**Welcome to Claudio Muñoz's homepage**

**Postal Address:**

Departamento de Ingeniería Matemática,

Facultad de Ciencias Físicas y Matemáticas,

Universidad de Chile

Beauchef 851, Torre Norte, Piso 5,

Santiago, Chile

Phone: (+56)(2) 2978 0737

*
Research interests: Nonlinear dispersive equations, in particular: collisions, well-posedness, stability and asymptotic
stability and blow-up.
*

I obtained a Ph.D. in Mathematics at the University of Versailles Saint-Quentin, under the advise
of Yvan
Martel (Video) and Frank Merle (Video 1,
Video 2).

**Workshop
MathAmSud EEQUADD**,
to be held at Universidad de Chile, Santiago, on December 4-7 2017.

Partially funded by CAPDE Nucleo Milenio, CMM and EEQUADD MathAmSud Collaboration.

**
Recent preprints:
**

*Instability in nonlinear Schrodinger breathers*, arXiv:1608.08169.

*Nonexistence of small, odd breathers for a class of nonlinear wave
equations*,
(with M. Kowalczyk and Y. Martel), arXiv:1607.06421, accepted in Letters Math. Phys.

*
Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV
equation. II.
*
(with Anna Kazeykina),
arXiv:1603.06600.

*
Kink dynamics in the phi^4 model: asymptotic stability for odd perturbations in the energy space
*
(with M. Kowalczyk and Y. Martel), arXiv:1506.07420, accepted in
JAMS.

*
Dispersive estimates for rational symbols and local well-posedness of the nonzero energy NV equation
*
(with Anna Kazeykina),
arXiv:1502.00968, J. Funct. Anal. 270 (2016),
no. 5, 1744-1791.

*
Asymptotic Stability of high-dimensional Zakharov-Kuznetsov solitons
* (with R. Cote, D.
Pilod, and G. Simpson),
arXiv:1406.3196, Arch. Rat.
Mech. Anal. 220 (2016), no. 2, 639–710.

*
On the Variational Structure of Breather Solutions * (new and expanded
version, with M.A.
Alejo and J.M. Palacios),
arXiv:1309.0625. Part I
accepted in JMAA,
Part II accepted in EJDE.

*
Dynamics of complex-valued modified KdV solitons with applications to the stability of breathers
* (with M.A. Alejo), arXiv:1308.0998, Anal.
and PDE. 8 (2015), no. 3, 629–674.

*
All my papers are in the
ArXiv, and Mathscinet, done
in collaboration with several kind researchers.
*

My research is partially supported by Fondecyt Regular No. 1150202, Center for Mathematical Modelling (CMM), and Nucleus
Millenium Center CAPDE.

**
Some videos about soliton dynamics:
**
KdV Video
1, quartic KdV Video 2 and the wobbling kink of
Sine-Gordon Video 3.
A periodic mKdV breather with nonzero mean: Video 1, Video 2, and Video 3.

**
Projects:
**

I'm an associate researcher in the CAPDE collaboration, lead by
Manuel del Pino. We
run a biweekly seminar:
*
CAPDE Seminar 2017
*

I was also part of the organizing committee of the 2nd. Workshop on Nonlinear
Evolution Equations in
Valdivia, held at Universidad Austral de Chile, Valdivia, on December 12-16 2016.

Partially funded by ERC Blowdisol, CAPDE Nucleo Milenio, CMM
and
EEQUADD MathAmSud
Collaboration.

I was also organizer of the PDE session
at Somachi 2015.

I was also part of the organizing comitee at CLAM 2016 Nonlinear dispersive equations session, taking
place in Colombia between July 11-15 2016.

I'm also part of the MathAmSud collaboration EEQUADD 2016-2017.

**
Teaching:
**

*
Current teaching:
*

Multivariate Calculus (Fall 2017),

Advances dispersive PDEs (Fall 2017).

*
Past teaching:
*

Dispersive PDEs (Spring 2016)

Multivariate Calculus (Spring 2016)

ODEs (Spring 2016)

Advanced PDEs (Spring 2015) (Main documents, in Spanish: Midterm 1, Midterm 2, Final Exam, some additional lecture notes).

Multivariate Calculus (Fall 2015).

*
At the University of Chicago (2011-2013):
*

Multivariate Calculus II,

Introduction to Complex Analysis,

Honors Calculus I-II-III, and

Mathematical Methods for Physics.

*
At the University of Chile:
*

Ordinary Differential Equations (2011).