Mathematical Foundation for the Generalised Brillouin zone of m-banded Toeplitz operators.
My Interests
I am a PhD student with a strong interest in wave propagation in periodic media governed by partial differential equations (PDEs). I am also interested in the spectral properties of Toeplitz operators.
Short CV
I am a PhD Student in Computational and Applied Mathematics at the University of Oslo, under the supervision of Prof. Erik Orvehed Hiltunen. Previously, I was a master's student at ETH Zurich, where I worked under the supervision of Prof. Habib Ammari. During my master's degree I was also a Visiting Scholar in Applied Mathematics at Yale University.
My recent work involves studying the localisation phenomenon in metamaterials and quantitatively analysing localisation properties using the complex band structure.
Publications
Spectra and pseudospectra of non-Hermitian Toeplitz operators: Eigenvector decay transitions in banded and dense matrices
Complex Band Structure and localisation transition for tridiagonal non-Hermitian k-Toeplitz operators with defects
Complex Brillouin Zone for Localised Modes in Hermitian and Non-Hermitian Problems
Complex Band Structure for Subwavelength Evanescent Waves
Spectra and pseudo-spectra of tridiagonal k-Toeplitz matrices and the topological origin of the non-Hermitian skin effect
Code & Data
Mathematical Foundation for the Generalised Brillouin zone
Spectra of non-Hermitian m-banded Toeplitz operators
Localisation transition in non-Hermitian systems
Complex Band structure for the 1D & 2D Helmholtz scattering problem
Topological Origin of the non-Hermitian skin effect
Invited Talks
Wave scattering in periodic media
Wave localisation in periodic media
Complex Band Structure in the Spectral Theory of Toeplitz Operators and Applications to Metamaterials
Contact
University of Oslo
Moltke Moes vei 35
0851 Oslo
Norway
Office: NHA 1004
Email: yannicd@math.uio.no
My Departemental Page