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Abbreviated CV

Academic degrees

PH.D. in Mathematics, Medidas Tangenciales sobre Cilindros Convexos en E^n, 1983,
Department of Mathematics, F.C.E.y N., University of Buenos Aires.
Supervisor: Prof. Luis A. Santaló

Licenciatura en Matemática (equivalent to M.Sc.), 1980,
Department of Mathematics, F.C.E.y N., University of Buenos Aires.
Supervisor: Prof. Luis A. Santaló

 

Current Academic Appointments

  • Professor, Department of Mathematics,  University of Buenos Aires, September 2006 - present.
  • Researcher, CONICET, July 1987 - present.
  • Contributing Editor. Real Analysis Exchange. October 2009 – present.

Member of the research group: Real and Harmonic Analysis
Department of Mathematics, F.C.E.y N., Universidad de Buenos Aires.

Awards

  • Thalman Fellow, Universidad de Buenos Aires 2008.
  • Alβan Fellow, High Level European Union Fellowship 2005.
  • Guggenheim Fellow, 2003.
  • Fulbright Senior Research Award, 2003.


Membership in Academic Institutions:

  • Unión Matemática Argentina
  • American Mathematical Society

Selected Publications

(For a complete list of papers, download the PDF file of my CV.)
  • Cabrelli, C., Molter, U. and Romero, J. L.``Non-uniform painless decompositions for anisotropic Besov and Triebel-Lizorkin spaces''. Preprint.pdf-file.
  • Balazs, P., Cabrelli, C., Heineken, S. and Molter, U. ``Frames by Multiplication''. Current Developments in Theory and Applications of Wavelets. To appear 2011.pdf-file.
  • Molter U. , Rela E. ``Furstenberg sets for a fractal set of directions'' Proceedings of the American Mathematical Society. To appear 2011. pdf-file.
  • Aldroubi, A., Anastasio, M., Cabrelli, C., Molter, U., ``A dimension reduction scheme for the computation of optimal unions of subspaces.'' Sampling Theory in Signal and Image Processing., 10 (1-2) (2011) pp. 135 - 150. pdf-file.
  • Cabrelli, C. , Hare, K. , Molter, U. ``Classifying Cantor sets by their fractal dimensions''. Proceedings of the American Mathematical Society, 138 (11) (2010) pp. 3965-3974. pdf-file.
  • Molter U. , Rela E. ``Sharp dimension bounds for Furstenberg-type sets.'' Preprint. pdf-file.
  • Molter U. , Rela E. ``Improving dimension estimates for Furstenberg-type sets.'' Advances in Mathematics 223 (2010) pp. 672-688. pdf-file.
  • Aldroubi A. , Cabrelli C. , Heil C. , Kornelson K, Molter U. ``Invariance of a Shift-Invariant Space.'' Journal of Fourier Analysis and Applications. Vol 16, No 1, pp 60-75, 2010. pdf-file.
  • Molter, U. Zuberman, L. ``A fractal Plancherel Theorem.'' Real Analysis Exchange. 14,(34) 69-86, 2008/2009. pdf-file.
  • Feichtinger, H. G. , Molter, U. , Romero, J. L. ``Perturbation techniques in spline-type spaces.'' International Journal of Wavelets, Multiresolution and Information Processing. Special Issue on Multiscale Methods, Sparse Decompositions and Parsimonious Statistics. 2,(6) 249-277, 2008. pdf-file.
  • Aldroubi, A. , Cabrelli, C. , Molter, U.M. ``Optimal Non-Linear Models for Sparsity and Sampling.'' Journal of Fourier Analysis and Applications. 14,(5) 793-812, 2008. pdf-file.
  • García, I. , Molter, U.M. , Scotto, R. "Dimension Functions of Cantor sets". Proceedings of the American Mathematical Society, 135 (10) (2007) . pdf-file.
  • Aldroubi, A. , Cabrelli, C. , Hardin, D. and Molter, U.M. "Optimal shift invariant spaces and their Parseval frame generators". Applied and Computational Harmonic Analysis, 23 (2) (2007). pdf-file.
  • Cabrelli, C. , Molter, U.M. ``Density of the Set of Generators of Wavelets Systems'', Constructive Approximation, 26 (1) (2007). pdf-file.  
  • Cabrelli, C., Lacey, M., Molter, U.M. and Pipher, J. "Variations on the Theme of Journe's Lemma". Houston Journal of Mathematics, Electronic Edition. 32 (3) (2006) 833--861.
  • Cabrelli, C. , Heineken, S. , Molter, U. M. "Local Bases for Refinable Spaces". Proceedings of the AMS. 134 (2006) 1707-1718. pdf-file.
  • Cabrelli, C. , Molter, U.M. ``Geometric Methods in Wavelet Theory'', Revista de la UMA , 46 (2) (2005), 121-132.   pdf-file.
  • Cabrelli, C. , Heineken, S. , Molter, U. M. "Refinable Shift Invariant Spaces in R^n". International Journal of Wavelets, Multiresolution and Information Processing. Special issue on "Sampling and Frames in Wavelet Theory and Time-Frequency Analysis" 3 (2005), 3, 321-345. pdf file
  • Aldroubi, A. , Cabrelli, C. , Molter, U. " Wavelets on Irregular Grids with Arbitrary Dilation Matrices, and Frame Atoms for L2(Rd)". Applied and Computational Harmonic Analysis. Special Issue on Frames II. 119-140 (2004)   pdf-file.
  • Cabrelli, C. A. Heil, C. and Molter, U. M. "Self-Similarity and Multiwavelets in Higher Dimensions". Memoirs of the AMS. 170 (807) 82p. 2004 .  gzipped-pdf-file.
  • Cabrelli, C. , Mendevil, F. , Molter, U., Shonkwiler, R. " On the Hausdorff h-Measure of Cantor Sets". Pacific Journal of Mathematics. 217(1)45-59. (2004) pdf-file.

Invited Book Chapters

  • Cabrelli C., Darji, U., Molter, U.``Visible and Invisible Cantor sets''. Invited chapter in Excursions in Harmonic Analysis: The February Fourier Talks at the Norbert Wiener Center. Editors: Travis Andrews, Radu Balan, Wojciech Czaja, Kasso Okoudjou, John Benedetto.pdf-file.
  • Aldroubi, A., Cabrelli, C. A and Molter, U. M. "Learning the Right Model from the Data". Invited Chapter in Harmonic Analysis and Applications. In Honor of John J. Benedetto. C. Heil, ed., Birkhäaut;user, Boston, (2006): 325 -- 334. pdf-file.
  • Aldroubi, A., Cabrelli, C. A and Molter, U. M. "How to construct Wavelet Frames on irregular grids and arbitrary dilations in $R^n$". Invited Chapter in Wavelets, Frames and Operator Theory. C.Heil, P. Joergensen, D. Larson eds. Contemporary Mathematics. ( 345) 1 -- 9, 2004. pdf-file.
  • Aldroubi, A., Cabrelli, C. A, Hardin, D., Molter, U. M.and Rodado, A.. "Determining sets of shift invariant spaces" Proceedings of ICWA, Chennai, India, 2004. pdf-file.
  • Cabrelli, C. A., Heil, C. y Molter, U. M.."Multiwavelets in Rn with an arbitrary dilation matrix". Wavelets and Signal Processing, L. Debnath editor, Birkhäuser, Basel(2003). pdf-file.

Some Invited Lectures

06/11 "Irregular, anisotropic wavelets". Strobl2011 - From Abstract to Computational Harmonic Analysis. Strobl, Austria.
06/11 "Optimal non-linear models for Sparsity and Sampling". Coloquio del Instituto de Matemática, de la Universidad de Sevilla. Sevilla, Spain.
02/08 "Between Shift Invariante and Translation Invariance". February Fourier Talks. University of Maryland, Colelge Park, USA.
05/11 "Dimension Reduction in Sparsity and Sampling".International Symposium in Approximation Theory. Vanderbilt University, Nashville, Tennessee.
05/09 "Optimal Non-linear models".SAMPTA 2009. International Conference on Sampling Theory and Applications. Marseille, France.
01/08 "Geometric Methods in Harmonic Analysis". Colloquium. Department of Mathematics, University of Hawaii, Manoa, Honolulu, USA.
10/07 "Buscando nuevas herramientas para la digitalización de señales: las ondículas, una solución". Museo Arg. Cs. Naturales, Buenos Aires, Argentina.
09/06 "Density of Riesz Bases". Seminario del IMAL, Santa Fé, Argentina.
04/06 "Cantor Sets". Workshop on Frames and Operator Theory 2006. Nashville, TN, USA.
09/05 "Métodos Geométricos en Análisis Armónico". LV Reunión Anual de la Unión Matemática Argentina. Salta, Argentina.
05/05 "Riesz Basis Wavelets in L2 (Rd )". International Conference on Modern Methods in Harmonic Analysis, Strobl, Austria.

PHD Students 

Graduated:

  • Marcela C. Falsetti PHD in Mathematics, University of Buenos Aires. December 2001.
    Thesis: Dimensión de Minkowski y Aplicaciones.
  • Leandro Zuberman. PHD in Mathematics, University of Buenos Aires. Buenos Aires, Argentina. March 2008.
    Thesis: Un Teorema Fractal de Plancherel para ciertas Medidas no Duplicantes.
  • Ignacio García. PHD in Mathematics, Universidad del Litoral, Santa Fe, Argentina.
    Thesis:Conjuntos de Cantor No Lineales: Funciones de Dimensión, Dinámica y Sumas Aritméticas.
  • Ezequiel Rela. PHD in Mathematics, University of Buenos Aires. Buenos Aires, Argentina. December 2010.
    Thesis: Estimaciones de dimensión para conjuntos de tipo Furstenberg y Teoremas de Restricción para medidas de Hausdorf.
  • José Luis Romero. PHD in Mathematics, University of Buenos Aires. Buenos Aires, Argentina. March 2011.
    Thesis: Descomposiciones atómicas. Algunos problemas de localidad en el espacio de fases.

Current:

  • María Fernanda Barrozo. PHD in Mathematics, University of San Luis. San Luis, Argentina.
  • Alejandro Quintero. PHD in Mathematics, Universidad de Mar del Plata, Mar del Plata, Argentina.

Masters & Licenciatura Students 

Graduated:

  • Romina Jinkis Licenciatura en Cs. Físicas. FCEyN, University of Buenos Aires. December 1998.
  • Pablo Shmerkin. Licenciatura en Cs. Matemáticas, FCEyN, University of Buenos Aires. Buenos Aires, Argentina. August 2001.
  • Leandro Zuberman. Licenciatura en Cs. Matemáticas, FCEyN, University of Buenos Aires. Buenos Aires, Argentina. December 2001.
  • Lucía Babino. Licenciatura en Cs. Matemáticas, FCEyN, University of Buenos Aires. Buenos Aires, Argentina. December 2003.
  • Ezequiel Rela. Licenciatura en Cs. Matemáticas, FCEyN, University of Buenos Aires. Buenos Aires, Argentina. March 2006.
  • José Luis Romero. Licenciatura en Cs. Matemáticas, FCEyN, University of Buenos Aires. Buenos Aires, Argentina. March 2006.
  • María Fernanda Barrozo. Magister in Mathematics, University of San Luis. San Luis, Argentina. November 2010.
    Masters Thesis: Sistemas de Contracciones en Espacios Metricos Completos: Conjuntos y Medidas Invariantes

Latest Research Visits

  • April 2011 to July 2011: Visiting Professor, Department of Mathematics, Vanderbilt University, Nashville, TN, USA.
  • June 2011: Visiting Professor, Department of Mathematics, Universidad Autónoma de Madrid, Spain.
  • February 2008 to April 2008: Visiting Professor, Department of Mathematics, Vanderbilt University, Nashville, TN, USA.
  • January 2008: Visiting Professor, Department of Mathematics, University of Hawaii, Honolulu, HI, USA.
  • March 2005 to August 2005: Research Visitor, Erwin Schroedinger Institute; Visiting Professor, NuHAG Fakultät für Mathematik, Wien, Austria.
  • January 2004 to August 2004: Visiting Professor, Department of Mathematics, Vanderbilt University, Nashville, TN, USA.
  • May 2003: Research Visitor, Erwin Schroedinger Institute, Wien, Austria.
  • Summer 2002: Visiting Professor, Department of Mathematics, Vanderbilt University, Nashville, TN, USA.
  • January 2002 to May 2002: Visiting Associate Professor, Georgia Institute of Technology, Atlanta, GA, USA.
  • November 2001 to December 2001: Visiting Professor. UNL, Santa Fe, Santa Fe, Argentina. (I taught a special topic course on Geometric Measure Theory.
  • July 2001: Research Visit, Ecóle Polytechnique, Paris, France.
  • January 2000 to July 2000: Visiting Associate Professor, Georgia Institute of Technology, Atlanta, GA, USA.
  •  February 1999 to March 1999: Visiting Professor, Instituto Balseiro, CNEA. Bariloche, Argentina.
  • July 1998: Research Visit, Department of Pure Mathematics, University of Waterloo, Waterloo, Canada.
  • June 1998: Research Visit to Vanderbilt University, Nashville, TN, USA.

Thesis committees, selection committees, other

  • Member of the Committee for Mathematics CONICET (Argentine equivalent of the French CNRS), Argentina. (2011-2012) and (2004-2005)
  • Member of the selection Committee for research scholarships of the CONICET (Argentine equivalent of the French CNRS), Argentina. (2002)
  • Referee for Research Grants of the Agencia Nacional de Promoción Científica y Tecnológica, Argentina, 1998, 1999,    2000.
  • Referee for Research Grants of the University of Buenos Aires, 1997, 1996.
  • Referee for a Research Grants, Universidad de Mar del Plata, Argentina, 1996.

Referee for the following Journals:

  • Journal of Math Analysis and Applications
  • Journal of Fourier Analysis and Applications
  • Applied and Computational Harmonic Analysis
  • Computers and Mathematics with Applications
  • Random and Computational Dynamics