Scientific Organisers:
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Gonçalo dos Reis, University of Edinburgh
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Darrick Lee, University of Edinburgh
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Yue Wu, University of Strathclyde
About:
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.
Programme:
| MONDAY 19 MAY | ||
| Registration and refreshments | ||
| Welcome address by Terry Lyons | ||
| Nikolas Tapia, Weierstrass Institute Berlin | Mini-course: Algebraic aspects of path signatures and applications | |
| Refreshments | ||
| Nikolas Tapia, Weierstrass Institute Berlin | Mini-course continued | |
| Lunch | ||
| Francis Bischoff, University of Regina | Mini-course: Parallel transport along paths and surfaces | |
| Refreshments | ||
| Francis Bischoff, University of Regina | Mini-course continued | |
| TUESDAY 20 MAY | ||
| Harald Oberhauser, University of Oxford | Talk Title TBC | |
| Danyu Yang, Chongqing University | The Lipschitz continuity of the solution to branched rough differential equations | |
| Refreshments | ||
| Kurusch Ebrahimi-Fard, Norwegian University of Science and Technology | Talk Title TBC | |
| Lunch | ||
| Mie Kano Glückstad, University of Oxford | Signature reconstruction from randomized signatures | |
| Vincenzo Galgano, MPI-CBG Dresden | Discrete signature tensors for persistence landscapes | |
| Refreshments | ||
| Severin Bunk, University of Hertfordshire | Aspects of higher connections and parallel transport in geometry | |
| Damien Simon, LPSM, Sorbonne Universite | Typical images generated by 2D Markov Processes: from frustration to periodic tiles | |
| WEDNESDAY 21 MAY | ||
| Christian Litterer, University of York | Efficient constructions of high-degree cubature measures on Wiener space | |
| Emilio Ferrucci, University of Oxford | Rough differential equations for volatility | |
| Refreshments | ||
| Joao Faria Martins, University of Leeds | Hopf-algebraic higher gauge theory, path and surface signatures, and (mainly) beyond | |
| Free afternoon / Activity | ||
| THURSDAY 22 MAY | ||
| Rosa Preiß, TU Berlin | An algebraic geometry of paths via the iterated integral signature | |
| Nikolas Tapia, Weierstrass Institute Berlin | Branched Itô Formula and Natural Itô-Stratonovich Isomorphism | |
| Refreshments | ||
| Camilo Arias Abad, Universidad Nacional de Colombia | Chen’s iterated integrals and loop spaces | |
| Lunch | ||
| Felix Lotter, MPI MiS Leipzig | Signature matrices of membranes | |
| Tomás Carrondo, University of Vienna | Well-posedness and Approximation Properties of Signature CDEs | |
| Refreshments | ||
| Fabian Harang, BI Norwegian Business School | Signatures with memory - Exploring the Volterra signature | |
| Joscha Diehl, University of Greifswald | Tensor-to-Tensor Models with Fast Iterated Sum Features | |
| Workshop Dinner, hosted at Blonde Restaurant | 75 St. Leonard’s Street, Edinburgh EH8 7QR | |
| FRIDAY 23 MAY | ||
| Anke Wiese, Heriot-Watt University | The exponential Lie series and a Chen-Strichartz formula for Lévy stochastic differential equations | |
| Edward Eriksson, Max Planck Institute Leipzig | Edge exchangeable random graphs and the unseen species problem | |
| Refreshments | ||
| Leonard Schmitz, TU Berlin | Finite Gröbner bases for quantum symmetric groups |
