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Fault-tolerant quantum computers will compute by applying
a sequence of elementary unitary operations, or gates, to an
error-protected subspace.   While algorithms are typically expressed
over arbitrary local gates, there is unfortunately no known theory
that can correct errors for a continuous set of quantum gates.
However, theory does support the fault-tolerant construction of
various finite gate sets, which in some cases generate circuits that
can approximate arbitrary gates to any desired precision.   In this
talk, I will present a framework for approximating arbitrary qubit
unitaries over a very general but natural class of gate sets derived
from the theory of integral quaternions over number fields, where the
complexity of a unitary is algebraically encoded in the length of a
corresponding quaternion.  Then I will explore the role played by
higher-dimensional generalizations of the Pauli gates in various
physical and mathematical settings, from classifying bulk-boundary
correspondences of abelian fractional quantum Hall states to
generating optimal symmetric quantum measurements with surprising
connections to Hilbert's 12th problem on explicit class field theory
for real quadratic number fields.

Even the greatest scientists have made some serious blunders. "Brilliant Blunders" concerns the evolution of life on Earth, of the Earth itself, of stars, and of the universe as a whole.

In this talk, astrophysicist Dr. Mario Livio will explore and analyze major errors committed by such luminaries as Charles Darwin, Linus Pauling, and Albert Einstein. Dr. Livio will scrutinize the various types of blunders and attempt to explain how they happen. Blunders are not only inevitable, argues Dr. Livio, but also an integral component of the process of science.

100 years after the existence of gravitational waves was first postulated by Albert Einstein, the LIGO and Virgo Collaborations detected gravitational waves for the first time on September 14, 2015. The gravitational waves originated from a pair of black holes that merged over one billion years ago.  The merger was so powerful that it shook the very fabric of space and sent a ripple across the Universe that we observed here on Earth at present day. Although this event was but a blip in a sea of data taken by various experiments over the last several decades, it represents a paradigm shift in how we study our Universe.

In this colloquium, I will present some of the history of this great discovery and what it means for our future at the dawn of gravitational wave astronomy.

Recent findings on quantitative growth patterns have revealed striking generalities across the tree of life, and recurring over distinct levels of organization. Growth-mass relationships in 1) individual growth to maturity, 2) population reproduction, 3) insect colony enlargement and 4)  community production across wholeecosystems of very different types, often follow highly robust near ¾ scaling laws. These patterns represent some of the most general relations in biology, but the reasons they are so strangely similar across levels of organization remains a mystery. The dynamics of these distinct levels are connected, yet their scaling can be shown to arise independently, and free of system-specific properties. Numerous experiments in prebiotic chemistry have shown that minimal self-replicating systems that undergo template-directed synthesis, typically show reaction orders (ie. growth-mass exponents) between ½ and 1. I will outline how modifications to these simplified reaction schemes can yield growth-mass exponents near ¾, which may offer insight into dynamical connections across hierarchical systems.