### Research interests

• Orbital stability of standing-wave solutions to non-linear Partial Differential Equations (Schrödinger, Klein-Gordon, fractional Klein-Gordon) and related variational methods
• Spectral flows for paths of bounded operators
• Topology of spaces of projectors in Banach algebras or algebras of bounded operators.

### Publications

1. "Orbital stability and uniqueness of the ground state for the non-linear Schrödinger equation in dimension one", with Vladimir Georgiev, to appear on Discrete and Continuous Dynamical Systems - A, Vol. 37, N. 8, August 2017 (arXiv:1605.09095)
2. "On the connected components of the conjugacy class of projectors on $\ell_p\oplus\ell_q$" on Indagationes Mathematicae, Vol. 28, N. 2, 446-450, April 2017 (pdf)
3. "Orbitally stable standing-wave solutions to a coupled non-linear Klein-Gordon equation" on Advanced Studies in Pure Mathematics, Vol. 64, 387–398, April 2015
4. "Standing-wave solutions to a system of non-linear Klein-Gordon equations with a small energy/charge ratio", on Advances in Nonlinear Analysis, Vol. 3, N. 4, 237-245, November 2014
5. "On the orbital stability of standing-waves pair solutions of a coupled non-linear Klein-Gordon equation" on Advanced Nonlinear Studies, Vol. 12, N. 3, 639-658, August 2012 (arXiv:1009.2281, pdf )
6. "On the spectral flow for continuous paths of essentially hyperbolic operators on a Banach space" on Topological Methods in Nonlinear Analysis, Vol. 36 N. 2, 353-381, December 2010 (arXiv:0806.4094)

### Works in preparation

1. "Uniqueness of standing-waves for a non-linear Schrödinger equation with three pure-power combinations in dimension one" (with Vladimir Georgiev) (arXiv:1709.00586)
2. "Existence of traveling-waves solutions to the half-wave equation and orbital stability of the ground state" (with Vladimir Georgiev)
3. "Ordinary differential equations in Banach spaces and the spectral flow" (Ph.D. dissertation)
4. "Elliptic semi-linear systems on $\mathbb{R}^n$" (arXiv:1005.0134)

### Talks

1. "Uniqueness and non-degeneracy of Q-balls in dimension one" at the 2016 KMS Spring Meeting, on April 23, 2016 (slides)
2. "Orbital stability of standing-wave solutions to the non-linear Schrödinger equation in dimension one" at the 2016 Joint Mathematics Meetings, Washington State Convention Center (Seattle), on January 7, 2016 (slides)
3. "Minimal stable subsets of the ground state: the non-linear Schroedinger equation" at the 2015 KMS Spring Meeting, on April 25, 2015 (slides)
4. "On the uniqueness of $Q$-ball solutions to the non-linear Schroedinger equation" at University of Oklahoma, Norman, on January 16, 2015 (slides)
5. "Finiteness, up to translations, of standing-wave solutions to a nonlinear Schroedinger equation" at the 2015 JMM, San Antonio, on January 13, 2015 (slides)
6. "On the compactness of minimizing sequences of an energy functional arising from a system of non-linear Klein-Gordon equations” at the 2014 KMS Spring Meeting, Gangreung University (Gangreung), on April 25, 2014 (slides)
7. ”Traveling wave solutions to the half-wave equation” at the 2013 KMS Fall Meeting, Seoul University (Seoul), on October 26, 2013 (slides)
8. ”Standing-waves with a small energy/charge ratio” at the KSIAM 2013 Spring Conference, Yonsei University (Seoul), on May 28, 2013 (slides)
9. ”Orbital Stability by means of symmetric rearrangement” at the 2013 Joint Mathematics Meetings, San Diego Convention Center (San Diego), on January 10, 2013
10. ”Standing-waves solutions to a system of non-linear Klein-Gordon equations with a sub-critical growth non-linearity” at 2012 Joint Mathematics Meetings, Hynes Convention Center (Boston), on January 7, 2012
11. ”On the spectral flow for Banach spaces” at the 2011 KMS Fall Meeting, Gyeongbuk National University (Daegu), on October 22, 2011 (slides)
12. ”Orbitally stable coupled standing waves for a coupled non-linear Klein-Gordon equation” at the 4th MSJ-SI Nonlinear dynamics in Partial Differential Equations, Kyushu University (Fukuoka), on September 14, 2011 (slides)
13. ”Lyapunov functions for standing-wave solutions to a coupled NLKG equation” at The 3rd Kyushu University-POSTECH Joint Workshop, POSTECH (Pohang), on June 17, 2011
14. ”Orbitally stable coupled standing waves” at the Korean Mathematical Society conference, POSTECH, on October 22, 2010
15. ”A splitting property for two variables functions” at the Young Researcher in Mathematics 2010, Center for Mathematical Sciences (Cambridge), on March 26, 2010
16. ”Non-linear elliptic systems and stability” at the Joint Meeting KMS-AMS, Ewha University (Seoul), on December 19, 2009
17. ”On the spectral flow for Banach spaces” at Beyond Part III, Center for Mathematical Sciences (Cambridge), on April 16, 2009

### Teaching

Since Spring 2012 I have been working as a Teaching Professor at the College of Mathematics Education of Inha University (Incheon, South Korea) where I am teaching two classes a semester

On Spring 2016, I am teaching Set Theory (EMT2226, Syllabus and Exercises with solutions, Final Exam with solutions) and Measure Theory (EMT4425, Syllabus and Exercises)

Fall 2015, I taught Applied Analysis and Differential Equations

Fall 2014, Applied Analysis (EMT2226) and Differential Equations (EMT1128)

Spring 2014: Set Theory (EMT1135) and Measure Theory (EMT4425)

Fall 2013: Set Theory (EP135) and Applied Analysis (EP226)

Spring 2013: Differential Equations (EP226)

Fall 2012: Set Theory (EP135) and Applied Analysis (EP226)

Spring 2012: Differential Equations (EP128) and Measure Theory (EP425) .

From Spring 2007 to Fall 2008 I worked as a Teaching Assistant at Università degli Studi di Pisa

Fall 2008: Analisi Matematica III (Mathematical Analysis III) at the Faculty of Physics (with Professor Carlo Viola), Matematica and Matematica con elementi di statistica medica at the Faculty of Pharmacy (with Professor Adele Manes)

Fall 2007 and Spring 2008: Matematica II (Mathematics II) at the Faculty of Engineering (with Professor Lina Conti). This course lasted one academic year

Fall 2007: Matematica (Mathematics) and Matematica con elementi di statistica medica (Mathematics with foundations of medical statistics) at the Faculty of Pharmacy (with Professor Adele Manes)

Spring 2007: Matematica II (Mathematics II) at the Faculty of Engineering (with Professor Lina Conti). Here you can download some exercises prepared for the oral exam.