

João
Gouveia Faculdade de Ciências e
Tecnologia da Universidade de Coimbra 3001454 Coimbra, Portugal Email: jgouveia@mat.uc.pt 


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 59 we had a course on polynomial
optimization by Rekha Thomas. Course page available here. Research & Papers 

Published and accepted papers: 18 “FourDimensional 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 Onoff
scheduling schemes for powerconstrained electric vehicle charging” with
Xavier Fernandes, Joana Rebelo,
Rodrigo Maia and Nuno Bustorff
Silva. Accepted in 4ORQ J Oper Res (2016).
DOI:10.1007/s1028801603289 16 “Sums of Squares on the Hypercube”
with Grigoriy Blekherman
and James Pfeiffer. Accepted in Mathematische Zeitschrift (April 2016). DOI 10.1007/s0020901616447 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 133137 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 613637 12 “WorstCase 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 201212 11 “A
MIP model for locating slowcharging 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) 29212933. 8 “Polytopes of minimum positive semidefinite rank” with Richard Z. Robinson and Rekha
Thomas, Discrete and Computational Geometry (Vol.50, Issue 3, 2013) pp.
679699. 7 “Spectrahedral
Approximations of Convex hulls of Algebraic Sets” with Rekha Thomas, chapter in Semide 6 “Lifts of convex sets and cone factorizations” with Pablo Parrilo and Rekha Thomas,
Mathematics of Operations Research (Vol. 38, No.2, 2013) pp. 248264. 5 “Comparing SOS and SDP relaxations
of sensor network localization” with Ting Kei Pong Computational
Optimization & Applications 52, 2012, pp. 609627. [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 12, 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
JeanBernard 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 1635. Published NonResearch 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 “Nãonegatividade, 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 Talks 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 – “Psdminimality
and slack ideals” – SIAM meeting on Applied Algebraic Geometry (AG15) in Daejeon, South
Korea July’ 15 – “Psdminimality
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 highschool 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”.
SIAMOPT 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 MaxCut problem”  INFORMS meeting in San
Diego August'
09  “A new SDP approach to the MaxCut 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 MaxCut 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) coadvised 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) coadvised by Ercília Sousa Manuel Nhangumbe 
(Mestrado em Matemática) coadvised by Ercília Sousa Activities I’m
part of the Portuguese Mathematics Olympiad problem commission. I’m
a collaborator of Projecto Delfos, a school for talented young people. 


