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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...

### 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...

### A hidden variable model for universal quantum computation with magic states on qubits

MATHEMATICAL PICTURE LANGUAGE

June 30, 2020      10:00 am
Speaker: Robert Raussendorf - University of British Columbia

We 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...

### 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...

### 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...

### The sign problem and its relation to the spectral gap of quantum many-body systems

MATHEMATICAL PICTURE LANGUAGE

June 9, 2020      10:00 am
Speaker: Elizabeth Crosson - University of New Mexico

The 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...

### Slices of Thurston’s Master Teapot

INFORMAL GEOMETRY AND DYNAMICS

June 3, 2020      4:00 pm
Speaker: Kathryn Lindsey - Boston College

Thurston'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...

### 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...

### 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,...

### Fluctuation Results for General Ising Models — Block Spin Ising Models and Random Interactions

RANDOM MATRIX

May 20, 2020      2:00 pm
Speaker: Kristina Schubert - TU Dortmund

Starting 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...