Videos:
First steps in global Lie theory: wild Riemann surfaces, their character varieties and topological symplectic structures:  1) Séminaire Ngô, Collège de France 2023 (video, slides, resized slides)   [the rest of the story about the diagrams is recounted in these: slides/video/paper]  2) Wall-Crossing Structures, Analyticity and Resurgence, IHES 2023 (video, slides)   [A review of "pure wall-crossing" was added in this version, and there is even less on diagrams]  3) The Stokes Phenomenon and its Applications in Mathematics and Physics, SCGP 2023 (Video: Part 1, Part 2, slides, abstract)   [This is essentially the union of the two talks above]
Diagrams, fission spaces and global Lie theory, Vertex Algebras and Poisson Geometry, Les Diablerets 2022, Suisse (slides)
Topology of the Stokes phenomenon, IHES June 2019 (article)
Higgs bundles on the affine line and wild surface groups, Simons centre, April 2019
Nonabelian Hodge spaces and nonlinear representation theory, IHES (and Oxford) 2017 (slides)
Wild character varieties, meromorphic Hitchin systems and Dynkin diagrams, Perimeter Institute, Waterloo, Canada, 2017 (slides) (blackboard summary)
Non-perturbative hyperkahler manifolds, Newton Institute, Cambridge 2015 (slides)
Natural flat connections and wild mapping class groups, Padova, November 2014
Irregular connections, Dynkin diagrams and fission, Banff conference on hyperkähler manifolds, Mars 2012 (slides)

List of all talks: (here)

Some other slides:
Algebraic Poisson structures in global Lie theory, Global Poisson webinar, 5/2024
Wild character varieties and quantum groups, Quantization days 4.0 (2 hrs), 12/2023       (as well as §4 of this review, and the end of these slides of this talk)
Diagrams, nonabelian Hodge spaces and global Lie theory, Workshop on nonabelian Hodge theory, Saint Jacut de la Mer, 2022 (abstract)       (Similar talk: Heidelberg 2020, Hamburg, Versailles, Chemnitz 2021, slides)
Connections on curves and wild character varieties, Narasimhan-Seshadri @ 50, Chennai 2015 (slides of 1st talk of 3)(abstract)
Non-Perturbative symplectic manifolds and Non-Commutative algebras, RIMS 2015
Higgs bundles, Connections and Quivers, Pavia, Rennes, Singapore & Augsburg 2014
Beyond the fundamental group, JPM Lyon, 2014
Wild character varieties and multiplicative quiver varieties, Aberdeen ARTIN meeting, Novembre 2013
Wild character varieties, quiver varieties and G_2, Strasbourg, Novembre 2013
Transformation groups for isomonodromy equations I, et II, Journées isomonodromiques, Toulouse, Janvier 2013
Habilitation, Decembre 2012
Transformation groups for isomonodromy equations, RIMS Kyoto, Novembre 2012 (résumé)
Poisson geometry of moduli spaces of meromorphic connections on curves and their Stokes data, Poisson 2012, Utrecht
Irregular connections, Dynkin diagrams and fission, SEDIGA conference, Luminy, Juin 2012 (90 mins)
Painlevé equations, Dynkin diagrams and hyperkähler manifolds, IHES, Janvier 2012
Irregular connections, Dynkin diagrams and fission, Oxford Higgs bundle conference, Mars 2011
Some geometry of irregular connections on curves, IAS Princeton, Novembre 2007 (HAL)
Painlevé, Klein and the icosahedron, ICMAT Madrid, Septembre 2006
Survey of the known algebraic solutions of Painlevé VI, Slides from two talks at the Newton Institute (Talk I, Talk II), Cambridge 2006 (local copy in one file, archive: I, II)