In this episode, we interview Logan Kilpatrick. Logan currently splits his time between a number of professional commitments he is passionate about. He is a full-time Senior Technology Advocate at PathAI, the Developer Community Advocate for the Julia Programming Language, and a Teaching Fellow for Harvard University's Extension School course CSCI E-33A. Logan was previously an Applied Machine Learning Engineer and Software Engineer at Apple as well as the Community Manager for the Julia Programming Language. Additionally, Logan is on the Board of Directors at NumFOCUS and DEFNA. We started talking about the whole Julia Ecosystem with a particular focus on their pandemic response, touching a bit on the hot theme of the Metaverse. We spoke about why someone should use Julia with respect to other programming languages, mentioning some specific packages. We then switch to decentralisation/open source topics analyzing them ideologically, applicationally and financially. We then talked about Julia's future and the amazing interactions among Julia users. Given the background of Logan, we finally spoke about open science with NASA and the application of Julia in the aerospace sector, speaking also about PathAI, Logan's full-time company job. LINKS: https://julialang.org https://github.com/logankilpatrick https://twitter.com/OfficialLoganK https://scholar.harvard.edu/logankilpatrick RESOURCES: Anchor: https://anchor.fm/poincare-podcast Youtube: https://www.youtube.com/watch.v RSS: https://anchor.fm/s/84561ce0/podcast/rss Linktree: https://linktr.ee/poincaretrajectories Company: https://www.linkedin.com/company/poincaretrajectories/

Here is a conversation with Erik Van Winkle, Operations Lead at DeSci Labs, besides having been part of the core team at Constitution DAO. DeSci is a pioneering movement dedicated to exploring the capabilities of web3 technologies applied to the scientific ecosystem. We started talking about how DeSci works and the potential of sharing information while maintaining copyright. Then we jumped into the differences between decentralized science and open source, touching on the system design and business models. We then spoke about the story of DeSci and its relevant implementation choices. We finally discussed the new paradigm brought by DeSci, focusing on the ethics of interacting with traditional scientific media. LINKS: https://www.linkedin.com/in/erik-van-winkle/ https://desci.com/ https://discord.gg/TnTsAUUu https://t.me/BlockchainForScience RESOURCES: Anchor: https://anchor.fm/poincare-podcast Youtube: https://www.youtube.com/watch.v RSS: https://anchor.fm/s/84561ce0/podcast/rss Linktree: https://linktr.ee/poincaretrajectories Company: https://www.linkedin.com/company/poincaretrajectories/

The guest of this episode is Jean-Marc Mercier. Dr. Jean-Marc studies machine learning, both kernel methods and deep learning, in the context of mathematical finance. We start talking about the differences between kernel methods and deep learning and some history of machine learning, then about the relations between orthogonal polynomials, and deep learning and kernel methods, touching on the application of kernel principal component analysis in aerospace and optimal transport. Dealing with finance, we talk about his vision in AI algorithmic trading and in general more financial applications where AI can be useful. Then we move on modelling approach and assumptions of the observable that brought us to economic bubble formation. We reserve quite a lot of time to talk about "codpy" an open-source python library for machine learning, mathematical finance and statistics of which Jean-Marc is one of the authors. We end up speaking about "codpy" more in detail such as function representation, mesh free methods which bring us to its applicability in fluid dynamics and we conclude with the future expansions of this library. LINKS: https://www.researchgate.net/profile/Jean-Marc-Mercier https://pypi.org/project/codpy/ RESOURCES: Anchor: https://anchor.fm/poincare-podcast Youtube: https://www.youtube.com/watch.v RSS: https://anchor.fm/s/84561ce0/podcast/rss Linktree: https://linktr.ee/poincaretrajectories Company: https://www.linkedin.com/company/poincaretrajectories/

Joel Rosenfeld is Assistant Professor at the University of South Florida and his research covers machine learning, kernel methods, approximation theory, function analysis and many more. After a brief introduction about career strategies and issues caused by the pandemic, we talked about kernel functions with many digressions, such as the statistical description of dynamical systems and relationships between different spaces. We discuss the occupation of kernel functions and occupation measures (a branch of control theory) then we go on approximation of bounded operator using the densely defined operator and alternative approaches when operators are discontinuous in the domain. In the end, you'll find that sometimes one tries to make links between those subjects and dynamical systems and chaos, not all of them are congruent but is really interesting to hear the reasons. LINKS: https://scholar.google.com/citations?user=pqsepdcAAAAJ&hl=en https://www.thelearningdock.org https://youtube.com/c/ThatMathThing RESOURCES: Anchor: https://anchor.fm/poincare-podcast Youtube: https://www.youtube.com/watch.v RSS: https://anchor.fm/s/84561ce0/podcast/rss Linktree: https://linktr.ee/poincaretrajectories Company: https://www.linkedin.com/company/poincaretrajectories/

Gary Froyland is a professor at the School of Mathematics and Statistics at the University of New South Wales, and his research includes dynamical systems and optimization. We started talking about research life and the struggle with our limits to pursue it, and then we went technical arguing about applied mathematics. In particular, we touched on the chaotic nature of climate and ocean science and the determination of some geometric structures (coherent) in it. We moved on to linear operators in functional analysis for time-varying dynamical systems and transfer operators both in discrete and continuous time. We discussed the software he developed (GAIO) and its applicability to the aerospace sector concluding by discussing the applicability of chaotic maps (e.g. Anosov), the periodicity of a system and the usage of the operators in multiscale systems (e.g. deterministic chaos and turbulence, fractals structures). LINKS: https://scholar.google.com/citations?user=uAIy_MMAAAAJ&hl=en https://web.maths.unsw.edu.au/~froyland/ https://research.unsw.edu.au/people/professor-gary-froyland RESOURCES: Anchor: https://anchor.fm/poincare-podcast Youtube: https://www.youtube.com/watch.v RSS: https://anchor.fm/s/84561ce0/podcast/rss Linktree: https://linktr.ee/poincaretrajectories Company: https://www.linkedin.com/company/poincaretrajectories/

Miles Cranmer is a Ph.D. candidate at the University of Princeton. He is working on the interplay between astrophysics and AI. We talk about Symbolic Regression, Genetic Programming, and the peculiarities of Julia, the programming language, comparing it with C++ and Python. We then talk about his approach in studying new programming language features and about how to balance exploration versus exploitation. We largely discuss his work at Deepmind, outlining graph- and Lagrangian-Neural Networks, particularly in relation to the ability to investigate chaotic motion in dynamical systems. LINKS: https://astroautomata.com https://web.astro.princeton.edu/people/miles-cranmer https://github.com/MilesCranmer RESOURCES: Anchor: https://anchor.fm/poincare-podcast Youtube: https://www.youtube.com/watch.v RSS: https://anchor.fm/s/84561ce0/podcast/rss Linktree: https://linktr.ee/poincaretrajectories Company: https://www.linkedin.com/company/poincaretrajectories/

J. Nathan Kutz is the Robert Bolles and Yasuko Endo Professor within the Department of Applied Mathematics at the University of Washington in Seattle. He is also the director of the UW-led AI Institute for Dynamic Systems, founded by the National Science Foundation. His research interests are numerical methods and scientific computing, data analysis and dimensionality reduction methods, dynamical systems, bifurcation theory, linear and nonlinear wave propagation, perturbation and asymptotic methods, nonlinear analysis, variational methods, soliton theory, nonlinear optics, mode-locked lasers, fluid dynamics, Bose-Einstein condensation, neuroscience, gesture recognition, and video & image processing. LINKS: http://faculty.washington.edu/kutz/ https://www.youtube.com/channel/UCoUOaSVYkTV6W4uLvxvgiFA J. Nathan Kutz Google Scholar RESOURCES: Anchor: https://anchor.fm/poincare-podcast Youtube: https://www.youtube.com/watch.v RSS: https://anchor.fm/s/84561ce0/podcast/rss Linktree: https://linktr.ee/poincaretrajectories Company: https://www.linkedin.com/company/poincaretrajectories/

Igor Mezić is a mechanical engineer, mathematician, and Distinguished Professor of mechanical engineering and mathematics at the University of California, Santa Barbara. He is best known for his contributions to operator theoretic, data-driven approach to dynamical systems theory that he advanced via articles based on Koopman operator theory and his work on the theory of mixing. LINKS: Igor Mezic wiki Igor Mezic LinkedIn Igor Mezic ResearchGate Profile RESOURCES: Anchor: https://anchor.fm/poincare-podcast Youtube: https://www.youtube.com/watch.v RSS: https://anchor.fm/s/84561ce0/podcast/rss Linktree: https://linktr.ee/poincaretrajectories Company: https://www.linkedin.com/company/poincaretrajectories/

Emmanuel Blazquez is a Postdoctoral Research Fellow in Advanced Mission Analysis at the Advanced Concepts Team of the European Space Agency in Noordwijk, Nederland. His research areas are advanced mission analysis studies, with a focus on on-board real-time optimization asssisted by Artificial Intelligence. He also works on Autonomous Guidance and Control architectures, Multibody Astrodynamics and System Identification. We start talking about the structure and goals of the Advanced Concepts Team, its interactions with ESA and the overall space community. We talk, as it is often the case in this podcast, about the synergies between Dynamical Systems and Artificial Intelligence. In particular, we talk about the use of classification techniques to investigate chaos, focusing in particular on Poincare' maps, starting from the relevance of chaotic dynamics in trajectory design. We talk about potential interplay between convexification methods and Artificial Intelligence, in the context of optimal control and more in particular for randevouz, and how this has implications for the use of the Lunar Gateway. We also talk about the use of GPUs in space research, talking about the asteroid aggregation problem, and the hardware he is using to conduct his work now. LINKS: Emmanuel Blazquez LinkedIn https://www.esa.int/gsp/ACT/team/emmanuel_blazquez/ Emmanuel Blazquez ResearchGate Profile RESOURCES: Anchor: https://anchor.fm/poincare-podcast Youtube: https://www.youtube.com/watch.v RSS: https://anchor.fm/s/84561ce0/podcast/rss Linktree: https://linktr.ee/poincaretrajectories Company: https://www.linkedin.com/company/poincaretrajectories/

Richard Linares is an assistant professor at MIT’s Department of Aeronautics and Astronautics and is the Co-Director of the Space Systems Laboratory. His research areas are astrodynamics, estimation and controls, satellite guidance and navigation, space situational awareness, and space traffic management. We start talking about his interest in space traffic management, focusing on the importance of modelling the space environment: the thermosphere, the ionosphere and space weather. We discuss some of his works looking into reduced-order modelling techniques, like principal component analysis and dynamic mode decomposition, for the modelling of the thermospheric density field. We then discuss the use of machine learning techniques, like autoencoders and neural networks more in general, as promising generalizations, without neglecting their downsides. Discussing the use of the Koopman Operator Theory in the same context, we move to its relevance in low dimensional, highly nonlinear dynamical systems, encountered every day in astrodynamics. We talk about its use for the study of the earth gravity field and for the construction of halo orbits in the restricted three-body problem. We discuss its implications for the engineering community, talking about optimal control, estimation and uncertainty quantification, about which we also outline the unification potential of techniques such as polynomial chaos expansion, differential algebra. We then look into the potential of the Koopman Operator for dynamical systems theory in space. We discuss its potential for the analysis of invariant manifolds, its limitations for the study of chaotic systems, and finally its relations to the hamiltonian formalism of classical mechanics. LINKS: http://arclab.mit.edu/ https://aeroastro.mit.edu/people/richard-linares/ Richard Linares LinkedIn RESOURCES: Anchor: https://anchor.fm/poincare-podcast Youtube: https://www.youtube.com/watch.v RSS: https://anchor.fm/s/84561ce0/podcast/rss Linktree: https://linktr.ee/poincaretrajectories Company: https://www.linkedin.com/company/poincaretrajectories/