Research

My research interests are in the field of functional analysis, analysis on fractals, operator algebras, dynamical systems, wavelets. In particular, my work involves the interaction between operator theory/algebra and irreversible dynamical systems. In my thesis I studied the properties of operator algebras (self-adjoint and non-self-adjoint) associated with Mauldin-Williams graphs and the dynamical systems they determine.

Some problems I am currently pursuing include groupoids associated with dynamical systems and wavelets, the generalized Effros-Hahn conjecture for groupoids and groupoid dynamical systems, as well as the study of differential and pseudodiferrential operators on PCF self-similar fractals.

Here you can download a copy of my Research Statement.

Publications and Preprints

"Pseudodifferential operators on PCF Self-Similar Fractals", (with L.G. Rogers and R.S. Strichartz), in preparation.
"Complex powers of the Laplacian on PCF Self-Similar Fractals", (with R.S. Strichartz), in preparation.
"Markov Operators and $C^*$-Algebras", (with Paul S. Muhly), submitted.
"The Resolvent Kernel for PCF Self-Similar Fractals", (with E.P.J. Pearse, L. G. Rogers, H. Ruan, R.S. Strichartz), Trans. Amer. Math. Soc., accepted arXiv:0811.4203.
"The Generalized Effros-Hahn Conjecture for Groupoids", (with Dana P. Williams), Indiana Univ. Math. J., accepted arXiv:0807.4683.
"Irreducible representations of groupoid C*-algebras", (with Dana P. Williams), Proc. Amer. Math. Soc. 137 (2009), 1323-1332 Link to the paper.
"Groupoid Methods in Wavelet Analysis", (with Paul Muhly), Group representations, ergodic theory, and mathematical physics: a tribute to George W. Mackey, 193--208, Contemp. Math., 449, Amer. Math. Soc., Providence, RI, 2008., Link to the paper
$C^{\ast}$ -algebras associated with Mauldin-Williams graphs'', (with Y. Watatani), Can. Math. Bull, 51 (2008), no 4, 545--560. Link to the paper.
"Operator algebras and Mauldin-Williams graphs", Rocky Mountain Journal of Mathematics, 37 (2007), no. 3, 829 -- 849. , Link to the paper.
"Mauldin-Williams graphs, Morita Equivalence and isomorphisms", Proc. Amer. Math. Soc. 134 (2006), no. 4, 1087--1097 , Link to the paper.

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Department of Mathematics

Marius Ionescu, 27 Oct 2009