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I completed my PhD in 2017 from University of Illinois at Urbana-Champaing(UIUC). The area of my thesis was commutative algebra, more specifically the study of syzygies to do implicitization of parameterized surfaces. In parallel I also worked at the Illinois Geometry Lab on the rigidity problem for 2D and 3D quasicrystal frameworks. Although my mathematical training was initially oriented to pure mathematics, the problems I considered were inspired by concrete applications and computations. During Summer 2016 I did an internship at Wolfram Research where I worked on algorithms to find greatest common divisors of polynomials in several variables for the software Mathematica. Immediately after completing my PhD, I moved to Germany and held postdoctoral positions in the Nonlinear Algebra group at Max Planck Institute for Mathematics in the Sciences (MPI-MIS) in Leipzig, Germany, and the research training group Mathematical Complexity Reduction at Otto Von Guericke Universität Magdeburg. At this time I made a shift in my research area and started working on solving problems in statistics by using the commutative algebra tools that I learned during my PhD. The areas in statistics that I currently do research on are causal inference, probabilistic graphical models and maximum likelihood estimation. In 2021 I won a grant for individual scientific employment awarded by the FCT with the title "Algebraic Geometry with A View Towards Applications" and moved to the Universidade do Porto. During this time I started teaching Statistical Inference of Masters students which involved explaining introductory theory and supervising students projects. At the beginning of 2023 I returned to MPI-MIS in Leipzig, Germany to lead my own research group named "Statistical Data Analysis in the Algebraic Geometry Age". Finally in May 2023 I started as an Assistant Professor of Probability and Statistics at Universidade do Porto.
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Identificação

Identificação pessoal

Nome completo
Eliana Maria Duarte Gelvez

Nomes de citação

  • Gelvez, Eliana
  • Duarte, Eliana

Identificadores de autor

Ciência ID
001B-4A2F-9684
ORCID iD
0000-0002-0742-4151

Endereços de correio eletrónico

  • duarte@mis.mpg.de (Profissional)
  • Eliana.gelvez@fc.up.pt (Profissional)

Telefones

Telemóvel
  • (+351) 939479102 (Pessoal)

Moradas

  • Rua da Columbofilia, Bloco 1, 2 esqu, 4905-353, Barroselas, Viana do Castelo, Portugal (Pessoal)

Websites

Domínios de atuação

  • Ciências Exatas - Matemática - Matemática Pura
  • Ciências Exatas - Matemática - Matemática Pura
  • Ciências Exatas - Matemática - Estatística e Probabilidades

Idiomas

Idioma Conversação Leitura Escrita Compreensão Peer-review
Espanhol; Castelhano (Idioma materno)
Inglês Utilizador proficiente (C2) Utilizador proficiente (C2) Utilizador proficiente (C2) Utilizador proficiente (C2) Utilizador proficiente (C2)
Francês Utilizador independente (B2) Utilizador independente (B2) Utilizador independente (B1) Utilizador proficiente (C1) Utilizador elementar (A2)
Alemão Utilizador independente (B1) Utilizador independente (B1) Utilizador independente (B1) Utilizador independente (B1) Utilizador independente (B1)
Português Utilizador independente (B2) Utilizador proficiente (C1) Utilizador independente (B2) Utilizador independente (B2) Utilizador independente (B2)
Formação
Grau Classificação
2011/08/08 - 2017/05/13
Concluído
 Mathematics (Doctor of Philosophy)
Especialização em Mathematics
University of Illinois at Urbana-Champaign Department of Mathematics, Estados Unidos
"Syzygies and Implicitization of Tensor Product Surfaces" (TESE/DISSERTAÇÃO)
2009/08/06 - 2011/05/12
Concluído
 Master of Arts in Mathematics (Master)
Especialização em Mathematics
Binghamton University, Estados Unidos
2004/08/08 - 2009/05/12
Concluído
 Bachelor in Mathematics (Bachelor)
Especialização em Mathematics
Universidad de los Andes, Colômbia
"Ext in the category of abelian groups" (TESE/DISSERTAÇÃO)
Percurso profissional

Ciência

Categoria Profissional
Instituição de acolhimento 		Empregador
2019/03/01 - 2019/12/31 Investigador visitante (Investigação) Max-Planck-Institut für Mathematik in den Naturwissenschaften, Alemanha
Max-Planck-Institut für Mathematik in den Naturwissenschaften, Alemanha
2016/05/15 - 2016/07/10 Assistente de Investigação (carreira) (Investigação) Wolfram Research Inc, Estados Unidos
Wolfram Research Inc, Estados Unidos

Docência no Ensino Superior

Categoria Profissional
Instituição de acolhimento 		Empregador
2023/05/15 - Atual Professor Auxiliar (Docente Universitário) Universidade do Porto, Portugal
Universidade do Porto Faculdade de Ciências, Portugal

Cargos e Funções

Categoria Profissional
Instituição de acolhimento 		Empregador
2017/12/01 - 2021/09/30 Postdoctoral Researcher Otto-von-Guericke Universit ¨at Magdeburg Fakultät für Mathematik, Alemanha
Otto-von-Guericke Universit ¨at Magdeburg Fakultät für Mathematik, Alemanha
Produções

Publicações

Artigo em conferência
  1. Duarte, Eliana (001B-4A2F-9684); Lichtblau, Daniel. "Polynomial GCDs by Syzygies". 2016.
    10.1109/synasc.2016.021
  2. Duarte, Eliana (001B-4A2F-9684). "Stability of Quasicrystal frameworks in 2D and 3D". Trabalho apresentado em Proceedings of the First Conference Transformables 2013.In the Honor of Emilio Perez Piñero, Seville, 2013.
    Publicado
Artigo em revista
  1. Daniele Tramontano; L. Waldmann; M. Drton; Eliana Duarte. "Learning Linear Gaussian Polytree Models With Interventions". IEEE Journal on Selected Areas in Information Theory (2023): https://doi.org/10.1109/JSAIT.2023.3328429.
    10.1109/JSAIT.2023.3328429
  2. Eliana Duarte; Liam Solus. "A new characterization of discrete decomposable graphical models". Proceedings of the American Mathematical Society 151 3 (2022): 1325-1338. http://dx.doi.org/10.1090/proc/16212.
    10.1090/proc/16212
  3. Guerra, C.A.; Delgado-Baquerizo, M.; Duarte, E.; Marigliano, O.; Görgen, C.; Maestre, F.T.; Eisenhauer, N.. "Global projections of the soil microbiome in the Anthropocene". Global Ecology and Biogeography 30 5 (2021): 987-999. http://www.scopus.com/inward/record.url?eid=2-s2.0-85101251364&partnerID=MN8TOARS.
    10.1111/geb.13273
  4. Duarte, E.; Marigliano, O.; Sturmfels, B.. "Discrete statistical models with rational maximum likelihood estimator". Bernoulli 27 1 (2021): 135-154. http://www.scopus.com/inward/record.url?eid=2-s2.0-85097449378&partnerID=MN8TOARS.
    10.3150/20-BEJ1231
  5. Duarte, Eliana; Görgen, Christiane. "Equations defining probability tree models". Journal of Symbolic Computation 99 (2020): 127-146. http://dx.doi.org/10.1016/j.jsc.2019.04.001.
    Publicado • 10.1016/j.jsc.2019.04.001
  6. Duarte, E.; Seceleanu, A.. "Implicitization of tensor product surfaces via virtual projective resolutions". Mathematics of Computation 89 326 (2020): 3023-3056. http://www.scopus.com/inward/record.url?eid=2-s2.0-85090191108&partnerID=MN8TOARS.
    10.1090/MCOM/3548
  7. Duarte, Eliana. "Implicitization of tensor product surfaces in the presence of a generic set of basepoints". Journal of Algebra and Its Applications 16 10 (2017): 1750189. http://dx.doi.org/10.1142/s0219498817501894.
    10.1142/s0219498817501894
  8. Duarte, Eliana; Schenck, Hal. "Tensor product surfaces and linear syzygies". Proceedings of the American Mathematical Society 144 1 (2015): 65-72. http://dx.doi.org/10.1090/proc/12703.
    10.1090/proc/12703
Capítulo de livro
  1. Eliana Duarte; Benjamin Hollering; Maximilian Wiesmann. "Toric Fiber Products in Geometric Modeling". 2023.
    10.1007/978-3-031-38271-0_49

Outros

Outra produção
  1. ALGEBRAIC GEOMETRY OF QUANTUM GRAPHICAL MODELS. 2023. Duarte, E.; Pavlov, D.; Wiesmann, M.. http://www.scopus.com/inward/record.url?eid=2-s2.0-85170493639&partnerID=MN8TOARS.
    10.48550/arXiv.2308.11538
  2. DECOMPOSABLE CONTEXT-SPECIFIC MODELS. 2022. Alexandr, Y.; Duarte, E.; Vill, J.. http://www.scopus.com/inward/record.url?eid=2-s2.0-85163761220&partnerID=MN8TOARS.
  3. REPRESENTATION OF CONTEXT-SPECIFIC CAUSAL MODELS WITH OBSERVATIONAL AND INTERVENTIONAL DATA. 2021. Duarte, E.; Solus, L.. http://www.scopus.com/inward/record.url?eid=2-s2.0-85170888905&partnerID=MN8TOARS.
    10.48550/arxiv.2101.09271
  4. Families of polytopes with rational linear precision in higher dimensions. 2021. Davies, I.; Duarte, E.; Portakal, I.; Sorea, M.-S.. http://www.scopus.com/inward/record.url?eid=2-s2.0-85135743167&partnerID=MN8TOARS.
    10.48550/arXiv.2109.08151
  5. Global projections of the soil microbiome in the anthropocene. Manuscript submited to Nature Communications.. 2020. Duarte, Eliana; Guerra, Carlos; Delgado Baquerizo, Manuel; Marigliano, Orlando; Eisenhauer, Nico; Maestre, Fernando.
  6. ALGEBRAIC GEOMETRY OF DISCRETE INTERVENTIONAL MODELS. 2020. Duarte, E.; Solus, L.. http://www.scopus.com/inward/record.url?eid=2-s2.0-85170609300&partnerID=MN8TOARS.
    10.48550/arXiv.2012.03593
  7. Gröbner bases for staged trees. Submitted to Journal of Algebraic Statistics. Currently under revision.. 2019. Gelvez, Eliana. https://arxiv.org/pdf/1910.02721.pdf.
  8. Implicitization of tensor product surfaces via virtual projective resolutions. Submitted to Mathematics of Computation. Second revision.. 2019. Duarte, Eliana. https://arxiv.org/abs/1908.02086.
  9. Discrete statistical models with rational maximum likelihood estimator. Submitted to Bernoulli. Second revision.. 2019. Duarte, Eliana; Marigliano, Orlando; Sturmfels, Bernd. https://arxiv.org/abs/1903.06110.
Atividades

Apresentação oral de trabalho

Título da apresentação Nome do evento
Anfitrião (Local do evento)
2019/12/03 Staged trees and polytopes Einstein Workshop on Polytopes and Algebraic Geometry
Freie Universität Berlin (Leipzig, Alemanha)
2019/11/25 Gröbner Bases for Staged Trees Graphical Models: Conditional Independence and Algebraic Structures
Technical University Munich (Garching, Alemanha)
2019/08/22 Elimination via virtual resolutions Algebraic Spline Geometry Meeting
Swansea University (Swansea, Reino Unido)
2019/07/13 Virtual resolutions for implicitization of surfaces SIAM Conference on Applied Algebraic Geometry
University of Bern (Bern, Suiça)
2019/03/27 Discrete Statistical Models with Rational Maximum Likelihood Estimator Deep Learning Theory Kick- off Meeting
Max-Planck-Institute for Mathematics in the Sciences (Leipzig, Alemanha)
2019/02/26 Residual resultants and virtual resolutions Non-linear algebra seminar
Max-Planck-Institute for Mathematics in the Sciences (Leipzig, Alemanha)
2019/02/05 Toric staged tree models Optimality in Algebraic Statistics
Technische Universität Dortmund (Dortmund, Alemanha)
2018/11/04 Residual resultants for biprojective spaces Commutative Algebra Seminar
University of Nebraska Lincoln (Lincoln, Estados Unidos)
2018/10/19 Bigraded regularity for elimination theory Seminar in nonlinear algebra
ICERM (Providence, Estados Unidos)
2018/06/08 Defining equations of staged tree models SIAM Annual Meeting
Algebraic Statistics Minisymposia (Portland, Estados Unidos)
2018/06/06 Hidden variables Graphical Models: From Mathematical Foundations to Biological Applications
ETH Zurich (Basel, Suiça)
2018/05/27 Mixture models and hidden variables Algebraic Statistics in Berlin
Max-Planck-Gesellschaft Gagungsst ¨atte Harnack Haus (Berlin, Alemanha)
2018/05/18 What is Algebraic Statistics? Scientific Advisory Board meeting Max-Planck- Institute for Mathematics in the Sciences
Max-Planck-Institute for Mathematics in the Sciences (Leipzig, Alemanha)
2017/11/29 Combinatorial equations for staged trees Algebraic Methods in Statistics
Universität Osnabrück (Osnabrück, Alemanha)
2017/08/14 Implicit equations of tensor product surfaces with basepoints SIAM conference in applied algebraic geometry
Georgia Institute of Technology (Atlanta, Estados Unidos)
2017/01/14 Syzygies and tensor product surfaces AROMATH seminar
INRIA Sophia Antipolis (Nice, França)
2016/08/13 Tensor product surfaces with basepoints Banff International Research Station, Computational Algebraic Geometry and Geometric Modelling
Casa Matematica Oaxaca (Oaxaca, México)
2016/01/06 Linear syzygies and tensor product surfaces Joint Math Meetings - Special session on commutative algebra
American Mathematical Society (Seattle, Estados Unidos)

Organização de evento

Nome do evento
Tipo de evento (Tipo de participação) 		Instituição / Organização
2016/08/24 - Atual Founder and organizer of the Graduate Student Colloquium in the Mathematics Department at University of Illinois Urbana - Champaign (2016/08/24)
Seminário (Presidente da Comissão Organizadora)
 University of Illinois at Urbana-Champaign, Estados Unidos
2015/08/16 - Atual Organizer for the event Girls Engaged in Math and Science, outreach activity for middle school girls. (2015/08/16)
Outro (Membro da Comissão Organizadora)
 University of Illinois at Urbana-Champaign, Estados Unidos
2020/03/30 - 2020/04/03 Spring School in Mathematical Statistics (2020/03/30)
Oficina (workshop) (Membro da Comissão Científica)
 Max-Planck-Institut für Mathematik in den Naturwissenschaften, Alemanha
2018/11/26 - 2018/11/27 Complexity Reduction in Algebraic Statistics. (2018/11/26)
Conferência (Membro da Comissão Organizadora)
 Otto-von-Guericke Universitat Magdeburg Fakultat fur Mathematik, Alemanha
2018/06/04 - 2018/06/08 Macaulay 2 Workshop - The purpose of the workshop is to bring the Macaulay 2 developers Dan Grayson and Mike Stillman together with those who would like to share or to develop their skills on Macaulay 2. (2018/06/04)
Oficina (workshop) (Membro da Comissão Organizadora)
 Max-Planck-Institut für Mathematik in den Naturwissenschaften, Alemanha
2017/04 - 2017/07/05 Non-linear Algebra Seminar at MPI-MIS (2017/04/01)
Seminário (Membro da Comissão Organizadora)
 Max-Planck-Institut für Mathematik in den Naturwissenschaften, Alemanha

Participação em evento

Descrição da atividade
Tipo de evento 		Nome do evento
Instituição / Organização
2020/03/15 - 2020/03/20 Meeting for scientific interchange in the community of Algebraic Statistics.
Oficina (workshop)
 Algebraic structures in statistical methodology
Mathematisches Forschungsinstitut Oberwolfach, Alemanha
2018/08/04 - 2018/11/10 Semester on nonlinear algebra
Outro
 Semester on nonlinear algebra
he Institute for Computational and Experimental Research in Mathematics, Estados Unidos
2017/04/18 - 2017/04/23 Meeting for scientific interchange in algebraic statistics.
Oficina (workshop)
 Workshop on Algebraic Statistics
Mathematisches Forschungsinstitut Oberwolfach, Alemanha

Curso / Disciplina lecionado

Disciplina Curso (Tipo) Instituição / Organização
2019/10/20 - 2019/12/02 Seven Lectures in Algebraic Statistics (Doctor) Max-Planck-Institut für Mathematik in den Naturwissenschaften, Alemanha
2018/04/01 - 2018/07/04 Undergraduate seminar in Algebra and Geometry (Bachelor) Otto-von-Guericke Universit ¨at Magdeburg Fakultät für Mathematik, Alemanha
2011/08/06 - 2016/11/10 Teaching assistant for courses in: -Theory of arithmetic for elementary school Teachers -Differential Calculus -Integral Calculus -Vector Calculus (Bachelor) University of Illinois at Urbana-Champaign, Estados Unidos

Entrevista / Programa (rádio / tv)

Programa Tema
2018/06/07 - 2018/06/07 Modellansatz Podcast Algebraic Geometry and Computer Graphics

Membro de associação

Nome da associação Tipo de participação
2016/08/27 - 2017/05/13 President of the Association for Women in Math Student Chapter at University of Illinois Urbana-Champaign President

Membro de comissão

Descrição da atividade
Tipo de participação 		Instituição / Organização
2019/08/01 - 2019/12/15 Member of the postdoctoral hiring committee for the Nonlinear Algebra group at Max-Planck-Institute for Mathematics in the Sciences
Membro
 Max-Planck-Institut für Mathematik in den Naturwissenschaften, Alemanha
2016/04/03 - 2016/10/01 Member of the Graduate Affairs committee at the Mathematics Department in University of Illinois Urbana-Champaign
Membro
 University of Illinois at Urbana-Champaign, Estados Unidos

Tutoria

Tópico Nome do aluno
2018/08/20 - 2019/10/31 Mentoring of PhD student at Max-Planck-Institute for Mathematics in the Sciences Orlando Marigliano
2018/06/01 - 2019/06/01 Mentoring of PhD student in Algebraic Statistics Lamprini Ananiadi
2013/02/22 - 2016/05/18 Rigidity of 2D and 3D frameworks Mentored 9 students during three semesters
Distinções

Prémio

2018 2018 AWM Student Chapter Award for Community Outreach
Association for Women in Mathematics, Estados Unidos

Outra distinção

2016 Recipient of the Mathematics Department Fellowship
University of Illinois at Urbana-Champaign, Estados Unidos
2016 List of Teachers Ranked as Excellet Spring 2016
University of Illinois at Urbana-Champaign, Estados Unidos