MATHEMATICAL PICTURE LANGUAGE
July 14, 2020 10:00 amMany integrable critical classical statistical mechanical models and the corresponding quantum spin chains possess a fractional-spin conserved current. Such currents have been constructed by utilizing quantum-group algebras, fermionic and parafermionic...
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MATHEMATICAL PICTURE LANGUAGE
July 7, 2020 10:00 amThe connection between decay estimates for entropy and logarithmic Sobolev inequalities is well-established for dynamical systems on commutative systems. I will explain how to extend this to matrix-valued functions, and...
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MATHEMATICAL PICTURE LANGUAGE
June 30, 2020 10:00 amWe show that every quantum computation can be described by Bayesian update of a probability distribution on a finite state space. Negativity in a quasiprobability function is not required, neither in...
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MATHEMATICAL PICTURE LANGUAGE
June 23, 2020 10:00 amQuantum Fourier analysis is a subject that combines an algebraic Fourier transform (pictorial in the case of subfactor theory and topological quantum field theory) with analytic estimates. We give an...
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MATHEMATICAL PICTURE LANGUAGE
June 16, 2020 10:00 amInterference is an essential part of quantum mechanics. However, an important class of Hamiltonians considered are those with "no sign problem", where all off-diagonal matrix elements of the Hamiltonian are...
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MATHEMATICAL PICTURE LANGUAGE
June 9, 2020 10:00 amThe partition function of a quantum system without a sign problem can be represented by a path integral in which every amplitude is efficiently computable and nonnegative, which is a...
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INFORMAL GEOMETRY AND DYNAMICS
June 3, 2020 4:00 pmThurston's Master Teapot is the closure of the set of all points $(z,\lambda) \in \mathbb{C} \times \mathbb{R}$ such that $\lambda$ is the growth rate of a critically periodic unimodal self-map of...
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MATHEMATICAL PICTURE LANGUAGE
June 2, 2020 10:00 amKitaev's quantum double models in 2D provide some of the most commonly studied examples of topological quantum order. In particular, the ground space is thought to yield a quantum error-correcting...
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MATHEMATICAL PICTURE LANGUAGE
May 26, 2020 10:00 amI'll tell a mathematical story that runs from Archimedes' hat-box theorem of ~200BC (which he used to calculate the surface area of the sphere), to the properties of "Porter-Thomas" probability distributions,...
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RANDOM MATRIX
May 20, 2020 2:00 pmStarting from the classical Curie-Weiss model in statistical mechanics, we will consider more general Ising models. On the one hand, we introduce a block structure, i.e. a model of spins...
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