João Gouveia

Departamento de Matemática

Faculdade de Ciências e Tecnologia da Universidade de Coimbra

3001-454 Coimbra, Portugal










News & Events

The first Summer school of our joint Math PhD program with University of Porto, took place in Coimbra in September 2016. In the week of September 5-9 we had a course on polynomial optimization by Rekha Thomas. Course page 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. 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. 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 – OptimizationJoint 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.