Education Professional Achievements - ETH Math

Francesca DA LIO
Address:
Departement Mathematik, HG.J. 55, ETH,
Rämistrasse 101 8092 Zürich Switzerland.
Personal Data :
Italian citizenship
Two children: (2005), (2013)
Languages : Italian, English, German, French
E-mail : [email protected]
Homepage : https://www.math.ethz.ch/research/geometric-analysis-pde/francesca-da-lio.html
Education
• Ph.D in Mathematics, University of Padova, 1998.
• “Laurea” in Mathematics, University of Padova, 1994.
Professional Achievements
• September 2010-: Senior Scientist, (from June 2014 Titular Professor ), Department
of Mathematics, ETH, Zürich .
• September 2007- August 2010: Heinz-Hopf Lecturer, Department of Mathematics,
ETH, Zürich .
• June 2013: I got the Italian national qualification as Professore Ordinario.
• 2004-2013: “Ricercatore” in Mathematics, Department of Mathematics, University of
Padova (Italy) .
• 2000-2004: “Ricercatore” in Mathematics, Department of Mathematics, University of
Torino (Italy).
• August 1999-February 2000: post-doc fellowship, Department of Mathematics, University of Padova (Italy).
• February 1999-July 1999: post-doc fellowship, TMR European Project “Viscosity
solutions and their applications”, University of Tours (France).
Research Interests
Partial Differential Equations in Natural Science, Mathematical Finance and Geometry.
More specifically : viscosity solutions to fully nonlinear degenerate elliptic and parabolic equations,
deterministic and stochastic control, reaction diffusion equations, wave front propagations, ergodic
and homogenization problems, regularity and compactness properties of critical points of nonlocal
variational problems, fractional harmonic maps.
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Invited Speaker at International Conferences
• Advance Course and Workshop on Mathematical Control Theory, Levico Terme, June 1-10,
1998 .
• Equadiff99, Berlin August 1-7, 1999.
• Viscosity solutions and applications, Bressanone, July 3-5, 2000 .
• Nonlinear Analysis 2000, Courant Institute, New York, 28 May 28- June 2, 2000 .
• TMR Conference 2002: Viscosity Solutions and Applications, Tours, March 6-8 2002 .
• Workshop: Front Propagation and Viscosity Solutions, Institute Henri Poincaré, Paris,
December 12-13 2002 .
• XVII Congresso UMI, September 8-13, 2003, MIlano .
• Workshop : Equazioni alle derivate parziali, campi vettoriali, e controlli”, Padova, February
20-21, 2004 .
• Workshop: Front propagation and partial differential equations, Rouen (France), June 17-18,
2004 .
• SIMAI Congress, Mini-simposium: Metodi level-set, equazioni di Hamilton-Jacobi e applicazioni, September 20-24, 2004, Venice (Italy) .
• Workshop: Viscosity, metric and control theoretic methods in nonlinear pde’s, Serapo, September 27 - October 1, 2004 .
• Simposium: Stochastic Control, Filtering and Mathematical Finance, Osaka University, December 18-19, 2004 .
• Conference : Random Homogenization, Centre International de Recherches en Mathematiques,
Luminy, (France), June 11-15, 2005 .
• Oberwolfach Conference Calculus of Variation. July 9-15, 2006.
• Workshop: New trends in viscosity solutions and nonlinear pdes, Lisbon, July 24-28, 2006 .
• Conference : Geometry and Partial Differential Equations , Centre International de Recherches
en Mathèmatiques, Luminy , (France), June 18-22, 2007 .
• ICIAM 2007, Zürich, Mini-symposium: “Viscosity solutions of partial differential equations:
recent advances and applications” .
• Oberwolfach Conference: Partial Differential Equations. July 22-28, 2007.
• Banff workshop: Nonlocal operators and applications April 27-May 1, 2008.
• Oberwolfach Conference Calculus of Variation, July 6-11, 2008.
• Workshop: “Viscosity and control theoretic methods in Hamilton-Jacobi and elliptic-parabolic
PDEs”, Rome, (Italy), September 1-4, 2008, .
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• Workshop: Analysis of nonlinear PDEs and free boundary problems: Applications to homogenization”, Pacific Institute of Mathematical Science (PIMS), University of British
Columbia, July 20-24, 2009 .
• Workshop: New Connections Between Differential and Random turn Games, PDEs, and Image
Processing , Pacific Institute of Mathematical Science (PIMS), University of British
Columbia , July 27-31, 2009 .
• Workshop: Regularity for non-linear pdes , Centro di Ricerca Matematica Ennio De Giorgi,
Pisa, September 6-11, 2009 .
• Workshop: Loss of compactness in nonlinear problems : new trends and applications , Luminy,
(France) October 5-9, 2009 .
• Intensive research period on Nonlinear Problems in PDEs, Parma, June 6-12, 2010 .
• Oberwolfach Conference: Calculus of Variation, July 19-23, 2010.
• Workshop: Nonlinear PDE in Valparaiso, Valparaiso, Chile, January 10-14, 2011.
• Workshop: Nonlocal Operators: Analysis, Probability, Geometry and Applications, Bielefeld
, July, 9-14, 2012 .
• Mini-Workshop: Two Days on Nonlocal Operators and Applications, Parma, October 5-6,
2012 .
• Swiss-Japanese Seminar, Zürich, December 17-19, 2012 .
• Workshop: Nonlocal days, , Basel, December 15-17 2014.
• Workshop: Mostly Maximum Principle, Agropoli, September 16-18 2015.
• Conference: Nonlinear PDEs: Optimal Control, Asymptotic Problems and Mean Field Games,
Padova, February 25-26, 2016.
• Conference: Qualitative aspects of the theory of non- local equations, Fields Institute, Toronto,
May 16-20, 2016.
• BIRS workshop: Mostly Maximum Principle, Banff, April 3-7 2017.
Seminars
• “ Propagazione dei massimi per operatori non lineari ellittici degeneri”, July 20, 2000, Politecnico di Torino.
• “A geometrical approach to front propagation in bounded domains with Neumann boundary
conditions”, April 26, 2001, Courant Institute, New York.
• “ Soluzioni di viscosità e propagazione dei fronti”, January 31, 2002, Dept. of Mathematics,
University of Torino.
• “Un approccio geometrico ai problemi di propagazione dei fronti in domini limitati con condizione al bordo di tipo Neumann”, February 13, 2002, Dept. of Mathematics, University of
Bologna.
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• “A geometrical approach to front propagation problems in bounded domains with Neumann
boundary conditions”, April 15, 2002, Dept. of Mathematics, University of Texas at
Austin.
• “ Propagazione dei fronti in domini limitati con condizione al bordo di tipo Neumann”, May
9, 2003, Dept. of Mathematics, University of Padova.
• “ Propagazione dei fronti in domini limitati con condizione al bordo di tipo Neumann”, April
8, 2003, Dept. of Mathematics, University of Pavia.
• “ On the Generalized Dirichlet Problem for Viscous Hamilton-Jacobi Equations”, June 19,
2003, Bimestre Intensivo Indam, Politecnico di Torino .
• “Un risultato di unicità per equazioni di Hamilton-Jacobi con condizioni di crescita quadratica
e applicazioni”, December 17, 2003, University “ La Sapienza di Roma” .
• “Propagazione dei fronti in domini limitati con condizione al bordo di tipo Neumann”, January
28, 2004, Dept. of Mathematics, University of Parma.
• “Esistenza e unicità di grafici Lipschitziani con curvatura di Levi assegnata”, May 21, 2004,
Dept. of Mathematics, University of Torino.
• “A geometrical approach to front propagation problems in bounded domains with Neumann
boundary conditions”, December 15, 2004, University of Tokyo.
• “On the Generalized Dirichlet Problem for Viscous Hamilton-Jacobi Equations”, December 16,
2004, University of Waseda .
• “Ergodic Problems with Neumann boundary conditions and applications to homogenization”,
October 13, 2006, University of Stanford.
• “Problemi ergodici con condizione al bordo di Neumann e applicazione all’omogenizzazione”,
November 15, 2006, University of Padova .
• “ Ergodic problems and periodic homogenization for fully nonlinear equations with Neumann
boundary conditions”, November 28, 2006 , ETH, Zürich.
• “ Periodic Homogenization for Fully Nonlinear Equations in Half-Space Type Do mains with
Neumann Boundary Conditions”, Applied Math and Comp Sci Col loquium, February 29,
2008, University of Pennsylvania .
• “The analysis of 1/2-harmonic maps into manifolds - the critical case”, Max Planck Institute for Mathematics , Leipzig, January 13, 2009.
• “Stima di commutatori a tre termini e mappe semiarmoniche”, Padova, June 16, 2010.
• “Nonlocal Conformal Invariant Variational Problems”, Basel, September 10, 2010.
• “Problèmes variationnels non locaux invariants conformes”, Fribourg, December 10, 2010 .
• “Formule de representation de Hopf-Lax”, Groupe de travail sur le controle optimal et èquations
de Hamilton-Jacobi, Rennes, June 14, 2011.
• “Problèmes variationnels non locaux invariants conformes”, Rennes, June 16, 2011 .
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• “Nonlocal Conformal Invariant Variational Problems”, Sissa, Trieste, April 16, 2012.
• “Energy identities for fractional harmonic maps”, Analyse non-linaire et EDP, IHP,
Paris, January 22 , 2013 .
Visits Abroad
• April 2001: Courant Institute, New York University .
• Febbruary -March 2001 and May 2001: “Laboratoire de Mathématiques et Physique Théorique”,
University of Tours.
• March 2002: “Laboratoire de Mathématiques et Physique Théorique”, University of Tours.
• April 2002: Department of Mathematics, the University of Texas at Austin.
• May 2003: “Laboratoire de Mathématiques et Physique Théorique”, University of Tours .
• April 2004: “Laboratoire de Mathématiques et Physique Théorique”, University of Tours.
• Novembre 10-20 2004: Department of Mathematics, University of Paris Sud-Orsay.
• Dicember 2004: University of Tokyo, University of Waseda and University of Osaka
(Japan).
• March 14-19 2005 :“Laboratoire de Mathématiques et Physique Théorique”, University of
Tours (France).
• March 21-25 2005: CERMICS - ENPC, Paris.
• October 8-14 2006: Department of Mathematics, University of Stanford;
• October 15-22 2006: Courant Institute, New York University.
• 23-29 February 2008: Department of Mathematics, University of Pennsylvania, Philadelphia.
• 16-22 April 2011, 12-17 June 2011: Department of Mathematics, University of Rennes,
France.
Supervision of students
1. Matasci Luca, Master Thesis: Viscosity Methods for the Homogenization of First Order
Partial Differential Equations, April 2010, ETH, Zürich.
2. Pellegrini Fabio, Bachelor Thesis: Introduction to Conservation Laws, December 2010, ETH,
Zürich.
3. François Chalus, Bachelor Thesis: Continuous viscosity solutions of Hamilton-Jacobi equations and existence/uniqueness results, June 2016, ETH, Zürich.
4. Stanislav Gnap, Bachelor Thesis: Theory of Distribution and applications, September 2016,
ETH, Zürich.
5. Cecilia Lombardi, Bachelor Thesis: in progress, ETH, Zürich.
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6. Gustav Hermann , Bachelor Thesis: in progress, ETH, Zürich.
7. Francesco Palmurella, PhD Thesis: in progress, ETH, Zürich.
8. Vincenzo Ignazio, PhD Thesis, in progress (co-advised with Mete Soner), ETH, Zürich.
Member of hiring committees
1. 2011: assistant professor in Analysis, ETH, Zürich.
2. 2014: assistant professor in Mathematical Finance, ETH, Zürich.
3. 2015-: chair of the postdocs selection committee, ETH, Zürich.
Organization of Conferences and Seminars
1. Co-organizer of Viscosity solutions and Applications, Bressanone, July 3-5, 2000, Analysis
and control of deterministic and stochastic evolution equations, Bressanone, July 6-7, 2000
2. Co-organizer of TMR Conference 2002: Viscosity Solutions and Applications, Tours, March
6-8, 2002.
3. Co-organizer of Workshop : Equazioni alle derivate parziali, comportamento asintotico, soluzioni
stazionarie e regolarità, October 23-25, 2003 Torino.
4. Co-organizer of Workshop : Equazioni alle derivate parziali, campi vettoriali, e controlli,
Padova 20-21 February 20-22, 2004.
5. Co-organizer of Analysis Seminar, ETH, Zürich.
6. Co-organizer of the Conference: Recent advances in non-local and non-linear analysis: theory
and applications, ETH, Zürich, June 10-14, 2014 .
7. Member of Scientific Commitee of the conference celebrating Mete Soner’s 60th birthday, June
4-8, 2017, ETH, Zürich.
Research Projects
1. Member of the European Project TMR (Training and Mobility of Researchers): Viscosity
Solutions and Applications (terminated in March 2002).
2. 2000-2002: Member of Murst Project : Analisi e controllo di equazioni di evoluzione
deterministiche e stocastiche.
3. 2002-2004: Member of Murst Project Metodi di viscosità, metrici e di teoria del controllo in equazioni alle derivate parziali nonlineari.
4. Member of GNAMPA Project 2003 : Equazioni alle derivate parziali, campi vettoriali,
e controlli.
5. Member of GNAMPA Project 2004 : Equazioni alle derivate parziali, campi vettoriali,
e controlli.
6. 2-year MIUR projects PRIN ”Viscosity, metric, and control theoretic methods in nonlinear
PDEs” 2003-4, 2006-7, 2008-10.
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Refereeing activity for : Journal of Differential Equations, Integral and Differential Equations, Advances Differential Equations, Communications in PDE, Siam Journal Control and Optimization, Siam Journal of Mathematical Analysis, Applied Mathematics and Optimization, Journal
of Mathematical Analysis and Applications, Indiana University Mathematics Journal, Communication in Contemporary Mathematics, Transactions of the American Mathematical Society, Communications Pure and Applied Analysis, IEEE Transaction on automatic control, Calculus of Variations
and PDEs, Communications in Analysis and Geometry.
Teaching
• At the Faculty of Sciences of Torino:
Undergraduate Courses: Differential and Integral Calculus, Analysis 1, Analysis 2, Introduction to the study of partial differential equations.
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At the Faculty of Engineering of Torino:
Undergraduate Course: Analysis 2.
• At the Faculty of Engineering of Padova:
Undergraduate Courses: “Mathematics 3”, “Mathematics E”, Analysis 2.
• At ETH, Zürich:
Graduate Course: An Introduction to Viscosity Solutions: Methods and Applications I,,
D-MATH, HS07.
Graduate Course: An Introduction to Viscosity Solutions: Methods and Applications II,
D-MATH, FS08.
Undergraduate Course: Mathematik III-Partielle Differentialgleichungen, D-CHEM, HS08,
HS09, HS10, HS11, HS12, HS13, HS14, HS15, HS16.
Bachelor-Master Course: Introduction to partial differential equations, D-MATH, FS10,
FS17.
Undergraduate Course: Mass und Integral, D-MATH, FS09, FS11, FS16.
Undergraduate Course: Komplexe Analysis, D-ITET, FS12, FS13, FS14, FS15.
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Publications
1. (with M. Bardi), On the Bellman equation for some unbounded control problems, Nodea, Nonlinear Differential Equations Appl. 4 (1997), 491-510.
2. On the Bellman equation for infinite horizon problems with unbounded cost functional, Appl.
Math. Optim., 41 (2000), 171-197.
3. (with W.M. McEneaney), Finite Time Horizon Risk Sensitive Control and the Robust Limit
under a Quadratic Growth Assumption, Siam J. Control. Optim., 40 n.5 (2002), 1628-1661.
4. (with M. Bardi, S. Bottacin), Soluzioni di viscosita‘ di equazioni nonlineari ellittiche degeneri,
Giornate dell’Accademia delle Scienze di Bologna, 3-7 Febbraio 1997, Rapporto Interno Università di Padova.
5. (with M. Bardi) , Propagation of Maxima and Strong Maximum Principle for Degenerate
Elliptic Equations, Proceeding of the Eighth Tokyo Conference on Nonlinear PDE 1998, 1728.
6. (with M. Bardi), Propagation of maxima and strong maximum principle for viscosity solutions
of degenerate elliptic equations. Equadiff99, International conference on differential equations,
Berlin 1999. Ed. B.Fiedler,K.Groger and J.Sprekels, Equadiff99 , 2:589-591 , 1999.
7. (with M. Bardi), On the strong maximum principle for fully nonlinear degenerate elliptic equations, Arch.Math. 73 (1999), 276-285.
8. (with M. Bardi), Propagation of maxima and strong maximum principle for viscosity solutions
of degenerate elliptic equations. I: Convex operators, Nonlinear Anal., 44, no.8, Ser A:Theory
Methods (2001), 991-1006.
9. Strong Comparison Results for Quasilinear Equations in Annular Domains and Applications,
Comm. in PDE , 27, n.1 (2002), 283-323.
10. (with M. Bardi), Propagation of maxima and strong maximum principle for viscosity solutions
of degenerate elliptic equations. II: Concave operators, Indiana Univ. Math. J. 52 (2003),
607-628.
11. (with G. Barles), A Geometrical Approach to Front Propagation Problems in Bounded Domains
with Neumann-type Boundary Conditions, Interfaces and Free Boundaries, 5 (2003), 1-36.
12. (with G. Barles), Remarks on the Dirichlet and State-Constraint Problems for Quasilinear
Parabolic Equations, Advances Differential Equations, Vol. 8, n.8 (2003) 897-922.
13. Remarks on the Strong Maximum Principle for Viscosity Solutions to Fully Nonlinear Parabolic
Equations, Communications on Pure and Applied Analysis, Vol 3, n.3 (2004), 395-415
14. (with G. Barles), On the Generalized Dirichlet Problem for Viscous Hamilton-Jacobi Equations,
J. Math. Pures Appl. 83 (2004), 53-75.
15. (with I.Kim, D. Slepcev), Nonlocal Front Propagation Problems in Bounded Domains with
Neumann-type Boundary Conditions and Applications, Asymptotic Analysis 37 (3,4) (2004),
257-292.
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16. (with G. Barles), On the Boundary Ergodic Problem for Fully Nonlinear Equations in Bounded
Domains with General Nonlinear Neumann Boundary Conditions, Ann Inst. Henri Poincare,
Analyse non lineaire, Volume 22 (5) (2005), 521-541.
17. (with A. Montanari), Existence and Uniqueness of Lipschitz Continuous Graphs with Prescribed Levi Curvature, Ann Inst. Henri Poincare, Analyse non lineaire, Volume 23 (1) (2006),
1-28.
18. (with L. Rodino), A Pizzetti-Type Formula for the Heat Operator, Arch. Math. 87 (2006),
261-171.
19. (with O. Ley), Uniqueness Results for Second Order Bellman-Isaacs Equations under Quadratic
Growth Assumptions and Applications, Siam J.Control. Optim. 45 (2006), n.1 , 74-106.
20. (with G. Barles), Local C 0,α Estimates for Viscosity Solutions to Neumann-type Boundary
Value Problems, J. Differential Equations 225 (2006), 202-241
21. (with G. Barles), A weak comparison theorem and an example, appendix in the paper : R.K.
Kohn, S. Serfaty, A deterministic-control based approach to motion by curvature, Comm. Pure
Appl Math. 59, n.3 (2006), 344-407.
22. (with P. Cardaliaguet, N. Forcadel, R. Monneau) , Dislocation dynamics: a non-local moving boundary, proceedings du congres FBP 2005, Coimbra, Portugal, International Series of
Numerical Mathematics, Vol. 154, Birkhäuser Verlag Basel/Switzerland, 125-135, (2006).
23. (with B. Sirakov), Symmetry properties of viscosity solutions to nonlinear uniformly elliptic
equations, J. Eur. Math. Soc., 9, (2007), 317-330.
24. (with A. Cutrı̀), Comparison and existence results for non-coercive first order Hamilton-Jacobi
equations, ESAIM: COCV (2007), DOI: 10.1051/cocv: 2007021.
25. (with N. Forcadel, R. Monneau), Convergence of a nonlocal eikonal equation to anisotropic
mean curvature motion. Application to dislocation dynamics, J. Eur. Math. Soc., Volume 10,
Issue 4, (2008), 10611104.
26. Asymptotic Behavior of Solutions to Parabolic Equations with Neumann-Type Boundary Conditions , J. Math. Anal.Appl. 339 (2008), 384-398.
27. (with G. Barles, P.L. Lions, P. Souganidis), Ergodic problems and periodic homogenization
for fully nonlinear equations in half-space type domains with Neumann boundary conditions,
Indiana Univ. Math. J. , 57, n.5, (2008), 2355 - 2376.
28. Partial Regularity for Stationary Solutions to Liouville-Type Equation in dimension 3, Comm.
in PDE, Volume 33, Issue 10 (2008), 1890 - 1910 .
29. (with O. Ley), Convex Hamilton-Jacobi Equations Under Superlinear Growth Conditions on
Data, Applied Mathematics & Optimization, Volume 63, Issue 3 (2011), 309-339.
30. T. Rivière, 3-Commutators Estimates and the Regularity of 1/2-Harmonic Maps into Spheres,
APDE 4-1 (2011), 149–190. DOI 10.2140/apde.2011.4.149.
31. F. Da Lio, T. Rivière Sub-criticality of non-local Schrödinger systems with antisymmetric
potentials and applications to half-harmonic maps, Advances in Mathematics 227, (2011), 13001348.
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32. F. Da Lio Fractional Harmonic Maps into Manifolds in odd dimension n > 1, Calculus of
Variations and PDEs, Volume 48, Issue 3-4, (2013), 421-445 .
33. F. Da Lio, A. Schikorra, n/p-harmonic maps: regularity for the sphere case, Advances in
Calculus of Variations, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: 10.1515/acv2012-0107, October 2012 .
34. F. Da Lio, Compactness and Bubbles Analysis for 1/2-harmonic Maps, arXiv:1210.2653 , Annales de l’Institut Henri Poincarè / Analyse non linéaire 32 (2015), pp. 201-224 .
35. F. Da Lio, L. Martinazzi, T. Rivière, Blow-up analysis of a nonlocal Liouville-type equation,
arXiv:1503.08701, APDE Vol.8, no 7 (2015), 1757-1805.
36. F. Da Lio, P. Laurain, T. Rivière, A Pohozaev-type formula and Quantization of Horizontal
Half-Harmonic Maps, arXiv:1607.05504.
37. F. Da Lio, L. Martinazzi, The nonlocal Liouville-type equation in R and conformal immersions
of the disk with boundary singularities, arXiv:1607.03525.
38. T. Rivière, F. Da Lio, Horizontal α-Harmonic Maps, arXiv:1604.05461.
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