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A Flag Decomposition for Hierarchical Datasets
Nathan Mankovich, Ignacio Santamaria, Gustau Camps-Valls, Tolga Birdal CVPR 2025 Link to GitHub 
Featurizing Koopman Mode Decomposition for Robust Forecasting
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Analyzing Climate Scenarios using Dynamic Mode Decomposition with Control Flag Decomposition for Hierarchical Datasets
Nathan Mankovich, Shahine Bouabid, Peer Nowak, Deborah Bassotto, Gustau Camps-Valls EDS 2025 Link to GitHub 
Chordal Averaging on Flag Manifolds and Its Applications
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Fun with Flags: Robust Principal Directions via Flag Manifolds.
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Selected preprints
Improving Generalisation via Anchor Multivariate Analysis. Homer Durand, Gherardo Varando, Nathan Mankovich, Gustau Camps-Valls. (arXiv 2024)
Optimal codes in the Stiefel manifold. John Jasper, Nathan Mankovich, Dustin Mixon. (arXiv 2024)
Selected talks
Physics-aware Koopman Opeartor Estimation for Consistent Nonlinear Mode Decomposition (EGU, Remote 2025)
Dynamic Mode Decomposition With Control for Climate Analyses (XAIDA Webinar, Remote 2024)
Stiefel Packings for Coherent Communications (ICERM, Providence 2024)
Analyzing Climate Scenarios Using Dynamic Mode Decomposition With Control (EGU, Vienna 2024)
Analyzing Climate Scenarios Using Dynamic Mode Decomposition With Control (Dynamics, Data and Deep Learning at Bristol 2024)
Fun With Flags: Robust Averages and Principal Directions (Invited Talk at Universidad de Cantabria, Santander 2024) slides
Averaging and Dimensionality Reduction using Flag Manifolds (Joint Mathematics Meetings in San Francisco 2024)
Graph-Based Dimensionality Reduction and Clustering in Earth and Life Sciences (Learning on Graphs in Madrid 2023)
Chordal Averaging on the Flag Manifold and Its Applications (ICCV 2023)
Recovering latent confounders from high-dimensional proxy variables (First the Friday Talk at University of Valencia 2023)
Chordal Distance Averages on Grassmann and Flag Manifolds (Invited Talk at Imperial College of London 2023)
The Applications of Chordal Flag Averaging (First the Friday Talk at University of Valencia 2023)
Chordal Distance Averaging on Flag Manifolds and its Applications (Topology Seminar at CSU 2023)
Python Workshop (SIAM at CSU 2023) code
Central Prototypes on Manifolds of Subspaces and Feature Analysis Using Graphs (Greenslopes at CSU 2022)
An Introduction to Graph Neural Networks (Data Science Seminar 2022)
Subspaces and Network Averaging for Computer Vision and Bioinformatics (Michael Penn Patreon Seminar 2022)
Pathway Expression Analysis (qBio 2022)
FRD-NNs and Lessons Learned at PNNL (Greenslopes at CSU 2021) code
A Search for the Center in the Reals and Beyond (Greenslopes at CSU 2020)
Geodesic Regression on the Grassmannian (Grennslopes at CSU 2019)
Detecting Biomarkers for Influenza (Rocky Mountain Virology Club 2019)
Venture grant proposal at Colorado College to hike the Colorado Trail (Colorado College Venture Grant Talks 2015)
Teaching
Advances in Dimensionality Reduction Spring 2025 at University of Valencia
Dimensionality Reduction Fall 2023 at University of Valencia
Ordinary Differential Equations (MATH 340) Fall 2020 at CSU
Calculus 2 (MATH 161) Spring 2020 at CSU
Calculus 1 (MATH 160) Fall 2017, Fall 2018, Spring 2018, Fall 2019 at CSU
Improving Generalisation via Anchor Multivariate Analysis. Homer Durand, Gherardo Varando, Nathan Mankovich, Gustau Camps-Valls. (arXiv 2024)
Optimal codes in the Stiefel manifold. John Jasper, Nathan Mankovich, Dustin Mixon. (arXiv 2024)
Selected talks
Physics-aware Koopman Opeartor Estimation for Consistent Nonlinear Mode Decomposition (EGU, Remote 2025)
Dynamic Mode Decomposition With Control for Climate Analyses (XAIDA Webinar, Remote 2024)
Stiefel Packings for Coherent Communications (ICERM, Providence 2024)
Analyzing Climate Scenarios Using Dynamic Mode Decomposition With Control (EGU, Vienna 2024)
Analyzing Climate Scenarios Using Dynamic Mode Decomposition With Control (Dynamics, Data and Deep Learning at Bristol 2024)
Fun With Flags: Robust Averages and Principal Directions (Invited Talk at Universidad de Cantabria, Santander 2024) slides
Averaging and Dimensionality Reduction using Flag Manifolds (Joint Mathematics Meetings in San Francisco 2024)
Graph-Based Dimensionality Reduction and Clustering in Earth and Life Sciences (Learning on Graphs in Madrid 2023)
Chordal Averaging on the Flag Manifold and Its Applications (ICCV 2023)
Recovering latent confounders from high-dimensional proxy variables (First the Friday Talk at University of Valencia 2023)
Chordal Distance Averages on Grassmann and Flag Manifolds (Invited Talk at Imperial College of London 2023)
The Applications of Chordal Flag Averaging (First the Friday Talk at University of Valencia 2023)
Chordal Distance Averaging on Flag Manifolds and its Applications (Topology Seminar at CSU 2023)
Python Workshop (SIAM at CSU 2023) code
Central Prototypes on Manifolds of Subspaces and Feature Analysis Using Graphs (Greenslopes at CSU 2022)
An Introduction to Graph Neural Networks (Data Science Seminar 2022)
Subspaces and Network Averaging for Computer Vision and Bioinformatics (Michael Penn Patreon Seminar 2022)
Pathway Expression Analysis (qBio 2022)
FRD-NNs and Lessons Learned at PNNL (Greenslopes at CSU 2021) code
A Search for the Center in the Reals and Beyond (Greenslopes at CSU 2020)
Geodesic Regression on the Grassmannian (Grennslopes at CSU 2019)
Detecting Biomarkers for Influenza (Rocky Mountain Virology Club 2019)
Venture grant proposal at Colorado College to hike the Colorado Trail (Colorado College Venture Grant Talks 2015)
Teaching
Advances in Dimensionality Reduction Spring 2025 at University of Valencia
Dimensionality Reduction Fall 2023 at University of Valencia
Ordinary Differential Equations (MATH 340) Fall 2020 at CSU
Calculus 2 (MATH 161) Spring 2020 at CSU
Calculus 1 (MATH 160) Fall 2017, Fall 2018, Spring 2018, Fall 2019 at CSU
