- Introduction to P=W and mirror symmetry, Mirror symmetry and big algebras, ICTP, Trieste, December 2022
- Hitchin map on very stable and even very stable upward flows, ICMAT, Madrid, September 2022
- Enhanced mirror symmetry for Langlands dual Hitchin systems, Algebraic Geometry Section, ICM 2022
- Ubiquity of systems of homogeneous polynomial equations with unique solution, Colloquium UNC, April 2022
- Hitchin map as spectrum of equivariant cohomology, CMSA Colloquium, Harvard, October 2021
- Explicit Hitchin system on Lagrangians, ICMP, Geneva, August 2021
- Mirror symmetry for Langlands dual Higgs bundles at the tip of the nilpotent cone, WHCGP, January 2021
- Magic pictures about mirror symmetry for Langlands dual Higgs bundles, ISTA 4th year colloquium, January 2021
- P=W, HSE, Moscow, November 2017
- Perverse Hirzebruch y-genus of Hitchin systems , Perimeter Institute, Waterloo, February 2017
- Enumerative invariants of Higgs moduli spaces, UT Austin, February 2017
- Toric non-Abelian Hodge theory, Luminy, October 2015
- Toy models of hyperkähler moduli spaces, Newton Institute, Cambridge, July 2015
- Mirror symmetry in the character table of SL_n(F_q), Fields Institute, Toronto, October 2012
- Symmetries of SL_n Hitchin fibres, BIRS, Banff, March 2012
- Arithmetic and physics of Higgs moduli spaces, Kavli Institute for theoretical physics, Santa Barbara, July 2011
- Arithmetic and physics of Higgs moduli spaces, Newton Institute, Cambridge, June 2011
- Arithmetic and physics of Higgs moduli spaces, Simons Center Stony Brook, May 2011
- Mirror symmetry, Langlands duality and the Hitchin system, Simons Lecture Series, Stony Brook, Oct 2010
- Toric non-Abelian Hodge theory, Fields Institute, Toronto, Jan 2008
- Mixed Hodge Polynomials of Character Varieties, (slides) Center for the topology and quantization of moduli spaces, Aarhus, June 2007
- Intersection theory on the moduli space of Higgs bundles, MSRI, March 2002
- Intersection theory on toric hyperkahler varieties, MSRI, March 2002

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