The aim of this workshop was to discuss stochastic, geometric, and algebraic approaches to signatures and rough paths, including developments in machine learning applications. The study of signatures have highlighted interactions between these fields, including approximation theorems in path spaces, path development (parallel transport) based methods in ML, algebraic approaches to signature tensors, among many others. One focus of this workshop was the theory and applications of multi-parameter signatures, which builds upon these interactions. We brought together experts in these fields, as well as researchers interested in the theory and application of signatures, in order to discuss these developments and explore further relationships across these disciplines.
Workshop
Signatures and rough paths: from stochastics, geometry and algebra to machine learning
19 May 2025 - 23 May 2025
Edinburgh Futures Institute
Scientific Organisers
About Workshop
Programme
09.00-09.30
Registration and refreshments
09.30-10.00
Welcome address by Terry Lyons
10.00-11.00
Nikolas Tapia, Weierstrass Institute Berlin
Mini-course: Algebraic aspects of path signatures and applications
11.00-11.30
Refreshments
11.30-12.30
Nikolas Tapia, Weierstrass Institute Berlin
Mini-course continued
12.30-14.00
Lunch
14.00-15.00
Francis Bischoff, University of Regina
Mini-course: Parallel transport and the signature of paths and surfaces
15.00-15.30
Refreshments
15.30-16.30
Francis Bischoff, University of Regina
Mini-course continued
09.30-10.20
Harald Oberhauser, University of Oxford
Talk Title TBC
10.20-11.10
Danyu Yang, Chongqing University
The Lipschitz continuity of the solution to branched rough differential equations
Abstract 11.10-11.45
Refreshments
11.45-12.35
Kurusch Ebrahimi-Fard, Norwegian University of Science and Technology
Talk Title TBC
12.35-13.45
Lunch
13.45-14.15
Mie Kano Glückstad, University of Oxford
Signature reconstruction from randomized signatures
14.15-14.45
Vincenzo Galgano, MPI-CBG Dresden
Discrete signature tensors for persistence landscapes
14.45-15.15
Refreshments
15.15-16.05
Severin Bunk, University of Hertfordshire
Aspects of higher connections and parallel transport in geometry
16.05-16.55
Damien Simon, LPSM, Sorbonne Universite
Typical images generated by 2D Markov Processes: from frustration to periodic tiles.
09.30-10.20
Christian Litterer, University of York
Efficient constructions of high-degree cubature measures on wiener space
10.20-11.10
Emilio Ferrucci, University of Oxford
Rough differential equations for volatility
11.10-11.45
Refreshments
11.45-12.35
Joao Faria Martins, University of Leeds
Hopf-algebraic higher gauge theory, path and surface signatures, and (mainly) beyond
12.35
Free afternoon / Activity
09.30-10.20
Rosa Preiß, TU Berlin
An algebraic geometry of paths via the iterated integral signature
10.20-11.10
Nikolas Tapia, Weierstrass Institute Berlin
Branched Itô Formula and Natural Itô-Stratonovich Isomorphism
11.10-11.45
Refreshments
11.45-12.35
Camilo Arias Abad, Universidad Nacional de Colombia
Chen’s iterated integrals and loop spaces
12.35-13.45
Lunch
14.15-14.45
Tomás Carrondo, University of Vienna
Well-posedness and Approximation Properties of Signature CDEs
14.45-15.15
Refreshments
15.15-16.05
Fabian Harang, BI Norwegian Business School
Signatures with memory - Exploring the Volterra signature
16.05-16.55
Joscha Diehl, University of Greifswald
Tensor-to-Tensor Models with Fast Iterated Sum Features
19.00
Workshop Dinner hosted at Blonde Restaurant
09.30-10.20
Anke Wiese, Heriot-Watt University
The exponential Lie series and a Chen-Strichartz formula for Lévy stochastic differential equations
10.20-10.50
Edward Eriksson, Max Planck Institute Leipzig
Edge Exchangeable Random Graphs and the Unseen Species Problem
10.50-11.30
Refreshments
Sponsors and Funders
