Personal Data

Full name

Hugo Ricardo Nabais Tavares

Publishing name

Hugo Tavares

Birthday

1983-06-25T00:00:00

Academic Degrees

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

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

-

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 Bolsa de Estudo por Mérito Universidade de Lisboa
2002 Prémios Fundação FCUL - Melhores Alunos do 1º ano em 2000/01 Fundação FCUL

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"