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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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Identification

Personal identification

Full name
Eliana Maria Duarte Gelvez

Citation names

  • Gelvez, Eliana
  • Duarte, Eliana

Author identifiers

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

Email addresses

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

Telephones

Mobile phone
  • (+351) 939479102 (Personal)

Addresses

  • Rua São Miguel 4, 3040-555, Antanhol, Coimbra, Portugal (Personal)

Websites

Knowledge fields

  • Exact Sciences - Mathematics - Pure Mathematics
  • Exact Sciences - Mathematics - Pure Mathematics
  • Exact Sciences - Mathematics - Statistics and Probability

Languages

Language Speaking Reading Writing Listening Peer-review
Spanish; Castilian (Mother tongue)
English Proficiency (C2) Proficiency (C2) Proficiency (C2) Proficiency (C2) Proficiency (C2)
French Upper intermediate (B2) Upper intermediate (B2) Intermediate (B1) Advanced (C1) Elementary (A2)
German Intermediate (B1) Intermediate (B1) Intermediate (B1) Intermediate (B1) Intermediate (B1)
Portuguese Upper intermediate (B2) Advanced (C1) Upper intermediate (B2) Upper intermediate (B2) Upper intermediate (B2)
Education
Degree Classification
2011/08/08 - 2017/05/13
Concluded
 Mathematics (Doctor of Philosophy)
Major in Mathematics
University of Illinois at Urbana-Champaign Department of Mathematics, United States
"Syzygies and Implicitization of Tensor Product Surfaces" (THESIS/DISSERTATION)
2009/08/06 - 2011/05/12
Concluded
 Master of Arts in Mathematics (Master)
Major in Mathematics
Binghamton University, United States
2004/08/08 - 2009/05/12
Concluded
 Bachelor in Mathematics (Bachelor)
Major in Mathematics
Universidad de los Andes, Colombia
"Ext in the category of abelian groups" (THESIS/DISSERTATION)
Affiliation

Science

Category
Host institution 		Employer
2019/03/01 - 2019/12/31 Visiting Researcher (Research) Max-Planck-Institut für Mathematik in den Naturwissenschaften, Germany
Max-Planck-Institut für Mathematik in den Naturwissenschaften, Germany
2016/05/15 - 2016/07/10 Research Assistant (Research) Wolfram Research Inc, United States
Wolfram Research Inc, United States

Teaching in Higher Education

Category
Host institution 		Employer
2023/05/15 - Current Assistant Professor (University Teacher) Universidade do Porto, Portugal
Universidade do Porto Faculdade de Ciências, Portugal

Positions / Appointments

Category
Host institution 		Employer
2017/12/01 - 2021/09/30 Postdoctoral Researcher Otto-von-Guericke Universit ¨at Magdeburg Fakultät für Mathematik, Germany
Otto-von-Guericke Universit ¨at Magdeburg Fakultät für Mathematik, Germany
Outputs

Publications

Book chapter
  1. Eliana Duarte; Benjamin Hollering; Maximilian Wiesmann. "Toric Fiber Products in Geometric Modeling". 2023.
    10.1007/978-3-031-38271-0_49
Conference paper
  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". Paper presented in Proceedings of the First Conference Transformables 2013.In the Honor of Emilio Perez Piñero, Seville, 2013.
    Published
Journal article
  1. Eliana Duarte; Dmitrii Pavlov; Maximilian Wiesmann. "Algebraic geometry of quantum graphical models". Advances in Applied Mathematics (2025): https://doi.org/10.1016/j.aam.2025.102930.
    10.1016/j.aam.2025.102930
  2. Alexandr, Y; Duarte, E; Vill, J. "Decomposable Context-Specific Models". SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY (2024): https://www.authenticus.pt/P-010-JKW.
    10.1137/23m1575111
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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.
    Published • 10.1016/j.jsc.2019.04.001
  8. 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
  9. 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
  10. 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

Other

Other output
  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.
Activities

Oral presentation

Presentation title Event name
Host (Event location)
2019/12/03 Staged trees and polytopes Einstein Workshop on Polytopes and Algebraic Geometry
Freie Universität Berlin (Leipzig, Germany)
2019/11/25 Gröbner Bases for Staged Trees Graphical Models: Conditional Independence and Algebraic Structures
Technical University Munich (Garching, Germany)
2019/08/22 Elimination via virtual resolutions Algebraic Spline Geometry Meeting
Swansea University (Swansea, United Kingdom)
2019/07/13 Virtual resolutions for implicitization of surfaces SIAM Conference on Applied Algebraic Geometry
University of Bern (Bern, Switzerland)
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, Germany)
2019/02/26 Residual resultants and virtual resolutions Non-linear algebra seminar
Max-Planck-Institute for Mathematics in the Sciences (Leipzig, Germany)
2019/02/05 Toric staged tree models Optimality in Algebraic Statistics
Technische Universität Dortmund (Dortmund, Germany)
2018/11/04 Residual resultants for biprojective spaces Commutative Algebra Seminar
University of Nebraska Lincoln (Lincoln, United States)
2018/10/19 Bigraded regularity for elimination theory Seminar in nonlinear algebra
ICERM (Providence, United States)
2018/06/08 Defining equations of staged tree models SIAM Annual Meeting
Algebraic Statistics Minisymposia (Portland, United States)
2018/06/06 Hidden variables Graphical Models: From Mathematical Foundations to Biological Applications
ETH Zurich (Basel, Switzerland)
2018/05/27 Mixture models and hidden variables Algebraic Statistics in Berlin
Max-Planck-Gesellschaft Gagungsst ¨atte Harnack Haus (Berlin, Germany)
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, Germany)
2017/11/29 Combinatorial equations for staged trees Algebraic Methods in Statistics
Universität Osnabrück (Osnabrück, Germany)
2017/08/14 Implicit equations of tensor product surfaces with basepoints SIAM conference in applied algebraic geometry
Georgia Institute of Technology (Atlanta, United States)
2017/01/14 Syzygies and tensor product surfaces AROMATH seminar
INRIA Sophia Antipolis (Nice, France)
2016/08/13 Tensor product surfaces with basepoints Banff International Research Station, Computational Algebraic Geometry and Geometric Modelling
Casa Matematica Oaxaca (Oaxaca, Mexico)
2016/01/06 Linear syzygies and tensor product surfaces Joint Math Meetings - Special session on commutative algebra
American Mathematical Society (Seattle, United States)

Supervision

Thesis Title
Role 		Degree Subject (Type)
Institution / Organization
2021/12/01 - 2024/08/05 Nonlinear Algebra in Likelihood, Neurocomputing and Quantum Physics
Co-supervisor
 Mathematics (PhD)
Max-Planck-Institut für Mathematik in den Naturwissenschaften, Germany

Event organisation

Event name
Type of event (Role) 		Institution / Organization
2016/08/24 - Current Founder and organizer of the Graduate Student Colloquium in the Mathematics Department at University of Illinois Urbana - Champaign (2016/08/24)
Seminar (President of the Organising Committee)
 University of Illinois at Urbana-Champaign, United States
2015/08/16 - Current Organizer for the event Girls Engaged in Math and Science, outreach activity for middle school girls. (2015/08/16)
Other (Member of the Organising Committee)
 University of Illinois at Urbana-Champaign, United States
2020/03/30 - 2020/04/03 Spring School in Mathematical Statistics (2020/03/30)
Workshop (Member of the Scientific Committee)
 Max-Planck-Institut für Mathematik in den Naturwissenschaften, Germany
2018/11/26 - 2018/11/27 Complexity Reduction in Algebraic Statistics. (2018/11/26)
Conference (Member of the Organising Committee)
 Otto-von-Guericke Universitat Magdeburg Fakultat fur Mathematik, Germany
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)
Workshop (Member of the Organising Committee)
 Max-Planck-Institut für Mathematik in den Naturwissenschaften, Germany
2017/04 - 2017/07/05 Non-linear Algebra Seminar at MPI-MIS (2017/04/01)
Seminar (Member of the Organising Committee)
 Max-Planck-Institut für Mathematik in den Naturwissenschaften, Germany

Event participation

Activity description
Type of event 		Event name
Institution / Organization
2020/03/15 - 2020/03/20 Meeting for scientific interchange in the community of Algebraic Statistics.
Workshop
 Algebraic structures in statistical methodology
Mathematisches Forschungsinstitut Oberwolfach, Germany
2018/08/04 - 2018/11/10 Semester on nonlinear algebra
Other
 Semester on nonlinear algebra
he Institute for Computational and Experimental Research in Mathematics, United States
2017/04/18 - 2017/04/23 Meeting for scientific interchange in algebraic statistics.
Workshop
 Workshop on Algebraic Statistics
Mathematisches Forschungsinstitut Oberwolfach, Germany

Association member

Society Organization name Role
2016/08/27 - 2017/05/13 President of the Association for Women in Math Student Chapter at University of Illinois Urbana-Champaign President

Committee member

Activity description
Role 		Institution / Organization
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
Member
 Max-Planck-Institut für Mathematik in den Naturwissenschaften, Germany
2016/04/03 - 2016/10/01 Member of the Graduate Affairs committee at the Mathematics Department in University of Illinois Urbana-Champaign
Member
 University of Illinois at Urbana-Champaign, United States

Course / Discipline taught

Academic session Degree Subject (Type) Institution / Organization
2019/10/20 - 2019/12/02 Seven Lectures in Algebraic Statistics (Doctor) Max-Planck-Institut für Mathematik in den Naturwissenschaften, Germany
2018/04/01 - 2018/07/04 Undergraduate seminar in Algebra and Geometry (Bachelor) Otto-von-Guericke Universit ¨at Magdeburg Fakultät für Mathematik, Germany
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, United States

Interview (tv / radio show)

Program Topic
2018/06/07 - 2018/06/07 Modellansatz Podcast Algebraic Geometry and Computer Graphics

Mentoring / Tutoring

Topic Student name
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
Distinctions

Award

2018 2018 AWM Student Chapter Award for Community Outreach
Association for Women in Mathematics, United States

Other distinction

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