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Integrability and Braided Tensor Categories

MATHEMATICAL PICTURE LANGUAGE

July 14, 2020      10:00 am
Speaker: Paul Fendley - All Souls College, Oxford University

Many 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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Decay estimates and complete Bakry-Emry theory

MATHEMATICAL PICTURE LANGUAGE

July 7, 2020      10:00 am
Speaker: Marius Junge - University of Illinois at Urbana-Champaign

The 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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Quantum Fourier analysis

MATHEMATICAL PICTURE LANGUAGE

June 23, 2020      10:00 am
Speaker: Zhengwei Liu - Tsinghua University

Quantum 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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The power of adiabatic quantum computation with no sign problem

MATHEMATICAL PICTURE LANGUAGE

June 16, 2020      10:00 am
Speaker: Matthew Hastings - Microsoft (Station Q and Redmond)

Interference 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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Kitaev’s finite group model as an error correcting code

MATHEMATICAL PICTURE LANGUAGE

June 2, 2020      10:00 am
Speaker: Shawn Cui - Perdue University

Kitaev'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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From Archimedes to Quantum Supremacy

MATHEMATICAL PICTURE LANGUAGE

May 26, 2020      10:00 am
Speaker: Scott Aaronson - University of Texas at Austin

I'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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Euclidean quantum field theory: axioms and automorphic forms

MATHEMATICAL PICTURE LANGUAGE

May 12, 2020      10:00 am
Speaker: Werner Nahm - Dublin Institute for Advanced Study

The partition functions of euclidean quantum field theory can be described as functions on the moduli space of compact manifolds with Riemanninan metric that have few generalized derivatives. The conventional...
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