## Personal Data

Full name

Hugo Ricardo Nabais Tavares

Publishing name

Hugo Tavares

Birthday

1983-06-25T00:00:00

## Academic Degrees

MESTRADO(2)

Degree date

2012

Final grade

19/ Muito Bom

Degree granting institution

Universidade de Lisboa

School / College / Campus

Faculdade de Ciências

Thesis title

Sobre a concentração de soluções em equações e sistemas elípticos sobrelineares

Supervisor

Miguel de Paula Nogueira Ramos

Co-supervisor

N/A

Scientific area

Matemática

LICENCIATURA(4)

Degree date

2012

Final grade

19

Degree granting institution

Universidade de Lisboa

School / College / Campus

Faculdade de Ciências

Thesis title

N/A

Supervisor

N/A

Co-supervisor

N/A

Scientific area

Matemática

DOUTORAMENTO(4)

Degree date

2010

Final grade

Aprovado com distinção e louvor

Degree granting institution

Universidade de Lisboa

School / College / Campus

Faculdade de Ciências

Thesis title

Nonlinear elliptic systems with a variational structure: existence, asymptotics and other variational properties

Supervisor

Miguel de Paula Nogueira Ramos (Universidade de Lisboa)

Co-supervisor

Susanna Terracini (Universidade de Milão-Bicocca)

Scientific area

Matemática

## Profissional activity

Period | Position | Institution |
---|---|---|

01-09-2016 - | Professor Auxiliar (Assistant Professor) | Faculdade de Ciências da Universidade de Lisboa |

01-09-2013 - 31-08-2016 | Assistant Researcher (Investigador FCT, categoria Starting Grant) | Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Instituto Superior Técnico - Universidade de Lisboa |

01-09-2012 - 31-08-2013 | Professor Auxiliar Convidado (Invited Assistant Professor) | Faculdade de Ciências da Universidade de Lisboa |

01-04-2012 - 30-08-2012 | Post-Doc Fellowship | Centro de Matemática e Aplicações Fundamentais (CMAF) - Universidade de Lisboa |

## Area of scientific activity

Area of scientific activity

Mathematics: Mathematical Analysis, Partial Differential Equations, Free Boundary Problems, Shape Optimization

Specialization domain

Mathematical Analysis: Partial Differential Equations, Free boundary problems and Shape Optimization.

Current main scientific area

Elliptic equations and systems, in particular concerning the following subjects: variational methods, existence and multiplicity results, qualitative properties of positions (sign, symmetry, regularity, stability). Reaction-diffusion type systems, with both cooperative and competitive type interactions; Hamiltonian elliptic systems. Asymptotic study of solutions to systems depending on a parameter; free boundary problems and segregation phenomena; regularity of solutions and interfaces - free boundary problems; optimization; optimal partition problems. Obstacle-type problems. Solutions to Nonlinear Schrödinger Equations and Systems.

Other scientific activities

Outreach aimed at high school teachers. Consulting/Scientific review of high school manuals.

Referee for many journals such as Analysis & PDE; Calculus of Variations and PDE; Interfaces and Free Boundaries; Journal of Fixed Point Theory and Applications; Journal of the European Mathematical Society; NODEA; Nonlinear Analysis: Theory, Methods & Applications; Portugaliae Mathematica; Proceedings of the Royal Society of Edinburgh A; ZAMP.

Organization of many events, including:

-Thematic Session "Higher order PDEs and systems" at the meeting: Workshop in Nonlinear PDEs, Brussels, Belgium. September 7-11 2015;

-Special Session "Nonlinear Elliptic Systems and Applications" at the congress: AMS-EMS-SPM International Meeting, Porto, Portugal. June 10-13, 2015;

- Meeting "Variational Methods in Elliptic Equations and Systems" - in memory of Miguel Ramos, CMAF-UL, Portugal. January 7-10, 2014.

## Experience as scientific advisor

[2017/2018] Tutor of Mathias Hoffman in the PhD program LisMath

[2016/17] Post-Doc Supervisor of Alberto Saldaña

[2013/14] Co-advisor of the Master thesis of Vicente Fernandes, Faculty of Sciences of the University of Lisbon (with Ana Rute Domingos).

[2012/13] Supervisor of Vicente Fernandes in the course "Seminar in Mathematics", Faculty of Sciences of the University of Lisbon.

## Participations in R&D projects

[2014/18] - Full time member of the internacional project ERC Advanced Grant 2013 entitled: "Complex Patterns for Strongly Interacting Dynamical Systems - COMPAT". Principal Investigator (PI): Susanna Terracini.

[2013/16] Principal Investigator of the FCT Exploratory Project "Asymptotic study of reaction-diffusion systems with competition terms" with reference: IF/00584/2012 (50.000 euros)

[2008/12] Member of the R&D national project with the reference UTAustin/MAT/0035/2008, entitled: "Análise de equac¸o~es com derivadas parciais não-lineares". Principal Investigator: José Miguel Urbano.

[2007] Principal Investigator of one of the awarded national projects of the program: "Programa de Estímulo à Investigação 2007" in the field of Differential Equations and Dynamical Systems, Fundação Calouste Gulbenkian (10.000 euros)

## Awards

Year | Award | Awarding entity |
---|---|---|

2016 | "Prémio Científico Universidade de Lisboa/Caixa Geral de Depósitos", in the field of Pure and Applied Mathematics. | Universidade de Lisboa |

2007 | Programa Gulbenkian de Estímulo à Investigação | Calouste Gulbenkian Foundation |

2005 | Prémios BES - Licenciados em 2003/04 com Melhor Média Final | Fundação BES |

2004 | Bolsa de Estudo por Mérito | Universidade de Lisboa |

2003 | Bolsa de Estudo por Mérito | Universidade de Lisboa |

2002 | Prémios Fundação FCUL - Melhores Alunos do 1º ano em 2000/01 | Fundação FCUL |

2002 | Bolsa de Estudo por Mérito | Universidade de Lisboa |

## Publications

Artigos em revistas de circulação internacional com arbitragem científica

- [21] D. Bonheure, J. Földes, E. Moreira dos Santos, A. Saldaña, H. Tavares, Paths to uniqueness of critical points and applications to partial differential equations, 41 pp., accepted in Transactions of the American Math Society, arXiv:1607.05638

[20] N. Soave, H. Tavares, S. Terracini, A. Zilio, Variational problems with long-range interaction, Arch. Rational Mech. Anal. (2017), https://doi.org/10.1007/s00205-017-1204-2

[19] A. Pistoia, H. Tavares, Spiked solutions for Schro¨dinger systems with Sobolev critical exponent: the cases of competitive and weakly cooperative interactions, J. Fixed Point Theory Appl. 19 (2017), in honor of Paul Rabinowitz, 407–446

[18] S. Correia, F. Oliveira, H. Tavares, Semitrivial vs. fully nontrivial ground states in cooperative cubic Schrödinger systems with d>=3 equations, Journal of Functional Analysis, 271 (2016), 2247–2273.

[17] F. Oliveira, H. Tavares, Ground States for a nonlinear Schrödinger system with sublinear coupling terms, Advanced Nonlinear Studies, 16 (2016), 381–387.

[16] N. Soave, H. Tavares, New existence and symmetry results for least energy positive solutions of Schrödinger systems with mixed competition and cooperation terms, Journal of Differential Equations 261 (2016), 505–537.

[15] Nicola Soave, Hugo Tavares, Susanna Terracini, Alessandro Zilio, Hölder bounds and regularity of emerging free boundaries for strongly competing Schrödinger equations with nontrivial grouping, Nonlinear Analysis: Theory, Methods & Applications 138, in honor of Juan Luis Vázquez for his 70th birthday (2016), 388–427.

[14] M. Ramos, H. Tavares, S. Terracini, Extremality conditions and regularity of solutions to optimal partition problems involving Laplacian eigenvalues, Arch. Rational Mech. Anal. 220 (2016), 363–443.

[13] D. Bonheure, E. Moreira dos Santos, M. Ramos, H. Tavares, Existence and symmetry of least energy nodal solutions for Hamiltonian elliptic systems, J. Math. Pures Appl., 104 (2015), 1075–1107

[12] B. Noris, H. Tavares, G. Verzini, Stable solitary waves with prescribed L^2-mass for the cubic Schrödinger system with trapping potentials, Discrete Contin. Dyn. Syst. - Ser. A, 35 (2015), 5869–5877.

[11] B. Noris, H. Tavares, G. Verzini, Existence and orbital stability of the ground states with prescribed mass for the L2-critical and supercritical NLS on bounded domains, Analysis & PDE, 7-8 (2014), 1807–1838.

[10] D. Bonheure, E. Moreira dos Santos, H. Tavares, Hamiltonian elliptic systems: a guide to variational frameworks, Portugaliæ Mathematica 71, no.3, special issue dedicated to the memory of Miguel Ramos (2014), 301–395.

[9] J. F. Rodrigues, H. Tavares, Increasing powers in a degenerate parabolic logistic equation, Chinese Annals of Mathematics - ser. B 34, no.2, special issue in honor of the scientific heritage of Jacques-Louis Lions, (2013), 277–294.

[8] H. Tavares, T. Weth, Existence and symmetry results for competing variational systems, NoDEA - Nonlinear Diff. Equations and Appl. 20, no.3 (2013), 715-740.

[7] H. Tavares, S. Terracini, Regularity of the nodal set of segregated critical configurations under a weak reflection law, Calc. Var. Partial Differential Equations 45 (2012), no. 3-4, 273–317.

[6] B. Noris, H. Tavares, S. Terracini, G. Verzini, Convergence of minimax and continuation of critical points for singularly perturbed systems, J. Eur. Math. Soc. 14 (2012), 1245–1273.

[5] H. Tavares, S. Terracini, Sign-changing solutions of competition-diffusion elliptic systems and optimal partition problems, Ann. Inst. Henri Poincaré - AN 29 (2012), 279–300.

[4] H. Tavares, S. Terracini, G. Verzini, T. Weth, Existence and nonexistence of entire solutions for non-cooperative cubic elliptic systems, Comm. in Partial Differential Equations 36 (2011), 1988–2010.

[3] B. Noris, H. Tavares, S. Terracini, G. Verzini, Uniform Hölder bounds for nonlinear Schrödinger systems with strong competition, Comm. Pure Appl. Math. 63 (2010), 267–302.

[2] M. Ramos, H. Tavares, W. Zou, A Bahri-Lions theorem revisited, Adv. Math. 222 (2009), 2173–2195.

[1] M. Ramos, H. Tavares, Solutions with multiple spike patterns for an elliptic system, Calc. Var. Partial Differential Equations 31 (2008), 1–25.

Citation Metrics

MathSciNet: 291 citations from 162 authors, h-index: 8

Web of Science (ResearcherID: K-6290-2013) Citations: 288, h-index: 8

Reference [3] is, since May/June 2015, a Thompson Reuters Web of Science Highly Cited Paper.

OrCID: orcid.org/0000-0003-1435-7695

Google Scholar: Citations: 458, h-index: 11

Capítulos de livros

- - "Um modelo de competição entre espécies'', chapter of the book "Números, cirurgias e

nós de gravata: dez anos de Seminário Diagonal no IST", IST Press, 2011.

Outras publicações

- * A. Saldan~a, H. Tavares, Least energy nodal solutions of Hamiltonian elliptic systems with Neumann boundary conditions (2017), 34 pp., arXiv:1706.08391 (submitted)

* J.P. Dias, F. Oliveira, H. Tavares, On a coupled system of a Ginzburg-Landau equation with a quasilinear conservation law (2016), 26 pp., arXiv:1606.02640 (submitted)

* P.J. Freitas, H. Tavares, Dividing the circle, to appear in The College Mathematics Journal

## Communications

Comunicações orais por convite

[2017] First Belgium - Chile - Italy conference in PDEs. Belgium, Université Libre de Bruxelles, November 13-17 2017.

"Least energy nodal solutions of Hamiltonian elliptic systems with Neumann boundary conditions"

[2017] CAMGSD-CMAFCIO Differential Equations Meeting. Lisbon, Faculty of Sciences of the University of Lisbon, September 14-15 2017.

"Some aspects about reaction-diffusion systems with cooperative or competitive interactions"

[2017] 14th International Conference on Free Boundary Problems, invited speaker at Theme Session 13: Further connections with other areas, Shanghai, China, Jiao Tong University, July 9-14 2017.

"Variational problems with long-range interaction"

[2016] Workshop Asymptotic Patterns in Variational Problems: PDE and Geometric Aspects - CMO, Casa Matematica Oaxaca, Mexico, September 25-30 2016.

"Paths to uniqueness of critical points and applications"

[2016] National meeting Ciência 2016 - parallel session "Investigação em matemática e aplicações'' - Lisbon, July 4-6 of 2016.

"Phase Separation in Competitive Nonlinear Systems and Applications to Shape Optimization Problems"

[2016] PDEs at the Grand Paradis - 1st international conference on variational methods and PDEs, Cogne - Aosta Valey, Italy, June 20-24 2016.

"Spiked solutions for Schrodinger systems with Sobolev critical exponent"

[2016] Mini-course at the conference IX Jornada de EDP: DM-UFSCar Conference on Analysis of PDE's, São Carlos, Brazil, January 18-20, 2016.

"Asymptotic Study of Nonlinear Elliptic Systems with Strong Competition"

[2015] Contributed Talk at the international conference "Workshop on Calculus of Variations and its Applications'', on the occasion of Luísa Mascarenhas 65th birthday, FCT-UNL, Portugal, December 17-19, 2015.

"Existence and regularity of solutions to optimal partition problems involving Laplacian eigenvalues"

[2015] 1st joint meeting Brazil-Spain in Mathematics, invited speaker of the special session "Elliptic Partial Differential Equations'', Fortaleza, Brazil, December 7-10, 2015.

"Semitrivial and fully nontrivial solutions for cubic Schrödinger systems"

[2015] EquaDiff 2015, invited speaker at the Minisymposia M12: New Trends on Concentration Phenomena in Nonlinear Elliptic Equations. Lyon, June 6-10, 2015.

"Existence and symmetry of least energy nodal solutions for Hamiltonian elliptic systems"

[2014] 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Special Session 38: Recent trends in nonlinear Schrödinger systems, Madrid, July 7-11, 2014.

"Existence and regularity of solutions to optimal partition problems involving Laplacian eigenvalues"

[2014] Progress in Nonlinear Partial Differential Equations - celebrating the 80th birthday of V.A. Solonnikov and N.N. Uraltseva. Lisbon, May 29-31, 2014.

"Existence and regularity of solutions to optimal partition problems involving Laplacian eigenvalues"

[2014] ICMC Summer Meeting on Differential Equations - 2014 Chapter, Celebrating the 80th birthday of Djairo de Figueiredo (invited speaker at the Special Session in Elliptic Problems). São Carlos, Brazil, February 3-7, 2014.

"Existence and orbital stability of the ground states with prescribed L^2-norm for the NLS on bounded domains"

[2013] Existence and symmetry results for competing variational systems, Workshop Concentration phenomena and compactness issues in nonlinear PDE, Institut Mittag-Leffler. Djursholm, Sweden, July 20-24, 2013.

[2012] National Meeting of the Portuguese Mathematical Society, special session devoted to Mathematical Analysis and Partial Differential Equations. Faro, Portugal, July 9-11, 2012.

"Limite assintótico de soluções num problema parabólico de dinâmica populacional"

[2012] 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Special Session 29: Self-organized behavior of nonlinear elliptic equations and pattern formation of strongly interacting systems. Orlando - Florida, EUA, July 2-6, 2012.

"Optimal partition problems involving Laplacian eigenvalues"

[2010] Conference "Douro Meeting: Differential Equations and Applications''. Portugal, October 2-4 2010.

"Asymptotic study of nonlinear Schrödinger systems with strong competition"

[2008] National Meeting of the Portuguese Mathematical Society, special session devoted to Mathematical Analysis and Partial Differential Equations. Coimbra, Portugal, June 25-28, 2008.

"Sobre o efeito de segregação que ocorre em certos sistemas de reação-difusão"

Outras comunicações orais

[2017] New University of Lisbon, July 5, 2017. "Paths to uniqueness of critical points and applications to partial differential equations"

[2017] University of Coimbra, February 17, 2017. "Paths to uniqueness of critial points and applications to partial differential equations"

[2015] University of Rome “La Sapienza”, October 29, 2015. "Some aspects of cooperative and competitive gradient elliptic systems"

[2014] Instituto Superior Técnico, University of Lisbon, Portugal. June 4, 2014. "Existence and regularity of solutions to optimal partition problems involving Laplacian eigenvalues"

[2014] Polytechnic of Milan, Italy. May 7, 2014. "Existence and regularity of solutions to optimal partition problems involving Laplacian eigenvalues"

[2014] Université Libre de Bruxelles, Belgium. January 17, 2014. "Existence and orbital stability of the ground states with prescribed L^2–norm for the NLS on bounded domains"

[2013] University of Turim, Italy. November 20, 2013. "Existence and orbital stability of the ground states with prescribed L^2–norm for the NLS on bounded domains"

[2013] University of Aveiro, Portugal. October 31, 2013. "Existence and symmetry results for competing variational systems"

[2012] ICMC, University de São Paulo, Brazil. August 30, 2012. "Problemas de partições ótimas envolvendo autovalores lineares e não lineares: existência, regularidade e simetria"

[2012] University of Coimbra, Portugal. March 9, 2012. "Optimal partition problems involving Laplacian eigenvalues"

[2011] New University of Lisbon, Portugal. November 23, 2011. "Sign-changing solutions of competing-diffusion systems and optimal partition problems"

[2011] Minho University, Portugal. October 25, 2011. "Sign-changing solutions of competing-diffusion systems and optimal partition problems"

[2010] New University of Lisbon, June 23. 2010. "Asymptotic study of a reaction-diffusion system with competition terms"

[2010] University of Giessen, Germany. April 29, 2010. "Asymptotic study of a reaction-diffusion system with competition terms"

[2010] University of Frankfurt, Germany. April 22, 2010. "Asymptotic study of a reaction-diffusion system with competition terms"

[2010] University of Milan–Bicocca, Italy. February 9, 2010. "Asymptotic study of a system of nonlinear Schro¨dinger equations with competition terms"

[2007] CMAF, University of Lisbon, Portugal. November 14, 2007. "Segregation phenomena arising from competitive population systems"