This volume contains the proceedings of the AMS-EMS-SMF Special Session on Advances in Functional Analysis and Operator Theory, held July 18-22, 2022, at the Universite de Grenoble-Alpes, Grenoble, France. The papers reflect the modern interplay between differential equations, functional analysis, operator algebras, and their applications from the dynamics to quantum groups to number theory. Among the topics discussed are the Sturm-Liouville and boundary value problems, axioms of quantum mechanics, $C^{*}$-algebras and symbolic dynamics, von Neumann algebras and low-dimensional topology, quantum permutation groups, the Jordan algebras, and the Kadison-Singer transforms.
Nazim Kerimov and Yagub Aliyev, Minimality conditions for Sturm-Liouville problems with a boundary condition depending affinely or quadratically on an eigenparameter
Anar Assanova, Carsten Trunk, and Roza Uteshova, On the solvability of boundary value problems for linear differential-algebraic equations with constant coefficients
Kevin Aguyar Brix, Invertible and noninvertible symbolic dynamics and their C*-algebras
Volodymyr Derkach and Carsten Trunk, $\mathcal{PT}$-symmetric couplings of dual pairs
Vladimir Dragovic and Vasilisa Shramchenko, Chebyshev dynamics on two and three intervals and isomonodromic deformations
Gabor Etesi, The universal von Neumann algebra of smooth four-manifolds revisited
Amaury Freslon, Advances in quantum permutation groups
Oleg Friedman and Alexander A. Katz, A note on the quotient of a locally $JC$-algebra by a closed Jordan ideal
Cristian Ivanescu and Dan Kucerovsky, Villadsen idempotents
Dan Kucerovsky, A remark on the Kadison-Singer transform
Igor V. Nikolaev, Sharafevich-Tate groups of abelian varieties
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