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:

28- “General non-realizability certificates for spheres with linear programmingwith 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, 1-38 (2022)

26- “Lifting for Simplicity: Concise Descriptions of Convex Sets” with Hamza Fawzi, Pablo Parrilo, James Saunderson and Rekha Thomas to appear in SIAM Review

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- “Quantum marginal, faces and coatoms” with Stephan Weis

2-     Complex psd-minimal polytopes in dimensions two and three” with Tristram Bogart and  Juan Camilo Torres

 

3-     The phase rank of a matrix” with António Goucha

 

4-     Self-dual polyhedral cones and their slack matrices” with 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

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 1Problem SetSketch 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” – 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

 

Teaching

           2ºSemestre 2020/21 – Matemática Discreta – Lic. Matemática     

           2ºSemestre 2020/21 – 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] - coadvised with Tristram Bogart

          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)

           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.

           I am part of the direction of Centro Internacional de Matemática