João Gouveia Departamento de Matemática Faculdade de Ciências e Tecnologia da Universidade de Coimbra 3001-454 Coimbra, Portugal E-mail: jgouveia@mat.uc.pt
Research	Talks	Teaching	Students		Activities
Research & Papers
Published and accepted papers: 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 (in press) 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 phaseless rank of a matrix” with António Goucha 2- “On sums of squares of k-nomials” with Alexander Kovacec and Mina Saee 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 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 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 2011/12 – Vasco Mota (Novos Talentos da Matemática) 2012/13 – António Goucha (Novos Talentos da Matemática) Joana Cavadas (Mestrado em Matemática) co-advised by Gonçalo Correia Joana Rebelo (Mestrado em Matemática) Xavier Fernandes (Projecto MobiOS) 2013/14 – Sagar Pratapsi (Novos Talentos da Matemática) 2015/16 – António Goucha (Mestrado em Matemática) Pedro Silva (Novos Talentos da Matemática) Mina Saee (Seminário do Programa de Doutoramento) Maria Carolina Rasquinho (Mestrado em Métodos Quantitativos em Finanças) Carla Jesus (Projeto AdditiveMilling) co-advised by Ercília Sousa Manuel Nhangumbe (Mestrado em Matemática) co-advised by Ercília Sousa 2016/17 – António Goucha (Seminário do Programa de Doutoramento) Maria Carolina Rasquinho (Mestrado em Métodos Quantitativos em Finanças) Mina Saee (Programa de Doutoramento) Manuel Nhangumbe - (Mestrado em Matemática) co-advised by Ercília Sousa Dulce Silva - (Mestrado em Matemática) co-advised by Ercília Sousa José Diogo Simão - (Novos Talentos da Matemática) 2017/18 – António Goucha (Programa de Doutoramento) Christopher Gadzinski (Novos Talentos da Matemática) Mina Saee (Programa de Doutoramento) 2018/19 – Juan Camilo Chaves (Visiting PhD student from Universidad de los Andes) Inês Ferrão (Mestrado em Matemática) António Goucha (Programa de Doutoramento) Mina Saee (Programa de Doutoramento) 2019/20 – António Goucha (Programa de Doutoramento) Pedro Barata de Tovar (Novos Talentos da Matemática) Activities I am an organizer of Projecto Delfos, a school for talented young people. I am part of the program committee of Optimization 2020 Starting in March 2020 I’ll be part of the direction of Centro Internacional de Matemática