October 2008

At a meeting in honor of Ivo Marek at Novisad, Serbia, in May 2008 I gave a talk "A comparison theorem in Population Dynamics" based on a joint paper with C.K. Li. I had previously given this talk in Cuernavaca, Mexico in 2001.

SPLITTINGS of LINEAR OPERATORS: LYAPUNOV and PERRON-FROBENIUS is a talk I have given several times, most recently at U. Connecticut in November 2007. It is based on one of my favorite papers. Though published in 1965, it has had more citations since 2000 than any of my other papers.

I gave the talk "Conditions for strict inequality in comparisons of spectral radii of nonnegative matrices" at an Oberwolfach meeting in November 2000. It led to a discussion which resulted in a paper joint with Elsner, Frommer, Nabben and Szyld with the same title but containing more material. . A subsequent paper Comparison theorems using general cones for norms of iteration matrices joint with Seidman and Arav on a related topic corresponds to the talk with the same title.

My talk at the Haifa Matrix Theory Conference in May 2009. It's based on the paper On visualization scaling, subeigenvectors and Kleene stars in max algebra, joint with Peter Butkovic and Sergei Sergeev. For a similar topic with a very different emphasis see my talk Why visualize in max algebra? given at the Montreal Workshop on tropical and idempotent mathematics in June 2009. I gave a related talk (putting more emphasis on diagonal scaling) at a meeting at Northern Illinois University in July 2009.

My talk at the Novi Sad meeting in May 2010. See ON COMMUTING MATRICES IN MAX ALGEBRA AND IN CLASSICAL NONNEGATIVE ALGEBRA for the corroesponding paper joint with RICARDO D. KATZ AND SERGEI SERGEEV.

Why I love Perron-Frobenius, a talk I gave to the Illinois Section of the MAA in 1997.

Why did Frobenius despise graph theory and was he right?, a talk I gave in 1996 in several places. It's a discussion of the famous controversy between Frobenius and Denes K"onig (starting with Frobenius' remark about another famous mathematician). It contains quite a bit of mathematics.