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

Former Master students:

1. José Palacios Armesto: Mathematical Engineering (2018)
Thesis title: Estabilidad de soluciones tipo soliton para ciertas ecuaciones dispersivas no lineales.
http://repositorio.uchile.cl/handle/2250/167768

2. Yasser Nanjari: Mathematical Engineering and Master in Mathematical Modeling (2019)
Thesis title: Sobre la Conjetura de Lazer-McKenna en el Caso no Local con Potencial Superlineal Bajo Condición de Simetría Parcial en el Dominio: Caso Crítico y Supercrítico,
Co-supervised with Prof. Fethi Mahmoudi.

Current Master Students:

1. Nicolás Valenzuela (starting end of 2020),
2. Javier Castro (starting end of 2020),
3. Ignacio Acevedo (starting March 2021).

Current Ph.D. Students:

1. Christopher Maulén (started March 2018, ending April 2021),
2. María E. Martínez (started June 2018, ending August 2021),
3. Jessica Trespalacios (started March 2020).

Former postdocs:

1. Marcio Cavalcante (2017, now Assistant Professor at U. Alagoas, Brazil),
2. Chulkwang Kwak (2017-2020, now Assistant Professor at Ewha Womans U., Korea),
3. Hanne Van den Bosch (2018-2019, now Assistant Professor at DIM-CMM).

Current Postdocs:

1. Argenis Méndez (started November 2019), funded by ANID postdoctorate March 2021.
2. Oscar Jarrín (started March 2021, funded by CMM Basal project).

Visiting Ph.D. fellows:

1. Oscar Jarrin, (1 month in December 2016, Ph.D. U. Evry 2018).
2. Vinh Nguyen (1 month in September 2018, Ph.D. Ecole Polytechnique 2019).
3. Ky Duong Giao (1 month in August 2019, current Ph.D. at U. Paris Nord).

Fellowships and Interns (one month) at University of Chile:

José Palacios (2016), Camilo Gómez (2016), Jessica Espinoza (2019), Nicolás Valenzuela (2020) and Javier Castro (2020).

Projects:

1. Associate member of the Center for Mathematical Modeling (CMM), funded by Conicyt Grant PIA AFB-170001.

2. Main researcher in Fondecyt Regular project No. 1191412 (2019-2023)

3. Main researcher in Fondecyt Regular project No. 1150202 (2015-2019).

4. Chilean head of France-Chile ECOS-Sud C18E06 (2019-2021). French counterpart: Frédéric Rousset (U. Paris-Saclay).

5. Associate member of EEQUADD II MathAmSud project 20-MATH-04 (2020-2021).

6. Chilean head of the EEQUADD I MathAmSud project (2016-2017).

7. Associate researcher in the CAPDE Nucleus Millenium collaboration (2015-2017).

8. Chilean Head of the "Projet d'échanges CNRS LISA" Santiago-Lille 2021.

Organization:

1. Co-organizer of the CMM FLACAM conference (November 2019)
http://eventos.cmm.uchile.cl/flacam2019/.

2. Co-organizer with J. Angulo (Sao Paulo, Brazil) and D. Chamorro (Evry, France) of a dispersive-fluid session at CLAM 2020, Montevideo, Uruguay
(https://clam2020.cmat.edu.uy/) (postponed to 2021).

3. Organizer and scientific committee member of the 2nd. Workshop on Nonlinear Evolution Equations in Valdivia, held at Universidad Austral de Chile, Valdivia, on December 12-16 2016, see http://eventos. cmm.uchile.cl/valdivia2016/.

4. Organizer of the PDE session at Somachi 2015, held in Pucón, Chile, November 2015.

5. Co-organizer of the CLAM 2016 Nonlinear Dispersive Equations session, Colombia July 11-15 2016 (https://www.uninorte.edu.co/web/vclam/ana8).

6. Organizer of the Workshop MathAmSud EEQUADD, Universidad de Chile, Santiago, on December 4-7 2017, see http://eventos.cmm.uchile.cl/eequadd2017.

7. Co-organizer of the 60th birthday congress in honor of Frank Merle (2023).

8. Co-organizer of the workshop "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.

Recent important talks (past 5 years)

1. Local energy decay in KdV like equations, Analysis and PDE Seminar, U. of Kentucky, October 2020 (online).

2. Asymptotic stability for some 1+1 dimensional scalar field models, MIT Analysis seminar, October 2020 (online).

3. Sufficient condition for the asymptotic stability of kinks in general 1+1 dimensional scalar field models, Texas A&M Mathematical Physics and Harmonic Analysis Seminar, September 2020 (online).

4. Understanding soliton dynamics in Boussinesq systems, SN PDEA webinar, September 2020.

5. Local energy decay in Zakharov-Kuznetsov equations, Seminario latinoamericano de EDPs dispersivas, UFMG, Brazil, July 2020 (online).

6. Decay of abcd nonlinear waves, Mittag-Leffler Institute, Sweden, June 2019.

7. Decay of nonlinear waves in one dimension and nonexistence of breathers in gKdV models, U. de Granada, Spain, 2019.

8. Decay of nonlinear waves in one dimension and nonexistence of breathers in gKdV models, U. de Sevilla, Spain, 2019.

9. Decay of nonlinear waves in one dimension and nonexistence of breathers, Oberwolfach, Germany. 2017.

10. Decay of small perturbations on 1+1 scalar field equations y equations from fluids, Fields Institute, Canada 2017.

11. Decay of small perturbations on 1D scalar field equations, Mathematical Congress of the Americas MCA 2017, Canada.

12. Scattering in the energy space for Boussinesq equations, Third Workshop Nonlinear Dispersive Equations, Campinas, Brazil 2017.

13. Asymptotic Stability of Kink solutions, SIAM NLW, Philadelphia, USA, 2017.

14. Asymptotic stability for kinks in scalar field equations, U. Bonn, Germany 2016.

15. On the variational structure of breather solutions, IHES Nonlinear Waves Seminar, Bures-sur-Yvette, France 2016.

16. The Calderon problem for quasilinear equations, V Congreso Latinoamericano de Matema ?ticos (CLAM) Barranquilla, Colombia 2016.

17. Asymptotic stability for kinks in scalar field equations, Long time Behaviour of Nonlinear Waves, Bielefeld Germany 2015.

18. Dispersive estimates for rational symbols and local well-posedness of the nonzero energy Novikov-Veselov equation, workshop U. Osaka, Japan 2015.

Research courses:

1. Summer Schools on PDEs (2016 and 2018), Amarun association (Quito, Ecuador).
http://www.amarun.net/index.php/menu-general/men-eventos-2/94-cat-eventos/118-cursos-y-seminarios

2. Mini-course at "Jornadas Matemáticas de la Zona Sur" (UACh, Valdivia), 2018.

Research stays (last 5 years):

2019 Universidad Paris-Saclay, Orsay, Francia
2019 Universidad de Bergen, Noruega
2019 Instituto Mittag Leffler, Suecia.
2019 Universidad de Granada, España
2019 Universidad de Sevilla, España
2018 Ecole Polytechnique, Francia
2018 Universidad La Sapienza Roma, Italia
2017 Wolfgang Pauli Institute Vienna Austria
2017 University of Toronto / Fields Institute Canada
2017 Instituto de Matemática, Estadística e Computaçao Científica, UNICAMP Campinas Brasil
2017 Instituto de Matemáticas de Oberwolfach Alemania
2017 University of Montreal Canada
2016 Universidad Paris Sud Centre Scientifique d’Orsay, Francia
2016 Universidad de Washington Estados Unidos
2016 IHES Francia
2016 UniversitadeTriesteItalia
2016 Orberwolfach Institute Alemania
2015 MRSI University of California Berkeley Estados Unidos
2015 Universidade Estadual de Campinas Brasil
2015 University of Bielefeld Alemania
2015 Universidad de Osaka Japon

Visitors (last 5 years)

1. 2020 Lucrezia Cossetti, KIT Germany.
2. 2019 Jean-Claude Saut, U Paris Sud
3. 2019 Miguel A. Alejo, UFSC Brasil
4. 2019 Juan Carlos Pozo Vera, UFRO
5. 2019 Diego Chamorro, U. Evry Francia
6. 2019 Oscar Jarrín, U. T. Ambato, Ecuador
7. 2019 Yvan Martel, E. Polytechnique
8. 2019 Gustavo Ponce, UCSB
9. 2019 Francesco Fanelli, U. Lyon
10. 2018 Marcio Cavalcante, U. Alagoas Brasil
11. 2018 Miguel A. Alejo, UFSC Brasil
12. 2018 Felipe Poblete (UACh)
13. 2018 Juan Carlos Pozo Vera (UFRO)
14. 2018 Frédéric Rousset, U. Paris-Sud, Francia (June 2018)
15. 2018 Manuel Fernando Cortez, Escuela Politécnica Quito, Ecuador
16. 2018 Felipe Poblete, Universidad Austral de Chile
17. 2017 Juan Carlos Pozo Vera, UFRO, Chile
18. 2017 Mauricio Andres Romo, Institute for Advanced Study, Princeton, NJ, USA
19. 2017 Manuel Fernando Cortez, Escuela Politécnica Quito Ecuador
20. 2017 Francisco Correa, Universidad Austral de Valdivia Chile
21. 2017 Felipe Poblete, Universidad Austral de Chile, Chile
22. 2016 André de Laire, Université de Lille, Francia
23. 2016 Frank Merle, Université Cergy-Pontoise e IHES, Francia
24. 2016 Miguel Angel Alejo Plana, Universidad Federal de Santa Catarina, Brasil
25. 2016 Oscar Jarrin, Université de Evry, Francia
26. 2015 Didier Pilod, UFRJ, Brasil
27. 2015 Anna Kazeykina, Université Paris Sud 11, Francia
28. 2015 Evelyne Miot, Ecole Polytechnique, Francia
29. 2015 Yvan Martel, Ecole Polytechnique De Paris, France
30. 2015 Miguel Angel Alejo Plana, Universidade Federal de Santa Catarina, Brasil

Reviewer for the following journals (among others):

Inventiones Mathematicae, (x2)
Duke Math J., (x2)
J. European Math. Soc., (x2)
Geom. Funct. Analysis, (x1)
Comm. Math. Phys., (many times)
Advances in Math., (x2)
Proc. London Math. Soc., (x2)
Analysis and PDE, (many times)
Annales IHP Analyse Nonlineaire, (many times)
Comm. PDE, (x1)
J. Functional Analysis, (many times)
J. Differential Equations, (many times)
Transactions of the AMS, (many times)
International Mathematics Research Notices, (many times)
DCDS A, (many times)
SIAM J. Mathematical Analysis, (many times)
SIAM J. Dynamical Systems, (x1)
SIAM J. Applied Math. (x1)
Revista Matematica Iberoamericana, (x1)
Nonlinearity. (many times)