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Prof. Dr. Carlos Enrique Améndola Cerón
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Email: amendola (at) math.tu-berlin.de
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I am an assistant professor (tenure-track) of Algebraic and Geometric Methods in Data Analysis at the Institute of Mathematics of the Technical University of Berlin.
My main research interest is Algebraic Statistics. I am also very interested in developments concerning Applied Algebraic Geometry.
Previously I was part of the Nonlinear Algebra research group at the Max-Planck Institute for Mathematics in the Sciences. I was a postdoc at TU Munich in the research groups Mathematical Statistics led by Mathias Drton (formerly by Claudia Klüppelberg) and Optimization and Data Analysis led by Felix Krahmer. During the Winter Semester 2020/2021, I was substitute professor at the Institute of Stochastics of Ulm University.
I graduated as a Mathematics PhD student in Bernd Sturmfels' Einstein Fellowship research group in Nonlinear Algebra at TU Berlin. My co-advisor was Christian Haase.
I have a B.S. in Applied Mathematics from Instituto Tecnológico Autónomo de México and an additional B.S. in Mathematics degree from Universidad Nacional Autónoma de México .
I also obtained an M.S. in Mathematics from Courant Institute at New York University.
During 2020-2021, I helped organize the Algebraic Statistics Online Seminar (ASOS). I am an editor of the Algebraic Statistics (AStat) journal, check it out for the latest research and for submitting your own work.
From July 2021 - 2023, I was the Bernoulli Society Web editor. Before that, I was the e-Briefs editor.
In 2023, Eliana Duarte, Thomas Kahle, and I organized an Algebraic Statistics Seminar between Berlin, Leipzig and Magdeburg.
Publications and Preprints
Likelihood Geometry of Reflexive Polytopes (with J. Oldekop), submitted.
Decomposing Tensor Spaces via Path Signatures (with F. Galuppi, A. Ríos, P. Santarsiero and T. Seynnaeve), submitted.
Differential Equations for Gaussian Statistical Models with Rational Maximum Likelihood Estimator (with L. Gustafsson, K. Kohn, O. Marigliano and A. Seigal), submitted.
Convex Hulls of Curves: Volumes and Signatures (with D. Lee and C. Meroni),Geometric Science of Information (GSI'23) , (2019) 455-464.
Identifiability in Continuous Lyapunov Models (with P. Dettling, R. Homs, M. Drton and N. Hansen), SIAM Journal on Matrix Analysis and Applications, 44(4) (2023).
Third-Order Moment Varieties of Linear Non-Gaussian Graphical Models (with M. Drton, A. Grosdos, R. Homs and E. Robeva), Information and Inference, 12(3) (2023).
Estimating Gaussian Mixtures Using Sparse Polynomial Moment Systems (with J. Lindberg and J. Rodriguez), submitted.
Markov Equivalence of Max-Linear Bayesian Networks (with B. Hollering, S. Sullivant and N. Tran), Uncertainty in Artificial Intelligence, PLMR 161 (2021) 1746-1755.
An Invitation to Tropical Alexandrov Curvature (with A. Monod), Algebraic Statistics, to appear.
Computing Maximum Likelihood Estimates for Gaussian Graphical Models with Macaulay2 (with L. García Puente, R. Homs, O. Kuznetsova and H. Motwani), Journal of Software for Algebra and Geometry 12(1) (2022) 1-10.
Toric Invariant Theory for Maximum Likelihood Estimation in Log-linear Models (with K. Kohn, P. Reichenbach and A. Seigal), Algebraic Statistics 12(2) (2021) 187-211.
Likelihood Geometry of Correlation Models (with P. Zwiernik), Le Matematiche , 76(2) (2021) 559-583.
The Maximum Likelihood Degree of Linear Spaces of Symmetric Matrices (with L. Gustafsson, K. Kohn, O. Marigliano and A. Seigal), Le Matematiche , 76(2) (2021) 535-557.
Structure Learning for Cyclic Linear Causal Models (with P. Dettling, M. Drton, F. Onori and J. Wu), Uncertainty in Artificial Intelligence, UAI 2020.
Invariant Theory and Scaling Algorithms for Maximum Likelihood Estimation (with K. Kohn, P. Reichenbach and A. Seigal), SIAM Journal on Applied Algebra and Geometry , 5(2) (2021) 304-337.
Conditional Independence in Max-linear Bayesian Networks (with C. Klüppelberg, S. Lauritzen and N. Tran), Annals of Applied Probability, 31(1) (2022) 1-45.
Maximum Likelihood Estimation of Toric Fano Varieties (with D. Kosta and K. Kubjas), Algebraic Statistics 11(1) (2020) 5-30.
Moment Identifiability of Homoscedastic Gaussian Mixtures (with D. Agostini and K. Ranestad), Foundations of Computational Mathematics 21 (2021) 695-724.
Autocovariance Varieties of Moving Average Random Fields (with V.S. Pham), Journal of Symbolic Computation (2020), presented at MEGA 2019.
Tapas of Algebraic Statistics (with M. Casanellas and L. García Puente), Notices of the American Mathematical Society , Vol. 65, No. 8 (2018) 936-938.
Varieties of Signature Tensors (with P. Friz and B. Sturmfels), Forum of Mathematics, Sigma , 7 (2019) e10.
Discrete Gaussian Distributions via Theta Functions (with D. Agostini), SIAM Journal on Applied Algebra and Geometry , 3(1) (2019) 1-30.
Computing Tropical Varieties in Macaulay2 (with K. Kohn, S. Lamboglia, D. Maclagan, B. Smith, J. Sommars, P. Tripoli and M. Zajaczkowska), submitted.
Maximum Number of Modes of Gaussian Mixtures (with A. Engström and C. Haase), Information and Inference: A Journal of the IMA , 9(3) (2019) 587-600.
The Maximum Likelihood Degree of Toric Varieties (with N. Bliss, I. Burke, C. Gibbons, M. Helmer, S. Hoşten, E. Nash, J. Rodriguez and D. Smolkin), Journal of Symbolic Computation , 92 (2018) 222-242.
Solving Parameterized Polynomial Systems with Decomposable Projections (with J. Lindberg and J. Rodriguez), presented at MEGA 2017 Code
Algebraic Identifiability of Gaussian Mixtures (with K. Ranestad and B. Sturmfels), International Mathematics Research Notices , 21 (2018) 6556-6580.
Moment Varieties of Gaussian Mixtures (with J-C. Faugère and B. Sturmfels), Journal of Algebraic Statistics , 7 (2016) 14-28.
Maximum Likelihood Estimates for Gaussian Mixtures are Transcendental (with M. Drton and B. Sturmfels),
Mathematical Aspects of Computer and Information Sciences , (eds. I. Kotsireas, S. Rump and C. Yap), MACIS 2015, Berlin, (2016) 579-590.
PhD Thesis Algebraic Statistics of Gaussian Mixtures (2017). Advisor: Bernd Sturmfels , Christian Haase
Thesis Bases de Gröbner: una variedad de aplicaciones (Gröbner Bases: a variety of applications) (2013). Advisor: Dr. Leon Kushner Schnur
Thesis Una Introducción a la Estadística Algebraica (An Introduction to Algebraic Statistics) (2012). Advisor: Dra. Araceli Reyes Guerrero
Google Scholar
PhD Students
Janike Oldekop (2022-)
Kamillo Ferry (2023-)
Teaching
Summer Semester 2024:
Discrete Geometry I
Winter Semester 2023-2024:
Algebraic Statistics
Summer Semester 2023:
Discrete Geometry III
Winter Semester 2022/2023:
Discrete Geometry II
Winter Semester 2021/2022:
Fundamentals of Mathematical Statistics [MA5441]
Advanced Student Seminar: Algebraic Statistics
Summer Semester 2021:
Statistical Inverse Problems [MA5428]
Winter Semester 2020/2021:
Angewandte Stochastik II [MA6902]
Markov-Ketten [MA2019]
Graphical Models [MA2025]
Summer Semester 2020:
Statistik: Grundlagen [MA2402]
Winter Semester 2019/2020:
Fundamentals of Mathematical Statistics [MA5441]
Summer Semester 2019:
Reading Seminar: High-Dimensional Statistics
Winter Semester 2018/2019:
Probabilistic Methods and Algorithms in Data Analysis [MA4803]
Advanced Student Seminar: Algebraic Statistics
Summer Semester 2018:
Statistics for Business Administration (with Introduction to R) [MA9712]
Activities
May 5 - 10, 2024: 6th Meeting of Mexican Mathematicians in the World, Casa Matemática Oaxaca
April 10 - 13, 2024: Mathematics of data streams: signatures, neural differential equations, and difussion models, Greifswald
April 2 - 5, 2024: Heavy Tails in Machine Learning, Alan Turing Institute
March 18 - 23, 2024: Combinatorial Coworkspace, Kleinwalsertal
March 13 - 15, 2024: Mathematics, Data Science and Education, Hagen
March 11 - 13, 2024: Algebraic, analytic, geometric structures emerging from QFT, Chengdu
Feb 26 - March 8, 2024: CIMPA School on Algebra and Algebraic Geometry for Applications, Lahore / Karachi
Feb 12 - 16, 2024: Causality in Extremes, Geneva
Feb 1 - 2, 2024: European Workshop on Algebraic Statistics and Graphical Models, Garmisch-Partenkirchen
Jan 22 - 26, 2024: Applied and Computational Algebraic Geometry, Isaac Newton Institute
Dec 16 - 18, 2023: Computational and Methodological Statistics (CMStatistics 2023), HTW Berlin
Dec 1, 2023: Talk at Real Geometry and Algebra Seminar, University of Konstanz
Nov 2, 2023: Talk at Nonlinear Algebra Seminar, MPI-MiS Leipzig
Sept 18 - Oct 13, 2023: Algebraic Statistics and Our Changing World, IMSI Chicago
Aug 30 - Sept 1, 2023: Geometric Science of Information (GSI 2023), Saint-Malo
Aug 5 - 10, 2023: Joint Statistics Meetings (JSM 2023), Toronto
July 10 - 14, 2023: SIAM Applied Algebraic Geometry, Eindhoven
June 26 - 30, 2023: Extreme Value Analysis (EVA 2023), Bocconi University Milano
June 13 - 18, 2023: Foundations of Computational Mathematics (FoCM 2023), Paris
May 14 - 19, 2023: Computations and Data in Algebraic Statistics, Casa Matemática Oaxaca
April 26 - 28, 2023: Graduate Student Meeting on Applied Algebra and Combinatorics, Stockholm
April 3 - 4, 2023: Solving Hard Polynomial Systems, MPI-MiS Leipzig
March 13 - 14, 2023: Research Data in Discrete Mathematics, MPI-MiS Leipzig
March 7 - 10, 2023: German Probability and Statistics Days, Essen
Dec 4 - 10, 2022: Algebraic Structures in Statistical Methodology, Oberwolfach
Nov 24 - 25, 2022: MOM: MaRDI, OSCAR and MathRepo, TU Berlin
Nov 21 - 23, 2022: Tensors in statistics, optimization and machine learning, Warsaw
Nov 18, 2022: Talk at Statistics Seminar, EPFL Lausanne
Nov 9 - 16, 2022: 8th Mexican Workshop on Applied Geometry and Topology
Oct 25 - 28, 2022: Mathematics of Machine Learning, Bilbao
Oct 20 - 21, 2022: Mathematical optimization and statistical theories using geometric methods, Osaka
Oct 10 - 14, 2022: Workshop on Graphical Models, Raitenhaslach
Sept 19 - 23, 2022: AGATES Kickoff Workshop, Warsaw
Sept 12 - 16, 2022: DMV Annual Meeting, FU Berlin
Aug 23 - 26, 2022: Computational Statistics, Bologna
July 7 - 9, 2022: Latinx in the Mathematical Sciences, IPAM, UCLA
June 27 - July 1, 2022: CCAAGS Bernd Sturmfels 60th birthday, UW Seattle
June 13 - 16, 2022: Mathematics of Complex Data, KTH Stockholm
May 16 - 20, 2022: Algebraic Statistics 2022, University of Hawai'i at Manoa
May 4th, 2022: Talk at Mathematical Statistics Research Seminar, WIAS Berlin
April 28, 2022: Two Questions About Mathematical Software, MPI-MiS Leipzig
March 28, 2022: Special Colloquium in honor of Bernd Sturmfels' 60th birthday, MPI-MiS Leipzig
March 16, 2022: Talk at Seminar on Nonlinear Algebra, MPI-MiS Leipzig
March 11, 2022: Convex and Discrete Day, FU Berlin
Nov 17, 2021: 7th One World Webinar, Novel Algebraic Approaches to ML Estimation
Nov 2 - 4, 2021: MaRDI Kickoff Workshop, MPI-MiS Leipzig
Sept 14 - 17, 2021: Statistische Woche (virtual)
Aug 16 - 20, 2021: SIAM Applied Algebraic Geometry (virtual)
June 21 - 25, 2021: GO60, Torino (virtual)
June 7 - 11, 2021: Effective Methods in Algebraic Geometry (MEGA 2021), Arctic University of Norway (virtual)
May 31 - June 2, 2021: Workshop on Software and Applications of Numerical Nonlinear Algebra, MPI-MiS Leipzig (virtual)
March 8 - June 11, 2021: Tensor Methods and Emerging Applications Long Program, IPAM
March 16, 2021: Talk at Applied CATS Seminar, KTH (online)
March 11, 2021: Talk at Algebra in Statistics and Computation Seminar, University of Wisconsin-Madison (online)
Jan 26 - 29, 2021: Sanya Workshop on Algebraic Geometry and Machine Learning
Dec 18, 2020: Talk at Imperial College London Statistics Seminar (online)
Dec 8, 2020: Talk at the Algebra and Geometry Seminar, OvGU Magdeburg (online)
Oct 30, 2020: Talk at the London Geometry and Topology Seminar (online)
Oct 23 - 24, 2020: Barcelona Mathematical Days (BMD 2020), Institut d'Estudis Catalans (online)
Aug 24 - 28, 2020: Bernoulli-IMS One World Symposium (Virtual Online)
Aug 11 - 14, 2020: Geometry of curves in time series and shape analysis, MPI-MiS Leipzig
Aug 3 - 6, 2020: Conference on Uncertainty in Artificial Intelligence, Toronto (Virtual Online)
July 10, 2020: Talk at Online Applied Algebra and Analysis Seminar, TU Braunschweig / U Osnabrück
June 22 - 26, 2020: Algebraic Statistics 2020 Virtual Conference, University of Hawai'i at Manoa
June 1 - 5, 2020: Macaulay2 Online Workshop, University of Warwick
May 6, 2020: Talk at Webinar series on Recent Connections to GCT, Chennai Mathematical Institute
April 6 - 9, 2020: British Mathematical and Applied Mathematics Colloquia (BMC-BAMC), University of Glasgow (postponed)
March 30 - April 3, 2020: Spring School on Mathematical Statistics, MPI-MiS Leipzig (postponed)
March 27, 2020: Talk at Nonlinear Algebra Seminar Online (NASO), MPI-MiS Leipzig
March 26 - 27, 2020: Nonlinear Algebra Workshop, TU Berlin (canceled)
March 15 - 21, 2020: Algebraic Structures in Statistical Methodology, Oberwolfach (canceled)
March 17, 2020: Talk at Nonlinear Algebra Seminar Online (NASO), MPI-MiS Leipzig
Dec 14 - 16, 2019: Computational and Methodological Statistics, CMStatistics 2019, London
Nov 27, 2019: Talk at Lucerne University of Applied Sciences and Arts, Hochschule Luzern
Nov 26, 2019: Talk at Algebra and Geometry Seminar, University of Basel
Oct 23 - 25, 2019: Graphical Models: Conditional Independence and Algebraic Structures, TU Munich
Oct 7 - 11, 2019: Algebraic Geometry: Varieties, Polyhedra, Computation , Berlin
Aug 19 - 23, 2019: Stochastics Workshop in memory of Fr. Matúš, Prague
July 22 - 26, 2019: European Meeting of Statisticians (EMS 2019), Palermo
July 15 - 19, 2019: International Congress on Industrial and Applied Mathematics (ICIAM), Valencia
July 9 - 13, 2019: SIAM Applied Algebraic Geometry, Bern
July 1 - 4, 2019: Randomness and Learning in Nonlinear Algebra, MPI-MiS Leipzig
June 17 - 21, 2019: Effective Methods in Algebraic Geometry (MEGA 2019), Madrid
March 18 - 22, 2019: DAGStat 2019, LMU Munich
Feb 14 - 15, 2019: Optimality in Algebraic Statistics, TU Dortmund
Jan 31, 2019: Talk at Algebra and Algebraic Geometry Seminar, University of Oslo
Jan 14, 2019: Talk at Facets of Complexity Colloquium, FU Berlin
Jan 11, 2019: Berlin-Leipzig Day Mathematical Statistics, HU Berlin
Dec 11 - 14, 2018: Advances in Applied Algebraic Geometry, Bristol
Dec 10, 2018: Talk at Algebra and Geometry Seminar, University of Bristol
Nov 26 - 27, 2018: Complexity Reduction in Algebraic Statistics, OVGU Magdeburg
Nov 14, 2018: Talk at Mathematics and Statistics Seminar, University of Cyprus
Sept 24 - 28, 2018: Summer School in Algebraic Statistics, Tromsø
Sept 5 - 21, 2018: Nonlinear Algebra, ICERM
Aug 13 - 17, 2018: Numerical Computing in Algebraic Geometry, MPI-MiS Leipzig
July 9 - 13, 2018: SIAM Annual Meeting, Portland
June 14 - 16, 2018: Berlin-Oxford Meeting, WIAS
May 25 - 27, 2018: Introduction to Algebraic Statistics Course, Berlin
April 30, 2018: Talk at Stochastic Analysis Seminar, Oxford
April 19, 2018: Talk at Rough Paths, SPDEs and related topics Seminar, TU Berlin
Feb 27 - March 2, 2018: German Probability and Statistics Days, Freiburg
Feb 19 - 23, 2018: Linking Topology to Algebraic Geometry and Statistics, MPI Leipzig
Feb 7, 2018: Talk at Seminar on Statistics and Risk Management, TU Munich
Jan 10 - 13, 2018: Joint Mathematics Meetings (JMM 2018), San Diego
Dec 11 - 12, 2017: OSCAR, MPI-MIS Leipzig
Nov 30 - Dec 2, 2017: Algebraic Methods in Statistics, Osnabrück
Nov 12 - 13, 2017: Talk at Berlin-Leipzig Seminar, FU Berlin
Nov 10, 2017: 2nd Algebraic Statistics Day, MPI Leipzig
Nov 6 - 7, 2017: Algebra Meets Numerics Workshop, TU Berlin
Nov 3, 2017: Talk at What is...? Seminar, TU Berlin
Oct 9 - 10, 2017: BMS-BGSMath Junior Meeting, Barcelona
Sept 19, 2017: Talk at Applied Algebra and Geometry Seminar, MIT
Aug 11, 2017: Algebraic Statistics Day, MPI Leipzig
July 31 - Aug 4, 2017: SIAM Applied Algebraic Geometry, Atlanta
July 27 - 29, 2017: Applied Macaulay2 Tutorials, Georgia Tech
July 10 - 19, 2017: Foundations of Computational Mathematics, Barcelona
July 3 - 7, 2017: Real Algebraic Geometry Workshop, MPI Leipzig
June 12 - 16, 2017: Effective Methods in Algebraic Geometry (MEGA 2017), Nice
June 10, 2017: Polynomials and Polytopes, TU Berlin
May 27, 2017: Interactions between Algebra and the Sciences, MPI Leipzig
May 22 - 24, 2017: Chow Lecture, MPI and University of Leipzig
May 11 - 12, 2017: Computing in Tropical Geometry Workshop, Zuse Institute Berlin
April 16 - 22, 2017: Algebraic Statistics Workshop, Oberwolfach
Feb 3, 2017: Polymake Workshop, TU Berlin
Jan 21, 2017: Reinhold-Baer Colloquium, TU Berlin
Jan 10 - 11, 2017: Workshop on Non-linear Algebra, Max Planck Institute Leipzig
Jan 8, 2017: Numerical Algebraic Geometry adjoint meeting, Georgia Tech
Jan 4 - 7, 2017: Joint Mathematics Meetings (JMM 2017), Atlanta
Dec 13 - 15, 2016: Einstein Workshop on Lattice Polytopes, FU Berlin
Dec 13, 2016: Talk at Modern Methods in Applied Stochastics and Nonparametric Statistics Seminar, WIAS Berlin
Dec 12 - 13, 2016: Tensors: Algebra Meets Numerics, Max Planck Institute Leipzig
Nov 3 - 4, 2016: National Algebra Meeting, Oslo
Oct 12 - 14, 2016: Conference on Conditional Independence Structures and Extremes, TU Munich
Aug 29, 2016: Talk at Seminario de Matemáticas ITAM, México
Aug 17, 2016: Talk at Coloquio Instituto de Matemáticas UNAM, Cuernavaca
July 28 - 30, 2016: Crossroads: Workshop on Stochastic Analysis and Related Fields, HU Berlin
July 18 - 22, 2016: 7th European Congress of Mathematics, TU Berlin
July 11 - 15, 2016: SIAM Annual Meeting, Boston
July 4 - 8, 2016: Goethe Universität Summer School on Geometry of Valuations, Frankfurt
June 27 - July 2, 2016: Aalto Summer School on Algebra, Statistics and Combinatorics, Helsinki
June 12 - 18, 2016: AMS Mathematics Research Communities: Algebraic Statistics, Utah
May 23 - 26, 2016: Macaulay2 Workshop, University of Warwick
May 20 - 21, 2016: Geometry and Optimization with ALgebraic methods (GOAL) Workshop, Paris
May 9 - 13, 2016: Hausdorff School: Economics and Tropical Geometry, Bonn
March 18, 2016: Talk at Combinatorics Seminar, UC Berkeley
March 2, 2016: Talk at Algebra-Geometry-Combinatorics Seminar, San Francisco State University
Feb 27, 2016: MAA Golden Section Meeting, UC Davis
Feb 1, 2016: Talk at Applied Algebra Seminar, UC Berkeley
Jan 6 - 9, 2016: Joint Mathematics Meetings (JMM 2016), Seattle
Dec 10, 2015: NonLinear Algebra Seminar, TU Berlin
Nov 18, 2015: Talk at Forschungszentrum Biosystemtechnik CDS theory seminar, Universität Magdeburg
Nov 17, 2015: Talk at Institut für Algebra und Geometrie, Universität Magdeburg
Nov 16, 2015: Talk at Graduiertenkolleg: Methods for Discrete Structures, FU Berlin
Nov 11 - 13, 2015: Mathematical Aspects of Computer and Information Sciences, ZIB Berlin
Oct 8 - 9, 2015: Meeting on Algebraic Vision, TU Berlin
June 29 - July 10, 2015: BMS Summer School: Convex Geometry, Berlin
June 15 - 19, 2015: Effective Methods in Algebraic Geometry (MEGA 2015), Trento
June 8 - 11, 2015: Algebraic Statistics 2015, Genova
May 29 - 30, 2015: Workshop on Nonlinear Algebra, Berlin
May 27 - 28, 2015: Tropical Döner Workshop, FU Berlin
April 10 - 11, 2015: Applied Math Days, Rensselaer Polytechnic Institute, New York