João Gouveia

Departamento de Matemática

Faculdade de Ciências e Tecnologia da Universidade de Coimbra

3001-454 Coimbra, Portugal











Please check the Summer school of our joint Math PhD program with University of Porto, taking place in Coimbra in September. Special attention to the week of September 5-9 where we will have a course on polynomial optimization by Rekha Thomas. Complete schedule and registrations available here.


Research & Papers


Published and accepted papers:

18- “Four Dimensional Polytopes of Minimum Positive Semidefinite Rank” with Kanstanstin Pashkovich, Richard Z. Robinson and Rekha R. Thomas. Accepted in Journal of Combinatorial Theory, Series A (2016)

17- On-off scheduling schemes for power-constrained electric vehicle charging” with Xavier Fernandes, Joana Rebelo, Rodrigo Maia and Nuno Bustorff Silva. Accepted in 4OR-Q J Oper Res (2016). DOI:10.1007/s10288-016-0328-9

16- “Sums of Squares on the Hypercube” with Grigoriy Blekherman and James Pfeiffer. Accepted in Mathematische Zeitschrift (April 2016). DOI 10.1007/s00209-016-1644-7

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 Semide
finite 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- “On ranks of regular polygons”, with António Pedro Goucha and Pedro M. Silva. CMUC preprint 16-35.


Published Non-Research Papers (in Portuguese)

3-   “Representações mínimas de polítopos” com Richard Z. Robinson e Rekha R. Thomas a aparecer 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, 2004



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” – 4th SDP days in CWI - slides

September’ 12 – “Conic lifts of polytopes” – MAP 2012 in Konstanz - slides

August’ 12 – “Semidefinite lifts of polytopes” – 21st 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” – 2nd 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” - 20th 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



           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.



           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



           I’m part of the Portuguese Mathematics Olympiad problem commission.

           I’m a collaborator of Projecto Delfos, a school for talented young people.