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Academics

Position: Since September 1, 2008, 1-year assistant professor in the Department of Mathematics (MAT) at the Technical University of Denmark (DTU). My advisor is Professor Ole Christensen. I am part of the functional analysis group at the MAT department and a member of the Danish Center for Applied Mathematics and Mechanics (DCAMM)

Research interest: In general: functional analysis, Hilbert space theory, Fourier analysis, numerical analysis, and signal processing. In particular: L^2 theory of wavelet frames, constructions and characterizations results, explicit constructions of dual wavelet frames, canonical and alternate duals. Also: Quasi wavelet frames, shift invariant spaces.

Background: Master of Science of Engineering in Applied Mathematics degree from the DTU in April 2005. Master's thesis project at the MAT department: Wavelet Frames and Their Duals (download in pdf).

Current ongoing research projects:
1. Generalization of [2] to R^n. For any given expansive nxn matrix A we want a procedure that allow for constructions of pairs of dual frame wavelets for L^2(R^n) in a very explicit way. Keywords: Characterizing equations for dual wavelet frames in L^2(R^n), the unit ball in the adaptive norm associated with A^t, densest regular (lattice) packing of ellipsoids in R^n, A-dilative partition of unity.
2. (with Prof. Bownik) Affine and quasi affine frames with adaptive oversampling for rational nxn dilations. Keywords: (Generalized) shift-invariant systems, integral sublattice and extended integral superlattice in R^n, oversampling SI-systems, translational averaging wavelet functionals.

Conferences: 2005 Fall Western Section Meeting of AMS: Special Session on Wavelets, Frames, and Related Expansions at the University of Oregon, Eugene, November 11-13, 2005. Workshop on Wavelets at Washington University of St. Louis, April 3-7 2006. 11th internal DCAMM Symposium at SAS Radisson Silkeborg, March 2007. Trends in Harmonic Analysis in Strobl, Austria, June 18-22 2007, Poster. New Trends and Directions in Harmonic Analysis, Approximation Theory, and Image Analysis in Inzell, September 16-21 2007, Presentation.

Recently Attended Courses: Data Representation in Redundant Systems at the Department of Control Engineering at Aalborg University, October 2004. Wavelet Frames and Multiscale Analysis (Part I and II) at the MAT, DTU, August 2005. Seminar Course in Mathematics, Statistics, Operations Research and Numerical Analysis at the IMM, DTU, Fall 2005. Discontinuous Galerkin Methods for Solving Partial Differential Equations: A Mathematical Introduction at IMM, DTU, November 2005. Distribution Theory at the Department of Mathematics at University of Copenhagen, Feb.-April 2006. Wavelets, fractals, iterated function systems, operator representations and applications at Centre for Mathematical Sciences, Lund University, June 11-13 2007. Discrete Inverse Problems at IMM, DTU, Spring 2008.