Internship

(April-July 2022)

My mathematical research is focused on the interplay between the harmonic and the geometric analysis of Lie groups. Mainly my research links the applications of the theory of pseudo-differential operators and Fourier integral operators to partial differential equations and the Index theory.

Duvan Cardona Sanchez obtained his BsC. in mathematics at Universidad del Valle in Cali-Colombia. He is doing an internship at the ERC- DyCon Project under the supervision of Prof. Enrique Zuazua (FAU, University of Deusto, UAM) at DeustoCCM -Deusto Foundation/University of Deusto.

Duvan is member of the Ghent Analysis and PDE Center and his thesis in Harmonic Analysis and Partial Differential Equations has been supervised by Prof. Michael Ruzhansky (Ghent University and Queen Mary University of London).

In view of his research achievements, Duvan in 2021 was named Life Member of the International Society for Analysis, its Applications, and Computation (ISAAC) and in 2021 he was named scientific reviewer for The Ministry of Sciences, Technology, and Innovation of Colombia.

  • Internship (Apr. 2022 – Jul. 2022). DeustoCCM -Chair of Computational Mathematics. Deusto Foundation-University of Deusto, Spain
  • Doctoral Student (2019 - present), Ghent University, Belgium
  • Internship (2016). Mathematics Department, Imperial College of Science and Technology, London-UK. Mentor: Prof. Dr. Michael Ruzhansky
  • Bachelor’s Degree in Mathematics (2008 - 2013). University of Valle (Universidad del Valle), Cali, Colombia.

Submitted

Spectral inequalities for elliptic pseudo-differential operators on closed manifolds

D. Cardona. Spectral inequalities for elliptic pseudo-differential operators on closed manifolds (2022) Abstract. Let (M,g) be a closed Riemannian manifold ...
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Previous publication

-Cardona, D. Ruzhansky, M. Oscillating singular integral operators on compact Lie groups revisited. submitted. arXiv:2202.10531
-Cardona, D. Ruzhansky, M. Boundedness of oscillating singular integrals on Lie groups of polynomial growth, submitted. arXiv:2201.12883
-Cardona, D. Ruzhansky, M. [v1: Weak (1,1) continuity and Lp-theory for oscillating singular integral operators],[v2: Oscillating singular integral operators on graded Lie groups revisited], submitted. arXiv:2201.12881
-Cardona, D. The Wodzicki residue for pseudo-differential operators on compact Lie groups, submitted. arXiv:2201.12336
-Cardona, D., Delgado, J., Ruzhansky, M. Analytic functional calculus and Gårding inequality on graded Lie groups with applications to diffusion equations., to appear in J. Geom. Anal. submitted. arXiv:2111.07469
-Cardona, D., Federico, S., Ruzhansky, M. Subelliptic sharp Gårding inequality on compact Lie groups., submitted. arXiv:2110.00838
-Cardona, D., Ruzhansky, M. Sharpness of Seeger-Sogge-Stein orders for the weak (1,1) boundedness of Fourier integral operators., to appear in Arch. Math. arXiv:2104.09695.
-Cardona, D., Delgado, J., Ruzhansky, M. Dixmier traces, Wodzicki residues, and determinants on compact Lie groups: the paradigm of the global quantisation. submitted. arXiv:2105.14949
-Cardona, D., Ruzhansky, M. Fourier multipliers for Triebel-Lizorkin spaces on compact Lie groups., Collect. Math. arXiv:2101.12314
-Cardona, D., Ruzhansky, M. Fourier multipliers for Triebel-Lizorkin spaces on graded Lie groups., submitted. arXiv:2101.05856.

02.05.2022. DeustoCCM Seminar: Fefferman-Stein Theory for Oscillating Singular Integrals - | Slides

08.06.2022. On the boundedness of oscillating singular integrals on Lie groups of polynomial growth | Slides

Meet our team!