João Gouveia Departamento de Matemática Faculdade de Ciências e Tecnologia da Universidade de Coimbra 3001-454 Coimbra, Portugal Google Scholar ORCID: 0000-0001-8345-9754 E-mail: jgouveia@mat.uc.pt
Research	Talks	Teaching	Students		Activities
Research & Papers
Published and accepted papers: 31- “Complex psd-minimal polytopes in dimensions two and three” with Tristram Bogart and Juan Camilo Torres, Journal of Algebra and its Applications, 23 (2024) 30- “The face lattice of the set of reduced density matrices and its coatoms” with Stephan Weis, Information Geometry 6, 293-326 (2023) 29- “Self-dual polyhedral cones and their slack matrices” with Bruno F. Lourenço, SIAM Journal on Matrix Analysis and Applications, 44 (2023) 28- “General non-realizability certificates for spheres with linear programming” with Antonio Macchia and Amy Wiebe, Journal of Symbolic Computation 114, 172-192 (2023) 27- “Combining realization space models of polytopes” with Antonio Macchia and Amy Wiebe, Discrete & Computational Geometry, 69 (2023) 26- “Lifting for Simplicity: Concise Descriptions of Convex Sets” with Hamza Fawzi, Pablo Parrilo, James Saunderson and Rekha Thomas, SIAM Review, 64 (2022) 25- “An Algebraic Approach to Projective Uniqueness with an Application to Order Polytopes” with Tristram Bogart and Juan Camilo Torres, Discrete & Computational Geometry 67 (2), 462-491 (2022). 24- “The phaseless rank of a matrix” with António Goucha, SIAM Journal on Applied Algebra and Geometry 5 (3), 526-551 (2021) 23- “On sums of squares of k-nomials” with Alexander Kovacec and Mina Saee, Journal of Pure and Applied Algebra 226 (1), (2022) 22- “Inner approximating the completely positive cone via the cone of scaled diagonally dominant matrices”, with Ting Kei Pong and Mina Saee. Journal of Global Optimization 76 (2), 383-405 21- “Projectively unique polytopes and toric slack ideals”, with Antonio Macchia, Rekha R. Thomas and Amy Wiebe. J. Pure Appl. Algebra. (2020) Volume 224(5) 20- “The Slack Realization Space of a Polytope”, with Antonio Macchia, Rekha R. Thomas and Amy Wiebe. SIAM J. Discrete Math. (2019) 33(3), Pages 1637-1653 19- “On ranks of regular polygons”, with António Pedro Goucha and Pedro M. Silva. SIAM J. Discrete Math., (2017) 31(4), Pages 2612–2625 18- “Four-Dimensional Polytopes of Minimum Positive Semidefinite Rank” with Kanstanstin Pashkovich, Richard Z. Robinson and Rekha R. Thomas. Journal of Combinatorial Theory, Volume 145, January 2017, Pages 184–226 17- “On-off scheduling schemes for power-constrained electric vehicle charging” with Xavier Fernandes, Joana Rebelo, Rodrigo Maia and Nuno Bustorff Silva. 4OR-Q J Oper Res (2017) 15: 163. 16- “Sums of Squares on the Hypercube” with Grigoriy Blekherman and James Pfeiffer. Mathematische Zeitschrift, Volume 284, Issue 1, October 2016, Pages 41-54. 15- “Rational and real positive semidefinite rank can be different” with Hamza Fawzi and Richard Robinson, Operations Research Letters, Volume 44, Issue 1, January 2016, Pages 59–60 14- “Positive semidefinite rank” with Hamza Fawzi, Pablo A. Parrilo, Richard Robinson and Rekha R. Thomas, Math Programming, Series B –Special Issue on Lifts of convex sets in optimization - Volume 153, Issue 1 (2015), Pages 133-137 13- “Approximate cone factorizations and lifts of polytopes” with Pablo A. Parrilo, and Rekha R. Thomas, Math Programming, Series B –Special Issue on Polynomial Optimization - Volume 151, Issue 2 (2015), Page 613-637 12- “Worst-Case Results For Positive Semidefinite Rank” with Richard Z. Robinson, and Rekha R. Thomas, Math Programming, Series B –Special Issue on Lifts of convex sets in optimization - Volume 153, Issue 1 (2015), Pages 201-212 11- “A MIP model for locating slow-charging stations for electric vehicles in urban areas accounting for driver tours” with Joana Cavadas and Gonçalo Homem de Almeida, Transportation Research Part E: Logistics and Transportation Review, Volume 75, March 2015, Pages 188–201 10- “A Semidefinite Approach to the Ki Cover Problem” with James Pfeiffer, Operations Research Letters, Volume 42, Issue 2, March 2014, Pages 156–160 9- “Which nonnegative matrices are slack matrices?” with Roland Grappe, Volker Kaibel, Kanstantsin Pashkovich, Richard Z. Robinson, and Rekha R. Thomas, Linear Algebra and its Applications 439 (2013) 2921-2933. 8- “Polytopes of minimum positive semidefinite rank” with Richard Z. Robinson and Rekha Thomas, Discrete and Computational Geometry (Vol.50, Issue 3, 2013) pp. 679-699. 7- “Spectrahedral Approximations of Convex hulls of Algebraic Sets” with Rekha Thomas, chapter in Semidefinite Optimization and Convex Algebraic Geometry, volume 13 of MOS-SIAM Series on Optimization, 2012, pp. 293-340. 6- “Lifts of convex sets and cone factorizations” with Pablo Parrilo and Rekha Thomas, Mathematics of Operations Research (Vol. 38, No.2, 2013) pp. 248-264. 5- “Comparing SOS and SDP relaxations of sensor network localization” with Ting Kei Pong Computational Optimization & Applications 52, 2012, pp. 609-627. [codes] 4-“Positive Polynomials and Projections of Spectrahedra” with Tim Netzer - SIAM Journal on Optimization (Vol.21, No.3, 2011) 3- “A new semidefinite programming hierarchy for cycles in binary matroids and cuts in graphs”, with Monique Laurent, Pablo Parrilo and Rekha Thomas - Mathematical Programming (Vol.133, Issue 1-2, 2012) 2- “Convex hulls of algebraic sets” with Rekha Thomas, chapter in the "Handbook of Semidefinite, Cone and Polynomial Optimization", International Series in Operations Research & Management Science, Vol. 166, Miguel Anjos and Jean-Bernard Lasserre (eds), Springer, 2012. 1- “Theta Bodies for Polynomial Ideals”, with Pablo Parrilo and Rekha Thomas – SIAM Journal on Optimization (Vol.20, No.4, 2010). Preprints and Technical Reports 1- “The phase rank of a matrix” with António Goucha 2- “Minimal hyperbolic polynomials and ranks of homogeneous cones” with Masaru Ito and Bruno F. Lourenço Published Non-Research Papers (in Portuguese) 3- “Representações mínimas de polítopos” com Richard Z. Robinson e Rekha R. Thomas no Boletim da SPM – (resumo da comunicação no Encontro Nacional da SPM 2012) 2- “Não-negatividade, somas de quadrados e optimização” capítulo em Números, Cirurgias e Nós de Gravata, IST Press 2012 1- “Notas Sobre o Rateio de Hamilton”, com Eduardo Marques de Sá em Seminário Diagonal, Proceedings IST II, 2004 Talks April’ 24 – “Self-dual polyhedral cones and their slack matrices” – COCANA Seminar Series at UBC Okanagan – Kelowna, Canada November’ 23 – “PSD matrices with bounded factor width and locally PSD matrices” – ISM seminar – Tokyo September’ 23 – “Polígonos, poliedros, polítopos” – Tardes de Matemática – Conversas Ímpares – Exploratório Ciência Viva - Coimbra June’ 23 – “Self-dual polyhedral cones and their slack matrices” – ILAS meeting 23 – Madrid June’ 23 – “Quantum marginals, faces and coatoms” – WONRA 23 – Coimbra April’ 23 – “Característica sem fase, amibas e polítopos” – Workshop dos Novos Talentos da Matemática - Coimbra April’ 23 – “Sobre polítopos e matrizes” – Encontro Nacional de Estudantes de Matemática (ENEMath23) in Porto December’ 22 - “Self-dual polyhedral cones and their slack matrices” - International Workshop on Continuous Optimization – (virtual talk) July’22 – “Self-dual polyhedral cones and their slack matrices” – ICCOPT 2022 – Bethlehem, PA January’22 – “Applications of slack matrices: a biased survey” – CMAFcIO 2nd Workshop – U. Lisboa (virtual talk) December’19 – “Cones of matrices of bounded factor width” – Workshop on Conic and Copositive Optimization – RICAM – Linz September’19 – “Phaseless rank, semidefinite lifts and amoebas” – Einstein Workshop on Real Applied Algebraic Geometry – TU Berlin August’19 – “Matrices of bounded factor width and sums of k-nomial squares” – ICCOPT 2019 – Berlin July’19 – “Matrices of bounded factor width and sums of k-nomial squares” – SIAM meeting on Applied Algebraic Geometry (AG19) – Bern May’19 – “Sums of Squares in Polynomial Optimization” – Summer School of IPCO 2019 – U. Michigan – Lecture 1 – Problem Set – Sketch of Solutions - Lecture 2 July’18 – “Phaseless rank of a matrix” – 23rd ISMP - Bordeaux February’18 – “Programação Semidefinida” – Jornadas de Matemática da Universidade do Porto -slides December’17 – “Programação Semidefinida: o que é e para que serve?” – Matemática^4 - NEMAT - Coimbra September’17 – “Semidefinite lifts and factorizations” – MSRI Workshop [VIDEO] August’17 – “On ranks of regular polygons” – SIAM meeting on Applied Algebraic Geometry (AG17) – Atlanta, GA July’17 – “Matrix Factorizations” – Encontro Ciência 2017 - Lisbon June’17 – “Polytopes, slack ideals and psd-minimality” – CEAFEL seminar in Lisbon April’17 – “Polytopes, slack ideals and psd-minimality” – CMUC seminar on Algebra and Combinatorics. April’17 – “O Teorema de Yannakakis” – Encontro Nacional de Estudantes de Matemática (ENEMath17) in Coimbra January’17 – “Extension complexities of polytopes” – 3rd CMUC Workshop October’16 – “Positive semidefinite rank and representations of polytopes” – UC|UP Math PhD Program Seminar June’16 – “Conic lifts of convex sets through slack operators” – Workskop on Operator Theory, Complex Analysis, and Applications 2016 (WOTCA 2016) in Coimbra January’16 – “Positive semidefinite rank and representations of polytopes” – TOPS seminar at University of Washington in Seattle January’16 – “Slack ideals and semidefinite representations of polytopes” – Joint Mathematics Meeting 2016 (JMM 2016) in Seattle September’15 – “O teorema de Yannakakis” – Escola de Verão da SPM August’ 15 – “Psd-minimality and slack ideals” – SIAM meeting on Applied Algebraic Geometry (AG15) in Daejeon, South Korea July’ 15 – “Psd-minimality and slack ideals” – 22nd ISMP in Pittsburgh, USA - slides February’ 15 – “Positive semidefinite rank” – Workshop on Limitations of convex programming, Dagstuhl Schloss, Germany - slides September’ 14 – “Positive semidefinite rank” – CMUC evaluation panel visit - slides July’ 14 – “Representing Polytopes, the Yannakakis Theorem” – Plenary Talk - Encontro Nacional SPM 2014 slides or slides (pt version) July’ 14 – “Dois problemas sobre carregamento de veículos eléctricos” – Encontro Nacional SPM 2014 – in Portuguese - slides June’ 14 – “Positive Semidefinite Rank” –Workshop on Computational Nonlinear Algebra – ICERM Providence - slides May’ 14 – “Sums of squares on the hypercube” – SIAM Optimization 2014 San Diego- slides March’ 14 – “Sums of squares on the hypercube” – CMUC seminar - slides November’ 13 – “From approximate factorizations to approximate lifts” – CIRM, Luminy - slides October’ 13 – “Sums of Squares with Multipliers” – CWMINLP 2013 Paris - slides August’ 13 – “A semidefinite approach to the K_i cover problem” – SIAM AG 2013 - slides August’ 13 – “Semidefinite Lifts of Polytopes” – SIAM AG 2013 - slides July’ 13 – “From approximate factorizations to approximate lifts” – ICCOPT 2013 Lisbon - slides July’ 13 – “Sums of squares for polynomial binary programming” – Euro 2013 Rome - slides April’ 13 – “Semidefinite lifts of polytopes” – CMUC Workshop - slides March’ 13 – “(Minimal) semidefinite lifts of polytopes” – 4^th SDP days in CWI - slides September’ 12 – “Conic lifts of polytopes” – MAP 2012 in Konstanz - slides August’ 12 – “Semidefinite lifts of polytopes” – 21^st ISMP in Berlin - slides July’ 12 – “Representações mínimas de polítopos” – Encontro Nacional SPM 2012 – in Portuguese - slides March’ 12 – “Semidefinite Representations” – CELC Seminar – University of Lisbon. slides March’ 12 – “Sums of Squares in Combinatorial Optimization” – 2^nd Combinatorics Day – University of Coimbra. slides March’ 12 – “Teorema de Yannakakis” – Oráculo Delfos – (talk for gifted high-school students at the University of Coimbra) – in Portuguese. slides December’ 11- “Lifts of convex sets and cone factorizations” – CORE seminar at Université Catholique de Louvain. slides September’ 11 – “Positivity, Sums of Squares and Real Algebraic Varieties” – CMUC seminar on Algebra and Combinatorics. September’ 11 – “Lifts of Convex Sets” – CMUC seminar on Numeric Analysis and Optimization July' 11 – “Lifts of Convex Sets”. Optimization 2011 – Universidade Nova de Lisboa. slides May' 11 – “Approximating Convex Hulls of Planar Quartics”. SIAM-OPT 2011 - Darmstadt. slides May' 11 – “Geometry of Sums of Squares Relaxations”. – Thesis defense slides September' 10 – “Sums of squares relaxations for Convex Hulls of Semialgebraic Sets”. - IPAM workshop in Convex Optimization and Algebraic Geometry. slides July' 10 - “Geometry of Sums of Squares Relaxations” - SIAM Annual meeting in Pittsburgh. slides October' 09 - “A new SDP approach to the Max-Cut problem” - INFORMS meeting in San Diego August' 09 - “A new SDP approach to the Max-Cut problem” - 20^th ISMP in Chicago. July' 09 - “Theta Bodies for Polynomial Ideals” - Seminar of Real Algebraic Geometry at the University of Konstanz. April ' 09 - “A new SDP approach to the Max-Cut problem” - West Section Meeting of the AMS at SFSU. slides March '09 - survey talk on “Semidefinite representable sets” - CWI in Amsterdam, in a DIAMANT seminar on combinatorics and optimization. October/November '08,- seminars on the paper “Theta Bodies for Polynomial Ideals” - UC Berkeley's Discrete Mathematics seminar, UC Davis' Algebra and Discrete Mathematics seminar and at U Washington's Optimization Seminar. slides Teaching 2ºSemestre 2022/23 – Matemática Discreta – Lic. Matemática 1ºSemestre 2022/23 – Programação Linear e Otimização Combinatória – Mestrado Matemática 1ºSemestre 2022/23 – Otimização e Análise em Grafos – Lic. em Eng. e Ciência de Dados 2ºSemestre 2021/22 – Matemática Discreta – Lic. Matemática 2ºSemestre 2021/22 – Otimização – Progr. Interuniversitário de Doutoramento em Matemática 1ºSemestre 2021/22 – Programação Linear e Otimização Combinatória – Mestrado Matemática 1ºSemestre 2021/22 – Otimização e Análise em Grafos – Lic. em Eng. e Ciência de Dados 2ºSemestre 2020/21 – Matemática Discreta – Matemática 2ºSemestre 2020/21 – Otimização Avançada – Mestrado em Eng. e Ciência de Dados 1ºSemestre 2020/21 – Teoria de Jogos – Matemática 2ºSemestre 2019/20 – Matemática Discreta – Matemática 1ºSemestre 2019/20 – Análise Matemática III – Física, Eng. Física e Eng. Biomédica 1ºSemestre 2019/20 – Teoria de Jogos – Matemática 2ºSemestre 2018/19 – Matemática Discreta – Matemática 1ºSemestre 2018/19 – Análise Matemática III – Física, Eng. Física e Eng. Biomédica 1ºSemestre 2018/19 – Teoria de Jogos – Matemática 2ºSemestre 2017/18 – Análise Matemática II – Engenharia Informática 1ºSemestre 2017/18 – Programação Linear e Otimização Combinatória – Matemática 1ºSemestre 2017/18 – Análise Matemática III – Eng. Mecânica e Eng. Gestão Industrial 2ºSemestre 2016/17 – Análise Matemática II - Engenharia Electrotécnica. 2ºSemestre 2016/17 – Optimization – Joint Math PhD Program UC/UP. 1ºSemestre 2016/17 – Programação Linear e Otimização Combinatória – Matemática 2ºSemestre 2015/16 – Matemática Computacional - Engenharia Electrotécnica. 2ºSemestre 2015/16 – Optimization – Joint Math PhD Program UC/UP. 1ºSemestre 2015/16 – Programação Linear e Otimização Combinatória – Matemática 1ºSemestre 2014/15 - Análise Matemática I – Eng. Mecânica e Eng. Gestão Industrial. 1ºSemestre 2014/15 - Análise Matemática III – Eng. Electrotécnica. 2ºSemestre 2013/14 – Matemática Computacional - Engenharia Electrotécnica. 1ºSemestre 2013/14 - Análise Matemática I - Engenharia Informática. 2ºSemestre 2012/13 - Estatística - Engenharia Informática. 1ºSemestre 2012/13 - Análise Matemática I – Eng. Mecânica e Eng. Gestão Industrial. 2ºSemestre 2011/12 – Matemática Computacional - Engenharia Electrotécnica. 2ºSemestre 2011/12 – Estatística - Engenharia Informática. 1ºSemestre 2011/12 - Análise Matemática III - Engenharia Civil. Students Phd Students: - Mina Saee – 2015/2020 - António Goucha – 2016/2021 - Juan Camilo Torres – 2018/2020 – [Universidad de los Andes] – co-advised with Tristram Bogart - João Marcelino – 2023/20?? – co-advised with Eliana Duarte Master Students: 2012/13 - Joana Cavadas (Mestrado em Matemática) co-advised by Gonçalo Correia 2012/13 - Joana Rebelo (Mestrado em Matemática) 2015/16 - António Goucha (Mestrado em Matemática) 2015/16 - Manuel Nhangumbe (Mestrado em Matemática) co-advised by Ercília Sousa 2016/17 - Maria Carolina Rasquinho (Mestrado em Métodos Quantitativos em Finanças) 2016/17 - Dulce Silva - (Mestrado em Matemática) co-advised by Ercília Sousa 2018/19 - Inês Ferrão (Mestrado em Matemática) 2020/21 – Nuno Lacximicant (Mestrado em Matemática) 2021/22 – Ana Maria Cruz (Mestrado em Matemática) 2022/23 – Inês Silva (Mestrado em Matemática) 2022/23 – Rúben Gregório (Mestrado em Matemática) Undergraduate Research Scholarships: 2011/12 – Vasco Mota (Novos Talentos da Matemática) 2012/13 – António Goucha (Novos Talentos da Matemática) 2012/13 – Xavier Fernandes (Projecto MobiOS) 2013/14 – Sagar Pratapsi (Novos Talentos da Matemática) 2015/16 – Pedro Silva (Novos Talentos da Matemática) 2015/16 – Carla Jesus (Projeto AdditiveMilling) co-advised by Ercília Sousa 2016/17 – José Diogo Simão - (Novos Talentos da Matemática) 2017/18 – Christopher Gadzinski (Novos Talentos da Matemática) 2019/20 – Pedro Barata de Tovar (Novos Talentos da Matemática) 2019/20 - Marco Frieden (Projeto Mobiwise) 2020/21 - Christopher Gadzinski (Projeto Mobiwise) 2021/22 - Pilar Branquinho (Verão com Ciência 2021) 2021/22 - Sérgio Dias (Verão com Ciência 2021) 2021/22 – Manuel Almeida (Bolsa de Iniciação Científica) Activities I am an organizer of Projecto Delfos, a school for talented young people.