Home Page of Daniele Garrisi

- 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.

- "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)- "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)- "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- "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- "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 )- "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)

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

- "Uniqueness and non-degeneracy of Q-balls in dimension one" at the 2016 KMS Spring Meeting, on April 23, 2016 (slides)
- "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)
- "Minimal stable subsets of the ground state: the non-linear Schroedinger equation" at the 2015 KMS Spring Meeting, on April 25, 2015 (slides)
- "On the uniqueness of $ Q $-ball solutions to the non-linear Schroedinger equation" at University of Oklahoma, Norman, on January 16, 2015 (slides)
- "Finiteness, up to translations, of standing-wave solutions to a nonlinear Schroedinger equation" at the 2015 JMM, San Antonio, on January 13, 2015 (slides)
- "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)
- ”Traveling wave solutions to the half-wave equation” at the 2013 KMS Fall Meeting, Seoul University (Seoul), on October 26, 2013 (slides)
- ”Standing-waves with a small energy/charge ratio” at the KSIAM 2013 Spring Conference, Yonsei University (Seoul), on May 28, 2013 (slides)
- ”Orbital Stability by means of symmetric rearrangement” at the 2013 Joint Mathematics Meetings, San Diego Convention Center (San Diego), on January 10, 2013
- ”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
- ”On the spectral flow for Banach spaces” at the 2011 KMS Fall Meeting, Gyeongbuk National University (Daegu), on October 22, 2011 (slides)
- ”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)
- ”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
- ”Orbitally stable coupled standing waves” at the Korean Mathematical Society conference, POSTECH, on October 22, 2010
- ”A splitting property for two variables functions” at the Young Researcher in Mathematics 2010, Center for Mathematical Sciences (Cambridge), on March 26, 2010
- ”Non-linear elliptic systems and stability” at the Joint Meeting KMS-AMS, Ewha University (Seoul), on December 19, 2009
- ”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.