Next time you lose your paddle whilst canoeing - don't despair. There is another way to push your canoe forwards: by jumping on it! Gunwale bobbing refers to the act of standing on the gunwales (side walls) of a canoe and forcing it into oscillations with one's legs. When forced at the right frequency, the canoe can surf from crest to crest of the generated wave field by pushing into positive surface gradients.
buckling
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K-theoretic classification of inductive limit actions of fusion categories on AF-algebras
Abstract
I will introduce a K-theoretic complete invariant of inductive limits of finite dimensional actions of fusion categories on unital AF-algebras. This framework encompasses all such actions by finite groups on AF-algebras. Our classification result essentially follows from applying Elliott's Intertwining Argument adapted to this equivariant context, combined with tensor categorical techniques.
Our invariant roughly consists of a finite list of pre-ordered abelian groups and positive homomorphisms, which can be computed in principle. Under certain conditions this can be done in full detail. For example, using our classification theorem, we can show torsion-free fusion categories admit a unique AF-action on certain AF-algebras.
Connecting with subfactors, inspired by Popa’s classification of finite-depth hyperfinite subfactors by their standard invariant, we study unital inclusions of AF-algebras with trivial centers, as natural analogues of hyperfinite II_1 subfactors. We introduce the notion of strongly AF-inclusions and an Extended Standard Invariant, which characterizes them up to equivalence.
Nonlinear and dispersive waves in a basin: theory and numerical analysis
Abstract
Surface water waves of significant interest, such as tsunamis and solitary waves, are nonlinear and dispersive waves. Unluckily, the equations derived from first principles that describe the propagation of surface water waves, known as Euler's equations, are immensely hard to study. For this reason, several approximate systems have been proposed as mathematical alternatives. We show that among the numerous simplified systems of PDEs of water wave theory there is only one that is provably well-posed (in Hadamard’s sense) in bounded domains with slip-wall boundary conditions. We also show that the particular well-posed system obeys most of the physical laws that acceptable water wave equations must obey, and it is consistent with the Euler equations. For the numerical solution of our system we rely on a Galerkin/finite element method based on Nitsche's method for which we have proved its convergence. Validation with laboratory data is also presented.