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Explore Ulam stability of Thompson groups through asymptotic cohomology. Gain insights into this rigidity property for discrete groups and its application to groups F, T, and V.
Explore Thompson's groups and finitely generated simple groups of homeomorphisms, with insights into joint research on finitely presented examples.
Explore percolation theory on groups, examining uniqueness and non-uniqueness of infinite clusters and their connections to group-theoretic concepts.
Explore topological and conformal dimensions of self-similar groups, examining their limit spaces and associated dynamical systems in geometric group theory.
Explore a non-symmetric version of Kesten's criterion for random walks on countable groups, relating to amenability and probability of return to identity.
Explore semi-classical analysis of strong cosmic censorship in General Relativity. Delve into quantum effects on Cauchy horizons and their implications for determinism in black hole spacetimes.
Explore a novel approach to gluing solutions of Einstein equations, removing obstructions and utilizing nonlinearity of constraint equations in General Relativity.
Explore Feynman and anti-Feynman inverses for wave operators on Lorentzian manifolds, connecting to self-adjointness and positivity properties of wave operators.
Explore new renormalisation group equations for curved spacetimes, focusing on perturbative algebraic quantum field theory and flow equations applicable to arbitrary globally hyperbolic spacetimes.
Explore Hadamard states for Maxwell fields through complete gauge fixing, delving into spectral theory and mathematical relativity concepts.
Explore electromagnetic scattering through a relative trace formula, examining perfectly conducting obstacles' impact on fields and the challenges posed by Maxwell's equations.
Explore infrared finite scattering theory in QFT and quantum gravity, addressing IR divergences, memory effects, and challenges in constructing IR-finite S-matrices across various theories.
Explore Feynman propagators on curved spacetime, their construction, and connection to quantum states. Delve into microlocal techniques and their application to wave and Dirac-type operators.
Explore wave equations in Kerr-de Sitter spacetimes, extending Vasy's results to the full subextremal range and analyzing photon trapping around black holes.
Explore nonlinear stability of slowly-rotating Kerr-de Sitter black holes, focusing on a new proof using vectorfield method and bootstrap scheme to uncover high-frequency spectral gap.
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