My research interests are in the field of harmonic and functional analysis. More specifically, my recent work involves projects in analysis on fractals, and the interaction between operator algebras and irreversible dynamical systems and wavelets. Some problems I am currently pursuing include the theory and applications of Calderón-Zygmund and pseudodiferrential operators on p.c.f. self-similar fractals, the construction and properties of groupoids associated with dynamical systems and wavelets, and a proof of the generalized Effros-Hahn conjecture for groupoids and Fell bundle over groupoids. You can download below the papers that I published or recently submitted for publication.
- Marius Ionescu, Alex Kumjian, Aidan Sims, and Dana P. Williams. A Stabilization Theorem for Fell bundles over groupoids, Royal Soc of Edinburgh - Proc A, accepted for publication, 2016.
- Marius Ionescu, Kasso A. Okoudjou, and Luke G. Rogers. Some spectral properties of pseudo-differential operators on the Sierpinski gasket, Proc. Amer. Math. Soc., accepted for publication, 2016.
- Marius Ionescu and Dana P. Williams. Inducing irreducible representations of Fell Bundles, Trans. Amer. Math. Soc. 367 (2015), no. 7, 5059–5079.
- Marius Ionescu and Alex Kumjian Groupoid actions on fractafolds SIGMA Symmetry Integrability Geom. Methods Appl. 10:Paper 068, 14, 2014
- Marius Ionescu and Luke G. Rogers. Complex Powers of the Laplacian on Affine Nested Fractals as Caldern-Zygmund operators, Comm. Pure and Applied Ann., 3(6):2155–2175, 2014.
- Marius Ionescu and Alex Kumjian. Hausdorff Measures and KMS States, Indiana Univ. Math. J., 62(2):443–463, 2013.
- Marius Ionescu, Luke G. Rogers, and Robert S. Strichartz. Pseudo-differential Operators on Fractals. Rev. Mat. Iberoamericana, 29(4):1159–1190, 2013.
- Marius Ionescu, Luke G. Rogers, and Alexander Teplyaev. Derivations and Dirichlet forms on fractals. J. Funct. Anal. 263 (2012), no. 8, 21412169.
- Marius Ionescu and Dana P. Williams. Remarks on the Ideal Structure of Fell Bundle C∗-algebras, Houston J. Math.38(2012), No. 4, 1241-1260
- Marius Ionescu, Paul S. Mulhy, and Victor Vega. Markov operators and C* -algebras, Houston J. Math, 38(3):775–798, 2012
- Marius Ionescu and Dana P. Williams. A classic Morita equivalence result for Fell bundle C* algebras, Math. Scand, 208(2):251–263, 2011.
- Marius Ionescu, Erin P.J. Pearse, Luke G. Rogers, Hujo-Jun Ruan, and Robert S. Strichartz. The Resolvent Kernel for PCF Self-Similar Fractals, Trans. Amer. Math. Soc., 362(8):44514479, 2010.
- Marius Ionescu and Dana P. Williams. The Generalized Effros-Hahn Conjecture for Groupoids, Indiana Univ. Math. J., 58(6):24892508, 2009.
- Marius Ionescu and Dana P. Williams. Irreducible representations of groupoid C∗algebras, Proc. Amer. Math. Soc. 137 (2009), 1323-1332
- Marius Ionescu and Yasuo Watatani. C* -algebras associated with Mauldin-Williams graphs, Can. Math. Bull, 51 (2008), no 4, 545–560.
- Marius Ionescu and Paul S. Muhly. Groupoid Methods in Wavelet Analysis, Group representations, ergodic theory, and mathematical physics: a tribute to George W. Mackey, 193–208, Contemp. Math., 449, Amer. Math. Soc., Providence, RI, 2008.
- Marius Ionescu. Operator algebras and Mauldin-Williams graphs. Rocky Mountain J. Math. 37 (2007), no. 3, 829–849.
- Marius Ionescu. Mauldin-Williams graphs, Morita Equivalence and isomorphisms, Proc. Amer. Math. Soc. 134 (2006), no. 4, 1087–1097.