
Prof. Dr. Carlos Enrique Améndola Cerón

Email: amendola (at) math.tuberlin.de


I am an assistant professor (tenuretrack) 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 MaxPlanck 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 coadvisor 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 20202021, 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 eBriefs editor.
In 2023, Eliana Duarte, Thomas Kahle, and I organized an Algebraic Statistics Seminar between Berlin, Leipzig and Magdeburg.
Publications and Preprints
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) 455464.
Identifiability in Continuous Lyapunov Models (with P. Dettling, R. Homs, M. Drton and N. Hansen), SIAM Journal on Matrix Analysis and Applications, to appear.
ThirdOrder Moment Varieties of Linear NonGaussian 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 MaxLinear Bayesian Networks (with B. Hollering, S. Sullivant and N. Tran), Uncertainty in Artificial Intelligence, PLMR 161 (2021) 17461755.
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) 110.
Toric Invariant Theory for Maximum Likelihood Estimation in Loglinear Models (with K. Kohn, P. Reichenbach and A. Seigal), Algebraic Statistics 12(2) (2021) 187211.
Likelihood Geometry of Correlation Models (with P. Zwiernik), Le Matematiche , 76(2) (2021) 559583.
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) 535557.
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) 304337.
Conditional Independence in Maxlinear Bayesian Networks (with C. Klüppelberg, S. Lauritzen and N. Tran), Annals of Applied Probability, 31(1) (2022) 145.
Maximum Likelihood Estimation of Toric Fano Varieties (with D. Kosta and K. Kubjas), Algebraic Statistics 11(1) (2020) 530.
Moment Identifiability of Homoscedastic Gaussian Mixtures (with D. Agostini and K. Ranestad), Foundations of Computational Mathematics 21 (2021) 695724.
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) 936938.
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) 130.
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) 587600.
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) 222242.
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) 65566580.
Moment Varieties of Gaussian Mixtures (with JC. Faugère and B. Sturmfels), Journal of Algebraic Statistics , 7 (2016) 1428.
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) 579590.
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
Students
Janike Oldekop (2022)
Kamillo Ferry (2023)
Teaching
Winter Semester 20232024:
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]
MarkovKetten [MA2019]
Graphical Models [MA2025]
Summer Semester 2020:
Statistik: Grundlagen [MA2402]
Winter Semester 2019/2020:
Fundamentals of Mathematical Statistics [MA5441]
Summer Semester 2019:
Reading Seminar: HighDimensional 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
Sept 18  Oct 13, 2023: Algebraic Statistics and Our Changing World, IMSI Chicago
Aug 30  Sept 1, 2023: Geometric Science of Information (GSI 2023), SaintMalo
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, MPIMiS Leipzig
March 13  14, 2023: Research Data in Discrete Mathematics, MPIMiS 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, MPIMiS Leipzig
March 28, 2022: Special Colloquium in honor of Bernd Sturmfels' 60th birthday, MPIMiS Leipzig
March 16, 2022: Talk at Seminar on Nonlinear Algebra, MPIMiS 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, MPIMiS 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, MPIMiS 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 WisconsinMadison (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: BernoulliIMS One World Symposium (Virtual Online)
Aug 11  14, 2020: Geometry of curves in time series and shape analysis, MPIMiS 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 (BMCBAMC), University of Glasgow (postponed)
March 30  April 3, 2020: Spring School on Mathematical Statistics, MPIMiS Leipzig (postponed)
March 27, 2020: Talk at Nonlinear Algebra Seminar Online (NASO), MPIMiS 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), MPIMiS 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, MPIMiS 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: BerlinLeipzig 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, MPIMiS Leipzig
July 9  13, 2018: SIAM Annual Meeting, Portland
June 14  16, 2018: BerlinOxford 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, MPIMIS Leipzig
Nov 30  Dec 2, 2017: Algebraic Methods in Statistics, Osnabrück
Nov 12  13, 2017: Talk at BerlinLeipzig 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: BMSBGSMath 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: ReinholdBaer Colloquium, TU Berlin
Jan 10  11, 2017: Workshop on Nonlinear 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 AlgebraGeometryCombinatorics 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