Personal Data
Full name
Hugo Ricardo Nabais Tavares
Publishing name
Hugo Tavares
Birthday
19830625T00:00:00
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
Cosupervisor
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
Cosupervisor

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)
Cosupervisor
Susanna Terracini (Universidade de MilãoBicocca)
Scientific area
Matemática
Profissional activity
Period  Position  Institution 

01092016   Professor Auxiliar (Assistant Professor)  Faculdade de Ciências da Universidade de Lisboa 
01092013  31082016  Assistant Researcher (Investigador FCT, categoria Starting Grant)  Centro de Análise Matemática, Geometria e Sistemas Dinâmicos, Instituto Superior Técnico  Universidade de Lisboa 
01092012  31082013  Professor Auxiliar Convidado (Invited Assistant Professor)  Faculdade de Ciências da Universidade de Lisboa 
01042012  30082012  PostDoc 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). Reactiondiffusion 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. Obstacletype 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 711 2015;
Special Session "Nonlinear Elliptic Systems and Applications" at the congress: AMSEMSSPM International Meeting, Porto, Portugal. June 1013, 2015;
 Meeting "Variational Methods in Elliptic Equations and Systems"  in memory of Miguel Ramos, CMAFUL, Portugal. January 710, 2014.
Experience as scientific advisor
[2017/2018] Tutor of Mathias Hoffman in the PhD program LisMath
[2016/17] PostDoc Supervisor of Alberto Saldaña
[2013/14] Coadvisor 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 reactiondiffusion 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 nãolineares". 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 longrange interaction, Arch. Rational Mech. Anal. (2017), https://doi.org/10.1007/s0020501712042
[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^2mass 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 L2critical and supercritical NLS on bounded domains, Analysis & PDE, 78 (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 JacquesLouis 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), 715740.
[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. 34, 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, Signchanging solutions of competitiondiffusion 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 noncooperative 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 BahriLions 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, hindex: 8
Web of Science (ResearcherID: K62902013) Citations: 288, hindex: 8
Reference [3] is, since May/June 2015, a Thompson Reuters Web of Science Highly Cited Paper.
OrCID: orcid.org/0000000314357695
Google Scholar: Citations: 458, hindex: 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 GinzburgLandau 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 1317 2017.
"Least energy nodal solutions of Hamiltonian elliptic systems with Neumann boundary conditions"
[2017] CAMGSDCMAFCIO Differential Equations Meeting. Lisbon, Faculty of Sciences of the University of Lisbon, September 1415 2017.
"Some aspects about reactiondiffusion 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 914 2017.
"Variational problems with longrange interaction"
[2016] Workshop Asymptotic Patterns in Variational Problems: PDE and Geometric Aspects  CMO, Casa Matematica Oaxaca, Mexico, September 2530 2016.
"Paths to uniqueness of critical points and applications"
[2016] National meeting Ciência 2016  parallel session "Investigação em matemática e aplicações''  Lisbon, July 46 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 2024 2016.
"Spiked solutions for Schrodinger systems with Sobolev critical exponent"
[2016] Minicourse at the conference IX Jornada de EDP: DMUFSCar Conference on Analysis of PDE's, São Carlos, Brazil, January 1820, 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, FCTUNL, Portugal, December 1719, 2015.
"Existence and regularity of solutions to optimal partition problems involving Laplacian eigenvalues"
[2015] 1st joint meeting BrazilSpain in Mathematics, invited speaker of the special session "Elliptic Partial Differential Equations'', Fortaleza, Brazil, December 710, 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 610, 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 711, 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 2931, 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 37, 2014.
"Existence and orbital stability of the ground states with prescribed L^2norm 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 MittagLeffler. Djursholm, Sweden, July 2024, 2013.
[2012] National Meeting of the Portuguese Mathematical Society, special session devoted to Mathematical Analysis and Partial Differential Equations. Faro, Portugal, July 911, 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: Selforganized behavior of nonlinear elliptic equations and pattern formation of strongly interacting systems. Orlando  Florida, EUA, July 26, 2012.
"Optimal partition problems involving Laplacian eigenvalues"
[2010] Conference "Douro Meeting: Differential Equations and Applications''. Portugal, October 24 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 2528, 2008.
"Sobre o efeito de segregação que ocorre em certos sistemas de reaçãodifusão"
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. "Signchanging solutions of competingdiffusion systems and optimal partition problems"
[2011] Minho University, Portugal. October 25, 2011. "Signchanging solutions of competingdiffusion systems and optimal partition problems"
[2010] New University of Lisbon, June 23. 2010. "Asymptotic study of a reactiondiffusion system with competition terms"
[2010] University of Giessen, Germany. April 29, 2010. "Asymptotic study of a reactiondiffusion system with competition terms"
[2010] University of Frankfurt, Germany. April 22, 2010. "Asymptotic study of a reactiondiffusion 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"