Research & Global Engagement

I am an Assistant Professor of Mathematics at the King Fahd University of Petroleum and Minerals (Dhahran, Kingdom of Saudi Arabia) and a Professor of Mathematics at Pontificia Universidad Javeriana (Xavierian Pontifical University, Bogotá-Colombia). In the period 2023-2026 I was an FWO Research Fellow at Ghent University-Belgium, funded by the Research Foundation Flanders (FWO). I also was a 2026 Oberwolfach Leibniz Fellow at the Mathematical Research Institute of Oberwolfach (MFO) in Germany.  My research focuses on Harmonic Analysis, PDE, Geometric Analysis and Control theory. 

In 2024, I made a research visit to UCLA (University of California, Los Angeles) under the supervision of Terence Tao. 

Previously, in 2022, I was a member of the Chair of Computational Mathematics at the Deusto Institute of Science and Technology, under the supervision of Enrique Zuazua. I obtained my PhD in Mathematics in August 2023 under the supervision of Prof. Dr. M. Ruzhansky and of Prof. Dr. J. Delgado.  I obtained my Bachelor's degree in Mathematics from Universidad del Valle in Cali-Colombia under the supervision of  Prof. Dr. J. Delgado.

Since 2022, I have served as member of the Executive Committee of ICMAM Latin America (International Community of Mathematicians from Latin America), an organization that I have co-founded and is dedicated to connecting mathematicians from developing countries, to increase the visibility of their scientific work and provide meaningful virtual mathematical experiences. 

Currently, I also serve on the Board of Directors of the International Society for Analysis, its Applications and Computation (ISAAC), and I am a member of the Applied and Industrial Mathematics Commission of the Colombian Mathematical Society.


Short Bio | Linkedin | ICMAM YouTube Channel | ORCID ID: 0000-0002-8148-2624 | Portfolio Site |

Some recent news:

• 2026. Announcement: In the article below I have proposed the bilinear smoothing conjecture and I obtain a partial progress. Also, I prove that this conjecture is implied by the celebrated local smoothing conjecture due to Sogge.
  
  Cardona, D., Local smoothing estimates for bilinear Fourier integral operators, to appear in:  Pacific J. Math. arXiv:2601.15667.
  Link
  
  Please also have a look at this talk at the Latin American Seminar of Mathematics (UMALCA-ICMAM).
  
  

• 2026; ICMAM Africa is a research organisation created for promoting mathematics in Africa. I will serve as the Scientific Director of this society.

• 2026; Invited Evaluator for the National Committee of Experts, “Becas para el Cambio” Program (CV 975); Ministry of Science, Technology and Innovation of Colombia. 

• 2026; Reviewer for FPIT – Foundation for the Promotion of Research and Technology, Bank of the Republic of Colombia. 

• 2026; my talk at the Latin American Seminar of Mathematics (UMALCA-ICMAM) about the Bilinear Smoothing Conjecture for Fourier Integral Operators (announced in this paper: Link).

• 2026. I has been awarded an Oberwolfach Leibniz Fellowship by the Mathematisches Forschungsinstitut Oberwolfach (MFO, Mathematical Research Institute of Oberwolfach), Germany.

• 2026. Reviewer for Oak Ridge Associated Universities (ORAU).

• 2026. Reviewer for the Nazarbayev University Research Council (Astana, Kazakhstan).

• 2025-now. Member of the Scientific Committee, Latin American Mathematics Seminar (UMALCA-ICMAM). 

• 2025. Co-chair, Latin American Mathematics Seminar (UMALCA-ICMAM). 

• 2025-Now. Editor in Chief, Newsletter of UMALCA (Mathematical Union for Latin America and the Caribbean).

• 2025-2027. Auditor of the International Society for Analysis, its Applications and Computation ISAAC.

• 2025-2026. Member of the Young Academy of the Colombian Academy of Exact, Physical and Natural Sciences.

• 2025. President's Award of the International Society for Analysis, its Applications and Computation (ISAAC).

• 2025–2027. Member of the Commission on Applied and Industrial Mathematics (CMAI) of the Colombian Mathematical Society.

• 2024-now. Board member of the International Society for Analysis, its Applications and Computation (ISAAC).

• Scientific Director of ICMAM Latin America (2022-).

• Book/Memoir:

Cardona, D., Ruzhansky, M. Subelliptic pseudo-differential operators and Fourier integral operators on compact Lie groups.
MSJ Memoirs, Math. Soc. Japan, 44: 175pp. (2025). arXiv:2008.09651.
Arxiv Link
Project Euclid Link

• Here is the link for my FWO Project (2023-2026) supported by the Belgian Research Foundation FWO: FWO Project Link.

• Life Member of ISAAC (International Society for Analysis, its Applications and Computation), 2021-. Member of the ISAAC Group in Partial Differential Equations, 2022-.

• Member of the BMS (Belgian Mathematical Society), 2021-now.

• Here is the link for my reviewer's page for MinCiencias, The Ministry of Sciences, Technology, and Innovation of Colombia: Reviewer's Page.

• My webpage for the ERC-DyCon Project is available here!

• President of the Scientific Board, ICMAM Latin America, 2022-2024.

• Interview with Charles Fefferman (Princeton University)

• To visit other posts, click here and explore!