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Claudio Antonio Muñoz Cerón

Full Professor

Universidad de Chile

Santiago, Chile

Líneas de Investigación


Mathematical Analysis, in particular: Partial Differential Equations Dispersive equations: local and global well-posedness, blow-up, stability and asymptotic stability, collisions Deep Learning techniques in Partial Differential Equations

Educación

  •  Mathematics, UNIVERSITE DE VERSAILLES SAINT-QUENTIN EN YVELINES. Francia, 2010
  •  Mathematics, UNIVERSITE PIERRE ET MARIE CURIE-PARIS VI. Chile, 2007
  •  Ingeniero Matemático, UNIVERSIDAD DE CHILE. Chile, 2006
  •  Mathematics, UNIVERSIDAD DE CHILE. Chile, 2005
  •  Astronomia, UNIVERSIDAD DE CHILE. Chile, 2006

Experiencia Académica

  •   Assistant professor Full Time

    UNIVERSIDAD DE CHILE

    Mathematical and Physical Sciences

    Santiago, Chile

    2015 - 2020

  •   LE Dickson Instructor Full Time

    UNIVERSITY OF CHICAGO

    Chicago, Estados Unidos

    2011 - 2013

  •   Charge de Recherche CNRS Full Time

    UNIVERSITE PARIS SUD - PARIS XI

    Sciences

    Orsay, Francia

    2013 - 2015

  •   Postdoctorate Full Time

    UNIVERSIDAD DE CHILE

    Mathematical and Physical Sciences

    Santiago, Chile

    2011 - 2011

  •   Postdoctorate Full Time

    UNIVERSIDAD DEL PAIS VASCO

    Bilbao, España

    2010 - 2011

  •   Coordinator of PhD studies Full Time

    UNIVERSIDAD DE CHILE

    Mathematical and Physical Sciences

    Santiago, Chile

    2016 - 2018

  •   Deputy Director Part Time

    UNIVERSIDAD DE CHILE

    Mathematical and Physical Sciences

    Santiago, Chile

    2020 - At present

  •   Member of Mathematics Fondecyt Evaluation Committe Part Time

    ANID

    Chile

    2018 - 2020

  •   Full Professor Full Time

    UNIVERSIDAD DE CHILE

    Mathematical and Physical Sciences

    Santiago, Chile

    2020 - At present

Experiencia Profesional

  •   Chargé de Recherche Full Time

    Centre National de la Recherche Scientifique CNRS

    Orsay, Francia

    2013 - At present

  •   Full Professor Full Time

    Universidad de Chile

    Santiago, Chile

    2020 - At present

  •   Assistant Professor Full Time

    Universidad de Chile

    Santiago, Chile

    2015 - 2020

  •   Editor Other

    Springer Nature Partial Differential Equations and Applications

    Alemania

    2020 - At present

  •   Editor Other

    Proyecciones Journal of Mathematics

    Chile

    2021 - At present

  •   Editor Other

    Nonlinear Analysis

    Holanda

    2020 - At present

Formación de Capital Humano


MSc. students (16):
Sebastián Gangas (2026-), Felipe Latorre (2025-), Alfredo Padilla (2025-), Nicolás Garay (2025-), Francisco Fernández (2025, joint with Felipe Poblete), Leila Reyes (2025-), Alonso Rojas (2024-2025), Alvaro Márquez (2024-2025, joint with Álvaro Rojas), Sebastián Tapia (graduated in April 2024, now PhD Student at U. Lille and INRIA Lille); Benjamín Tardy (graduated in April 2024, joint with Felipe Poblete); Enzo Iubini (graduated in December 2023, joint with Tomás Andrade); Ignacio Acevedo (graduated in August 2023, ANID Magister Fellowship, now PhD. student at U. Paris-Saclay France); Matías Morales (graduated in August 2023, Now PhD. student at U. Basque Country, Spain); Nicolás Valenzuela (graduated in August 2022, now PhD. student at U. Chile and Google LatinAmerica Fellowship in AI); Javier Castro (graduated in July 2022, now PhD. student at U.T. Berlin under Benjamin Gess, Germany); and José M. Palacios (graduated in August 2018, now postdoc at EPFL, Switzerland).

Ph.D. students (9):
Benjamín Tardy (2026-, joint with Felipe Poblete), Alvaro Márquez (2026-, joint with Álvaro Rojas and Paula Jofré), Alonso Rojas (2026-), Francisco Fernández (2026-, joint with Felipe Poblete), Vicente Salinas (2022-, joint with Felipe Poblete); Nicolás Valenzuela (2023-, Google Research LatinAmerica Fellow); Jessica Trespalacios (2024, ANID postdoc 2025-2028 at UACh, Valdivia), María E. Martínez (2021, now Assistant Professor at DIM-CMM U. Chile); and Christopher Maulén (defended July 2021, Assistant Professor at DIM-UDEC).

Postdocs (6): Juan Ricardo Muñoz (2026-2029); Ricardo Freire (2023-2026); Oscar Jarrín (2022, now Assistant Professor at University of the Americas, Ecuador); Argenis Mendez (2019-2021, now Assistant Professor at UNICAMP Brazil); Hanne Van den Bosch (2018-2019, now Assistant Professor at DIM-CMM); Marcio Cavalcante (2017, now Assistant Professor at U. Alagoas, Brazil); Chulkwang Kwak (2017-2020, now Assistant Professor at Ewha Womans U., S. Korea).


Difusión y Transferencia


ORGANIZED EVENTS
Being part of the following event organizations:
1. BANFF New Synergies in Partial Differential Equations (25w5403), Canada (2025).
2. 1st. (2023), 2nd. (2024), and 3rd. (2025) Symposia on PDEs and Number Theory.
3. 1st. WAFFLE meeting (2025). Second version: March 2026.
4. 1st (2024), 2nd (2024), 3rd (2025) and 4th (2025) PANDA meetings.
5. 1st and 2nd "Jornada Anual del Nuevos Edepistas", JANE.
6. 1st and 2nd UOH-DIM meeting (2024, 2025).
7. Nonlinear Dispersive PDEs session at MCA Miami 2025.
8. Trends in Nonlinear Dispersive Equations and Related Topics special session at CLAM 2024, Brazil.
9. BANFF New trends in Mathematics of Dispersive, Integrable and Nonintegrable Models in Fluids, Waves and Quantum Physics (22w5018), Canada (2022).
10. CMM FLACAM conference (November 2019).
11. Dispersive-fluid session at CLAM 2020, Montevideo, Uruguay.
12. 2nd. Workshop on Nonlinear Evolution Equations in Valdivia, December 12-16 2016.
13. PDE session at Somachi 2015, held in Pucón, Chile, November 2015.
14. CLAM 2016 Nonlinear Dispersive Equations session, Colombia July 11-15 2016.
15. Workshop MathAmSud EEQUADD, Universidad de Chile, Santiago, on December 4-7 2017, see http://eventos.cmm.uchile.cl/eequadd2017.
16. 60th birthday congress in honor of Frank Merle (2023).
17. "New trends in Mathematics of Dispersive, Integrable and Nonintegrable Models in Fluids, Waves and Quantum Physics" in October 2022, Banff, Canada.

Apparition in major national media because of a major result obtained in collaboration with M. Kowalczyk y Y. Martel. See e.g. the web page and video at

1. 24horas https://www.24horas.cl/nacional/en- chile- se- resolvio- una- ecuacion- matematica- imposible- durante- 40- anos- 2169033.

2. EMOL http://www.emol.com/noticias/Tecnologia/2016/10/20/827422/Investigadores- de- la- U- de- Chile- resuelven- una- ecuacion- que- estuvo- casi- 40- anos- sin- respuesta. html

3. LUN http://www.lun.com/Pages/NewsDetail.aspx?dt=2016- 10- 21&PaginaId=10&bodyid=0,

4. La Tercera http://www.latercera.com/noticia/matematicos- la- u- chile- resuelven- ecuacion- estuvo- casi- 40- anos- sin- respuesta/

5. El Mostrador http://www.elmostrador.cl/cultura/2016/10/21/matematicos-chilenos-resuelven-ecua cion-que-estuvo-casi-40-anos-sin-respuesta/

6. Radio ADN http://www.adnradio.cl/noticias/sociedad/investigadores-de-la-u-de-chile-resolviero n-ecuacion-que-estuvo-casi-40-anos-sin-respuesta/20161020/nota/3279733.aspx

7. Universidad de Chile http://www.uchile.cl/noticias/127718/investigadores-resuelven-ecuacion-que-estuvo -casi-40-anos-sin-solucion

8. Facebook ICMAT Madrid, España. https://www.facebook.com/permalink.php?story_fbid=1131670780203407&id=317 339304969896

9. La Cuarta https://www.lacuarta.com/cronica/noticia/cientificos-locos-descifran-ecuacion-tras- 40-anos/179685/

10. Bío-Bío Radio http://www.biobiochile.cl/noticias/ciencia-y-tecnologia/ciencia/2016/10/21/investig adores-de-u-de-chile-resuelven-ecuacion-que-estuvo-casi-40-anos-sin-respuesta.sht ml

Radio interviews:

1. Radio U. de Chile (http://radio.uchile.cl/programas/quiero-ser-cientifico/392879/), related with a Recoleta’s neighborhood high school;

2. Radio Tele13 (https://twitter.com/Tele13_Radio/status/981594952290377728), because of M. del Pino’s work.


Premios y Distinciones

  •   Prize Thesis

    UNIVERSITE DE VERSAILLES SAINT-QUENTIN EN YVELINES

    Francia, 2011

    Prize to the best thesis among all scientific areas at UVSQ in 2010.

  •   Chargé de Recherche CNRS

    CENTRE NATIONALE DE LA RECHERCHE SCIENTIFIQUE

    Francia, 2013

    The Chargé de Recherche CNRS is one of the most demanding and prestigious young researchers positions in the world. It allows one to perform research in full control and without teaching duties. In Mathematics, only fewer than 10 people are chosen, among more than 200 fully competitive applicants.

  •   Ramanujan Prize

    ABDUS SALAM INTERNATIONAL CENTRE FOR THEORETICAL PHYSICS

    Italia, 2025

    The Ramanujan Prize for young mathematicians from developing countries has been awarded annually since 2005 and is administered jointly by ICTP and IMU. It is usually awarded to one person, but may be shared equally among recipients who have contributed to the same body of work. The Prize is awarded to a researcher from a developing country who is less than 45 years of age on 31 December of the year of the award, and who has conducted outstanding research under difficult conditions in a developing country. Researchers working in any branch of the mathematical sciences are eligible. The Prize carries a $10,000 cash award. The Prize selection committee consists of eminent mathematicians appointed in consultation between the ICTP and the IMU.

  •   Keynote Speaker SIAM Nonlinear Waves and Coherent Structures 2026

    SIAM

    Canada, 2026

    The goals of the conference are to provide a forum for the development of mathematical methods and tools, to foster cross-fertilization among different fields of application, and most crucially to enable communication between the mathematicians who build the theory and the scientists who use it. The conference program will consist of presentations on subjects ranging from basic mathematical research to concrete applications.


 

Article (48)

Bounds on the approximation error for deep neural networks applied to dispersive models: nonlinear waves.
Uniqueness of quasimonochromatic breathers for the generalized Korteweg–de Vries and Zakharov-Kuznetsov models
Asymptotic stability of the fourth-order /4 kink for general perturbations in the energy space
Interaction of jamitons in second-order macroscopic traffic models
On uniqueness of KP soliton structures
The generalized Riemann zeta heat flow
Long time asymptotics of large data in the Kadomtsev-Petviashvili models
On local decay of inflaton and axion fields
On local energy decay for solutions of the Benjamin-Ono equation
The Calderón's Problem via DeepONets
ASYMPTOTIC STABILITY OF KDV SOLITONS ON THE HALF-LINE: A STUDY IN THE ENERGY SPACE
On Asymptotic Stability of the Sine-Gordon Kink in the Energy Space
Soliton dynamics for the 1D NLKG equation with symmetry and in the absence of internal modes
A Sufficient Condition for Asymptotic Stability of Kinks in General (1+1)-Scalar Field Models
On local energy decay for large solutions of the Zakharov-Kuznetsov equation
On the Dynamics of Zero-Speed Solutions for Camassa-Holm-Type Equations
On the Long Time Behavior of Solutions to the Intermediate Long Wave Equation
Stability and instability of breathers in the U(1) Sasa-Satsuma and nonlinear Schrödinger models
ASYMPTOTIC DYNAMICS FOR THE SMALL DATA WEAKLY DISPERSIVE ONE-DIMENSIONAL HAMILTONIAN ABCD SYSTEM
Decay in the one dimensional generalized Improved Boussinesq equation
The Calderón problem for quasilinear elliptic equations
Breathers and the Dynamics of Solutions in KdV Type Equations
Nonlinear stability of 2-solitons of the sine-Gordon equation in the energy space
ON THE ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO THE BENJAMIN-ONO EQUATION
Stability of KdV solitons on the half-line
The Akhmediev breather is unstable
The scattering problem for Hamiltonian ABCD Boussinesq systems in the energy space
ALMOST SHARP NONLINEAR SCATTERING IN ONE-DIMENSIONAL BORN-INFELD EQUATIONS ARISING IN NONLINEAR ELECTRODYNAMICS
Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation. II
Scattering in the Energy Space for Boussinesq Equations
Instability in nonlinear Schrödinger breathers
KINK DYNAMICS IN THE phi(4) MODEL: ASYMPTOTIC STABILITY FOR ODD PERTURBATIONS IN THE ENERGY SPACE
Nonexistence of small, odd breathers for a class of nonlinear wave equations
On the variational structure of breather solutions I: Sine-Gordon equation
Asymptotic Stability of High-dimensional Zakharov-Kuznetsov Solitons
Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation
THE GARDNER EQUATION AND THE STABILITY OF MULTI-KINK SOLUTIONS OF THE MKDV EQUATION
DYNAMICS OF COMPLEX-VALUED MODIFIED KDV SOLITONS WITH APPLICATIONS TO THE STABILITY OF BREATHERS
ON APPROXIMATE CONTROLLABILITY OF GENERALIZED KdV SOLITONS
Nonlinear Stability of MKdV Breathers
DYNAMICS OF SOLITON-LIKE SOLUTIONS FOR SLOWLY VARYING, GENERALIZED KdV EQUATIONS: REFRACTION VERSUS REFLECTION
Inelastic Character of Solitons of Slowly Varying gKdV Equations
On the nonlinear stability of mKdV breathers
On the solitary wave dynamics, under slowly varying medium, for nonlinear Schrodinger equations
SOLITON DYNAMICS FOR GENERALIZED KdV EQUATIONS IN A SLOWLY VARYING MEDIUM
On the Inelastic Two-Soliton Collision for gKdV Equations with General Nonlinearity
Singular limits for the bi-Laplacian operator with exponential nonlinearity in R-4
The two-dimensional Lazer-McKenna conjecture for an exponential nonlinearity

Proyecto (13)

Modelling Nature MNat - Modeling nature from nano to macro.
PRISMALab Patterns in Relativity: Interdisciplinary Studies between Mathematics and Astrophysics
PANDA PArtial differeNtial equations, Dispersive models and nonlinear Analysis
WAFFLE Waters, Atmosphere, Fluids and Friedman-Lemaître evolutions
Fondecyt Postdoctoral
Projet d’échanges CNRS IEA "LISA" Lille-Santiago
The PDE approach in two number theoretical monster problems
Basal - Center for Mathematical Modeling (CMM)
EEQUADD II
ECOS-Sud
EEQUADD
CAPDE Nucleus Millenium
Fondecyt Regular
1
Monica Musso

PONTIFICIA UNIVERSIDAD CATOLICA DE CHILE

Santiago, Chile

1
Raimund Bürger

Profesor Titular (Full Professor)

CI2MA & Departamento de Ingeniería Matemática

UNIVERSIDAD DE CONCEPCIÓN

Concepción, Chile

1
Manuel Del Pino

Professor

DEPARTAMENTO DE INGENIERIA MATEMATICA Y CMM UNIVERSIDAD DE CHILE

Santiago, Chile

2
Michal Kowalczyk

Professor Titular

Ingeniería Matemática

Universidad de Chile

Santiago, Chile

2
Juan Pozo

Academic

Mathematics

Universidad de Chile

Santiago, Chile

4
Felipe Poblete

Profesor Asistente

Facultad de Ciencias

Universidad Austral de Chile

Valdivia, Chile

61
Claudio Muñoz

Full Professor

Mathematical Engineering

Universidad de Chile

Santiago, Chile

1
Hanne Van Den Bosch

Profesor assistente

Ingeniería Matemática

Universidad de Chile

Santiago, Chile