Curriculum Vitae - Luca Rizzi - CMAP

Curriculum Vitae - Luca Rizzi
December 2014
Personal Informations
Surname: Rizzi
First Name: Luca
Place of Birth: Busto Arsizio (VA) - Italy
Date of Birth: October 17th 1984
Nationality: Italian
Present Address: 27 Rue Andr´e Theuriet, 92340, Bourg-la-Reine - France
Institution Email: [email protected]
Permanent Email: [email protected]
Homepage: www.cmap.polytechnique.fr/~rizzi/
Position
´
• November 2014 - Present: Ecole Polytechnique DRI Post Doc fellow, CMAP, Ecole
Polytechnique, Paris
• June 2014 - November 2014: ERC Post Doc fellow, CMAP, Ecole Polytechnique, Paris
Education
• October 2010 - May 2014: Ph.D. cum laude in Geometry, Scuola Internazionale di Studi Superiori
Avanzati (Trieste, Italy)
Supervisor: Prof. Andrei A. Agrachev
Thesis title: The curvature of optimal control problems and applications to sub-Riemannian geometry
• March 2010: Laurea Specialistica (M.Sc.) in Physics, Universitas Studiorum Insubriae, Como
Final mark: 110/110 summa cum laude
Supervisors: Prof. S. Cacciatori, Prof. V. Gorini, Dr. Francesco Belgiorno
Topic: Dielectric black holes and analogue Hawking radiation
• December 2006: Laurea Triennale (B.Sc.) in Physics, Universitas Studiorum Insubriae, Como
Final mark 110/110 cum laude
Supervisors: Prof. V. Gorini, Prof. S. Cacciatori
Topic: Hyperbolically symmetric vacuum solutions of Einstein’s Field Equations
Research Interests
• Sub-Riemannian Geometry, Curvature, Geometric Control Theory, General Relativity.
Fellowships and grants
´
• ERASMUS grant for a 3 months research visit at Ecole
Politechnique (Paris) - declined
• INDAM GDRE-CONEDP grant for a 2 weeks research visit at IHP (Paris)
• Research in Paris grant (joint project with D. Barilari) for a 5 weeks research visit at IHP (Paris)
• SISSA Ph.D. Fellowship (awarded on a merit basis), 2010-2014
Publications1
Submitted
• A. Lerario, L. Rizzi, How many geodesics joint two points on a contact sub-Riemannian manifold?,
arXiv:1405.4294
1 During
my undergraduate studies (2009-2010), I’ve been active in the field of analogue gravity and general relativity in collaboration with Profs. F. Belgiorno, S. Cacciatori, D. Faccio and V. Gorini and in other projects with Profs. O. Piattella, V.
Gorini et al. In fall 2010 I started a PhD program in mathematics, under the supervision of Prof. A. Agrachev. This is why
my ”production” is split in physics (2010-2011) and mathematics (2012 onward).
1
• D. Barilari, L. Rizzi, Comparison theorems for conjugate points in sub-Riemannian geometry, arXiv:1401.3193
• A. Agrachev, D. Barilari, L. Rizzi, The curvature: a variational approach, arXiv:1306.5318
Published
• A. Agrachev, L. Rizzi, P. Silveira, On conjugate times of LQ optimal control problems, Journal of Dynamical and Control Systems (2014)
• D. Barilari, L. Rizzi, A formula for Popp’s volume in sub-Riemannian geometry, Analysis and Geometry
in Metric Spaces, Volume 1 (2012)
• F. Belgiorno, S.L. Cacciatori, G. Ortenzi, L. Rizzi, V. Gorini, D. Faccio, Dielectric black holes induced
by a refractive index perturbation and the Hawking effect, Phys. Rev. D 83, 024015 (2011)
• F. Belgiorno, S.L. Cacciatori, M. Clerici, V. Gorini, G. Ortenzi, L. Rizzi, E. Rubino, V.G. Sala, D.
Faccio, Hawking radiation from ultrashort laser pulse filaments, Phys. Rev. Lett. 105, 203901 (2010)
• F. Belgiorno, S. L. Cacciatori, V. Gorini, G. Ortenzi, L. Rizzi, V. G. Sala, D. Faccio, Spacetime geometries
and light trapping in travelling refractive index perturbations, New J. Phys. 12 095021
• L. Rizzi, S. Cacciatori, V. Gorini, A. Kamenshchik, O.F. Piattella, Dark matter effects in vacuum
spacetime, Phys. Rev. D 82, 027301 (2010)
• L. Rizzi, O.F. Piattella, S.L. Cacciatori, V. Gorini, The Step-Harmonic Potential, Am. J. Phys. Volume
78, Issue 8, pp. 842 (2010). An extension of this paper is Two variants of the step-harmonic potential,
Preprint available on arXiv (2011)
In preparation
• Sub-Riemannian curvature of contact manifolds, in preparation (with A. Agrachev, D. Barilari, P. Lee)
• On the Measure Contraction Property of Sub-Riemannian manifold and the MCP conjecture for Carnot
groups in preparation (with D. Barilari)
• Counting geodesics on Carnot groups in preparation (with A. Lerario)
• On a Santal´
o formula in sub-Riemannian geometry and applications to the isoperimetric inequality of
Carnot groups (with D. Prandi and M. Seri
Reviewing and editorial activity
• Referee for Journal of Dynamical and Control Systems, Communications in Analysis and Geometry
• Reviewer for Zentralblatt Math
Invited Talks
• October 2014, IHP (Paris) - thematic day entitled “Optimal transport and sub-Riemannian manifolds”,
within the special trimester “Geometry, Analysis and Dynamics on Subriemannian Manifolds” - On
measure contraction properties of sub-Riemannian manifolds
• November 2014, RICAM (Linz) - Workshop: Geometric control and related fields - The curvature: a
variational approach
• August 2014, Lake Baikal - Conference: Geometric control theory and analysis on metric structures How many geodesics join two points on a contact sub-Riemannian manifold?
• June 2014, Institut Camille Jordan (Lyon) - Invited talk - How many geodesics join two points on a
contact sub-Riemannian manifold?
• April 2014, Steklov Mathematical Institute (Moscow) - Conference: Geometry and Control - Comparison
theorems in sub-Riemannian geometry
• April 2014, SISSA (Trieste) - Geometric control seminars - Enumerative geometry for geodesics in corank
1 Carnot groups
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• February 2014, SISSA (Trieste) - Geometric control seminars - On the curvature of Carnot groups
• December 2013, SISSA (Trieste) - Conference: Mathematical control in Trieste - On conjugate times of
LQ optimal control problems
• 22 Oct 2013, IHP (Paris) - S´eminaire de G´eom´etrie Sous-Riemannienne: Comparison theorems in subRiemannian geometry
• 14 June 2013, ICTP (Trieste) - ICTP-SISSA-Moscow School on Geometry and Dynamics: Sub-Riemannian
curvature
• 19 April 2013, Florence - Nonlinear Control: geometric approach and applications: Asymptotic measure
contraction property in sub-Riemannian geometry
• 21 March 2008, Bologna - Bo11 Conference: Dynamical effects in the pseudo - Schwarzschild vacuum
Schools, Conferences and Workshops attended
• 1 September - 12 December, 2014: Geometry, Analysis and Dynamics on Subriemannian Manifolds (IHP
trimester, Paris, France)
• 2-8 August 2014: Geometric control theory and analysis on metric structures (Baikal Lake, Russia)
• 13-18 April 2014: Geometry and Control (Steklov Mathematical Institute, Moscow)
• 15 July - 2 August 2013: Geometric Measure Theory and Optimal Transport (ICTP, Trieste)
• 24-28 June 2013: Norwegian Summer School on Analysis and Geometry for PhD students and young
researchers (Bergen, Norway)
• 3-15 June 2013: ICTP-SISSA-Moscow School on Geometry and Dynamics (ICTP, Trieste)
• 18-19 April 2013: Non Linear Control: Geometric Methods and Applications (Florence, Italy)
• 2-5 July 2012: Sub-Riemannian Geometry and PDEs (Levico Terme, Italy)
• 21-25 May 2012: INDAM meeting on Geometric Control and sub-Riemannian Geometry (Cortona, Italy)
• 16-21 May 2011: SIGRAV Graduate School - IX Edition - “Analogue Gravity” (Como, Italy)
• 11-15 May 2009: SIGRAV Graduate School - VIII Edition - “Gravity: where do we stand?” (Como,
Italy)
• 20-21 March 2008: Bo11 Conference (Bologna, Italy)
• 14-18 May 2007: SIGRAV Graduate School - VII Edition - “The Dark Side of the Universe” (Como,
Italy)
Research Visits
• Institut Henri Poincar´e, Sep-Dec 2014
• Institut Henri Poincar´e, Oct-Nov 2013, supported by the Research in Paris initiative (joint project with
D. Barilari)
• The Chinese University of Hong Kong, Nov-Dec 2012, invited by Prof. P. Lee
Teaching Experiences
• Universit´e Paris XI - Paris-Sud, 2014: Tutorials and exercises for the M2 course “Geometric Control
Theory”
• Universit´
a degli studi dell’Insubria (Como), 2009: Tutorials and exercises for the 2nd year course course
“Quantum Physics I”
• Universit´
a degli studi dell’Insubria (Como), 2009, 2008: Tutorials and exercises for the 2nd year course
course “Quantum Physics I”
3
• Universit´
a degli studi dell’Insubria (Como), 2009, 2007: Tutorials and exercises for the 2nd year course
“Quantum Physics I”
• Universit´
a degli studi dell’Insubria (Como), 2009, 2007: Lectures on Special Relativity for the 2nd year
course “Electromagnetism II and Special Relativity”
• Universit´
a degli studi dell’Insubria (Como), 2009, 2006: Tutorials and exercises for the 2nd year course
“Quantum Physics I”
Organizing activity
• Organizer for the cycle of seminars of the geometric control group at SISSA, and webmaster of the group
blog http://geomcontrol.wordpress.com/
• Member of the organizing committee of the exhibition: La fisica intorno a noi: come 100 anni di
scoperte hanno cambiato la vita quotidiana (translation: “Physics around us: how discoveries during the
last century changed daily life”) - (Como 15/12/2005 - 15/1/2006) and guide for the section dedicated
to Relativity, Quantum Mechanics and Chaos.
Languages
• Italian (mother tongue)
• English (advanced - C1)
• French (intermediate - B1)
Computer Skills
Proficient in Linux and Windows operating systems, Mathematica, Maple, Gnuplot, Xfig. Basic knowledge
of Matlab, C++, Fortran90, PAW and ROOT. I have a genius for computer related topics, and I can learn
anything else not listed above very quickly.
Main collaborators and contacts
• Andrei Agrachev (SISSA, Trieste, Italy) - [email protected]
• Davide Barilari (Universit´e Paris Diderot, Paris, France) - [email protected]
´
• Ugo Boscain (CNRS and CMAP, Ecole
Polytechnique) - [email protected]
Extras
• 5 May 2013: 18th Trieste Half Marathon (21.097 km)
• 6 June 2013: 3rd Moonlight Half Marathon - Jesolo (21.097 km)
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