Gabriel Riffo
I’m a PhD student with Professor Carlos Améndola at the research group of Algebraic and Geometric Methods in Data Analysis at Technische Universität Berlin. I am part of the DFG Collaborative Research Center Rough Analysis, Stochastic Dynamics and Related Fields CRC/TRR 388 as a research assistant for project B01: Statistical Learning from Path Observations.
My academic interests lie in the field of statistics, particularly in areas such as Algebraic Statistics and Topological Data Analysis, focusing on the application of algebra and geometry to statistical problems. I am especially interested in tackling problems that involve integrating multiple branches of mathematics. Additionally, I have strong interests in Spatial Statistics, Time Series, and Computational Statistics.
Previously, I obtained my Bachelor's degree in Mathematical Engineering and my Master's degree in Mathematics from Universidad Técnica Federico Santa María.
Session
We introduce SignatureTensors.jl, a new package for computing signature tensors of paths and membranes. By leveraging the symbolic computation framework provided by OSCAR, the package implements flexible algebraic structures for truncated
tensor signatures, and provides efficient constructors for path signatures. Furthermore, it features implementations of Lie group barycenters and optimized algorithms for learning from signature tensors. We illustrate the package’s versatility with practical applications in geometric statistics, feature extraction,
spline interpolation, and computational algebraic geometry.