Curriculum Vitae
Fourier Integral Operators and Pseudo-differential operators.
PDE , Control Theory and Harmonic Analysis, Spectral Theory and Index theory, Geometric Analysis.
Visit our intercontinental research group on non-commutative phase space analysis at Imperial College - London here.
Visit our intercontinental research group in Analysis and PDE centred at the Ghent University here.
FWO Postdoctoral Fellowship, 2023-2026. Awarded by the Research Foundation - Flanders (Fonds Wetenschappelijk Onderzoek - Vlaanderen, FWO).
2024 IMU-CDC Conference Support Program Grant. Awarded by the International Mathematical Union (IMU).
Reviewer (Par evaluador) for the Ministry of Sciences, Technology, and Innovation of Colombia. Colombian Science Ministry, 2020-.
Honorable mention of the Yu-Takeuchi Prize (awarded by the Colombian Academy of Sciences), Academia Colombiana de Ciencias Exactas, Físicas y Naturales, Dec- 03- 2018, Bogotá-Colombia.
Silver Medal at Olimpiada Universitaria de Matemáticas, UAO-Colombia, 2009.
Member of the Editorial Committee, Selecciones Matemáticas, 2024-now.
Assistant Editor. Book Series: Research Perspectives Ghent Analysis and PDE Center, Trends in Mathematics, Birkhäuser/Springer, 2023-now.
Managing Editor: ICMAM Latin America Editorial Project, 2023-now.
September 2024. UCLA, Department of Mathematics.
Mentor: Prof. Dr. Terence Tao.25 April-29 July, 2022: Chair of Computational Mathematics of Deusto Foundation at University of Deusto and Deusto Institute of Science and Technology, Bilbao (Basque Country, Spain).
Mentor: Prof. Dr. Enrique Zuazua.September 2016: Mathematics Department, Imperial College of Science and Technology, London-UK.
Mentor: Prof. Dr. Michael Ruzhansky.
2023-2026. Postdoctoral Fellow of the Research Foundation – Flanders (FWO) at Ghent University; Krijgslaan 281, Building S8, B 9000 Ghent-Belgium.
2019-2023. Doctoral student. Ghent University. Department of Mathematics: Analysis, Logic and Discrete Mathematics. Ghent-Belgium.
24 April-29 July, 2022. Research Internship. Chair of Computational Mathematics at Deusto Institute of Technology, Bilbao, Basque Country (Spain).
2017-2018. Lecturer. Pontificia Universidad Javeriana. Mathematics Department. Bogotá-Colombia.
2014-I/2015-2017. Graduate Assistant. Universidad de los Andes. Mathematics Department. Bogotá-Colombia. Courses: Integral calculus and Linear algebra; work: Besov boundedness of global pseudo-differential operators on compact Lie groups. Advisor: Alexander Cardona. Universidad de los Andes. Jury: Alexander S. Getmanenko (Universidad de los Andes), Jairo Hernández (Universidad del Norte).
2008-2013. Student/Bachelor. Universidad del Valle. Cali- Colombia.
Doctor of Science: Mathematics (Doctor in de Wetenschappen: wiskunde). Ghent University, Belgium. 2023.
Advisor: Prof. Dr Michael Ruzhansky. Co-Advisor: Prof. Dr Julio Delgado.
Thesis: Contributions to the theory of pseudo-differential operators: from compact to graded Lie groups. Video of my defense.
Jury: Elmar Schrohe (Leibniz Universität Hannover), Sylvie Paycha (Universität Potsdam), Simon Scott (King's College London), Hans Vernaeve (Ghent University), Denis Constales (Ghent University), Bart De Bruyn (Ghent University).Bachelor in Mathematics. Universidad del Valle. Cali- Colombia. 2015.
Advisor: Julio Delgado. Imperial College London, 2012-2019. (Current address: Universidad del Valle).
Thesis: Invertibilidad de operadores pseudo-diferenciales no elípticos.
Jury : José Raúl Quintero (Universidad del Valle), Guillermo Restrepo Sierra (in memoriam). Score: Meritorious.
Scientific Director of ICMAM Latin America (2022-).
Board member of the International Society for Analysis, its Applications and Computation (ISAAC).
(2023-2026) Working Group Member of CaLISTA, COST Action CA21109 “Cartan Geometry, Lie, Integrable Systems, quantum group Theories for Applications”, European Cooperation in Science & Technology, Horizon 2020, European Union.
Board Member ICMAM Latin America, 2022- now.
President of the Scientific Board - ICMAM Latin America 2022-2024.
(2021-∞) Life Member of the ISAAC, (International Society for Analysis, its Applications and Computation).
(2022-now). Member of the ISAAC Group in Partial Differential Equations.
(2021-now). Member of the BMS (Belgian Mathematical Society).
(2023-now). Board Member of ICMAM for Central America and the Caribbean.
Web of Science Researcher ID: AAE-9714-2020.
ORCID ID: 0000-0002-8148-2624.
Selected Books/Memoirs:
Cardona, D., Ruzhansky, M. Subelliptic pseudo-differential operators and Fourier integral operators on compact Lie groups, to appear in MSJ Memoirs, Mathematical Society of Japan, arXiv:2008.09651.
Selected Manuscripts/Scientific Reports:
Cardona, D. L2-Maximal functions on graded Lie groups, to appear in IMRN (Int. Math. Res. Not.) arXiv:2401.10830.
Cardona, D., Delgado, J., Ruzhansky, M. Estimates for sums of eigenfunctions of elliptic pseudo-differential operators on compact Lie groups, to appear in J. Geom. Anal. arXiv:2209.12092.
Cardona, D., Delgado, J., Ruzhansky, M. Boundedness of the dyadic maximal function on graded Lie groups, to appear in Quart. J. Math. arXiv:2301.08964.
Cardona, D. Ruzhansky, M. Björk-Sjölin condition for strongly singular convolution operators on graded Lie groups, Math. Z. 302, 1957–1981 (2022) arXiv:2205.03456.
Cardona, D., Federico, S., Ruzhansky, M. Subelliptic sharp Gårding inequality on compact Lie groups., to appear in Pure Appl. Anal. arXiv:2110.00838
Cardona, D., Delgado, J., Ruzhansky, M. A note on the local Weyl formula on compact Lie groups, to appear in J. Lie Theory, arXiv:2210.00311.
Cardona, D. Ruzhansky, M. Oscillating singular integral operators on compact Lie groups revisited., Math. Z. Vol. 303, 26 (2023) arXiv:2202.10531
Cardona, D, Ruzhansky, M. Littlewood-Paley theorem, Nikolskii inequality, Besov spaces, Fourier and spectral multipliers on graded Lie groups., to appear in Potential Analysis, arXiv:1610.04701
Cardona, D., Delgado, J., Ruzhansky, M. Drift diffusion equations with fractional diffusion on compact Lie groups. J. Evol. Equ. No. 22, Vol. 84, (2022). arXiv:2205.02320
Cardona, D., Ruzhansky, M. Sharpness of Seeger-Sogge-Stein orders for the weak (1,1) boundedness of Fourier integral operators., Vol. 119, 189–198 (2022). Arch. Math. arXiv:2104.09695.
Cardona, D., Delgado, J., Ruzhansky, M. Lp-bounds for pseudo-differential operators on graded Lie groups. J. Geom. Anal. Vol. 31, 11603-11647, (2021). arXiv:1911.03397
Cardona D., Delgado J., Grajales, B., Ruzhansky M. Control of the Cauchy problem on Hilbert spaces: a global approach via symbol criteria, Commun. Pure Appl. Anal., Vol. 22(11), 3295-3329, (2023). arXiv:2301.08999.
Cardona, D., Esquivel, L. On the Benjamin Ono equation in the half line., Nonlinear Analysis. Vol. 212, Art. 112427, (2021). arXiv:2101.06992
Cardona, D., Kumar, V. The nuclear trace of vector-valued pseudo-differential operators with applications to Index theory., Math. Nachr. Vol. 294(9), 1657-1683, (2021). arXiv:1901.10010
Cardona, D. Nuclear pseudo-differential operators in Besov spaces on compact Lie groups. J. Fourier Anal. Appl. Vol 23(5), (2017), 1238-1262. arXiv:1610.09042
Cardona, D. On the boundedness of periodic pseudo-differential operators. Monatsh. Math. Vol. 185(2), 189-206, (2018). arXiv:1701.08184
Conference Grant: 34th Brazilian Mathematics Colloquium, IMPA (Institute of Pure and Applied Mathematics), Rio de Janeiro, Brazil. July 24-28.
Conference Grant: Conference Harmonic Analysis and Partial Differential Equations (on the occasion of 60th birthday of Herbert Koch), Hausdorff Center for Mathematics, Bonn-Germany, May 29-June 2 2023.
Research Internship. (Supported by ERC-Advanced Grant DyCon Project 2015 H2020-694126). Chair of Computational Mathematics, University of Deusto/Deusto Foundation, Bilbao, Basque Country (Spain), 2022. My webpage for the DyCon Project is available here!
Heidelberg Laureate Forum Grant: Young researcher, Heidelberg Laureate Forum. Event organized by the Heidelberg Laureate Forum Foundation (HLFF), Germany. 2021.
Heidelberg Laureate Forum Grant: Young researcher, Heidelberg Laureate Forum. Event organized by the Heidelberg Laureate Forum Foundation (HLFF), Germany. 2020.
Proyecto semilla. Young researcher grant, Faculty of Sciences, Universidad de Los Andes, Bogotá-Colombia. 2016.
Trends in Mathematical Sciences. Member of the Organising Committee. Friedrich-Alexander-Universität, Erlangen-Nürnberg, June 10-14, 2024.
ICMAM Latin America Satellite Conference on Data Science, AI and Machine Learning. Member of the Scientific Board. Speakers: Enrique Zuazua, Macarena Estevez, Camelia Goga, Biswaranjan Senapati.
ICMAM Latin America Satellite Conference on Analysis and PDE 2023, 10-14 October 2023. Chair of the Organising Committee. Speakers: Charles Fefferman, Monica Visan, Tobias Colding, Felipe Linares, Michael Ruzhansky (Explore the complete list here!)
ICMAM Latin America Satellite Conference on Algebra, Combinatorics and Number Theory 2023, 27-29 September 2023. President of the Scientific Board. Speakers: Emanuel Carneiro, Kristin Lauter, Cesar Ceballos (Explore the complete list here!)
ICMAM 2022 Latin America: International Conference: Multidisciplinary Aspects in Mathematics and its applications, 25-28 October 2022. Universidad del Valle. Department of Mathematics. Plenary: Terence Tao, Michael Ruzhansky, David Dos Santos Ferreira, Enrique Zuazua, Simon Donaldson, Carlos Kenig, Tatiana Toro, Harald Helfgott.
International Conference on Pseudo-differential Operators, 7-8 July 2020, Ghent Analysis & PDE Center (organising committee: D. Cardona, M. Chatzakou, S. Federico, J. Huang, B. Sabitbek, D. Rottensteiner, M. Ruzhansky), Ghent-Belgium.
Mathematics & Memory: A seminar on Analysis and PDE for Latin America (Starting from March 2024).
Ghent Methusalem Microlocal Day #9: 5 March 2024.
Ghent Geometric Analysis Seminar at Ghent University (Starting from April of 2022). Organisers: Duván Cardona, Gihyun Lee, David Santiago Gómez Cóbos.
Ghent Methusalem Junior Seminar at Ghent University (February 2021/March 2023).
Ghent Methusalem Microlocal Day #8: 17 February 2023. Ghent University. Organisers: D. Cardona & B. Grajales. Previous Microlocal days at the Imperial College London and at Ghent university: #1 #2 #3 #4 #5 #6 #7 .
CONVImaTE 2022. Winter courses on pure and applied mathematics. (Big Data, PDE and Pseudo-differential Operators. Chair. Organisers: Julio Delgado, Duván Cardona, Karina Navarro, Liliana Esquivel. Open virtual version for Latin-America. Department of Mathematics, Universidad del Valle, Cali-Colombia.
Mathematical Reviews/MathSciNet. American Mathematical Society (AMS), [ISSN: 2167-5163 ], 2019-.
Zentralblatt MATH/ European Mathematical Society (EMS)/ FIZ Karlsruhe/ Heidelberg Academy of Sciences, [ISSN: 1436-3356] 2020-.
The peer review process includes articles published/reviewed in/for the following journals:
Mathematische Annalen., Springer, 2020-.
Journal of Geometric Analysis, Springer, 2023-.
Comptes Rendus Mathématique., Institute de France, Académie des sciences, 2021-.
Annals of Global Analysis and Geometry., Springer, 2021-.
(IMRN) International Mathematics Research Notices., Oxford University Press, 2021-,
Potential Analysis., 2022-.
Journal of Functional Analysis., Elsevier, 2020-.
Journal of Fourier Analysis and Applications, Springer, 2022-.
Forum of Mathematics. Sigma. Cambridge Univ. Press., 2020-.
Documenta Mathematica., Deutsche Mathematiker-Vereinigung (DMV)., 2020-.
Mathematische Nachrichten., Wiley-VCH Verlag, Wiley, 2019-.
Annali della Scuola Normale Superiore di Pisa. Scuola Normale Superiore. Pisa, Italy., 2022-.
Monatshefte für Mathematik., Springer, 2023-.
Journal of Pseudo-Differential Operators and Applications., Springer, 2016-.
Journal of Differential equations., Elsevier, 2020-.
Calc. Var. Partial Differential Equations., Springer 2023-.
SIGMA (Symmetry, Integrability and Geometry: Methods and applications)., 2019-.
Journal of the Australian Mathematical Society., Cambridge University Press, 2018-.
Bulletin of the Australian Mathematical Society., Cambridge University Press, 2019-.
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas., Springer, 2022-.
Differential and Integral Equations., Khayyam, 2019-.
Nonlinear Analysis: Real World Applications, Elsevier, 2021-.
Complex Analysis and Operator Theory Springer, 2022-.
Mathematical Models and Methods in Applied Sciences, World Scientific, 2021-.
Acta Mathematica Scientia, Wuhan Inst. Phys. and Math. & Chinese Acad. Sci., Springer, 2020-.
The Journal of the Indian Mathematical Society., The Indian Mathematical Society, 2021-.
Res. Inst. Math. Sci. (RIMS)., Kyoto University, Japan., 2018-.
Analysis and Mathematical Physics., Springer, 2021-.
Open Physics., De Gruyter, 2021.
Georgian Mathematical Journal., De Gruyter, 2022-.
Banach Journal of Mathematical Analysis, Springer, 2023-.
Annals of Functional Analysis, Springer, 2023-.
Vietnam Journal of Mathematics., Springer, 2022-.
Journal of Dynamics and Differential Equations, Springer 2021-.
Rendiconti del Circolo Matematico di Palermo Series 2, Springer 2023-.
Revista Integración, Temas de Matemáticas. Edited by Universidad Industrial de Santander (UIS), Colombia, 2023-.
Selecciones Matemáticas, 2024-. Edited by National University of Trujillo, Peru.
etc.
Universidad del Valle, Cali-Colombia. MV-Semisimple algebras and completely regular topological spaces. (Title in Spanish: MV-Álgebras semisimples y espacios topológicos completamente regulares); by Celimo Alexander Peña Rengifo, 2023; Advisor: Guillermo Órtiz Rico.