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There is a close relationship between derived loop spaces, a geometric object, and Hochschild homology, a categorical invariant, made possible by derived algebraic geometry, thus allowing for both intuitive insights and new computational tools.  In the case of a quotient stack, we discuss a "Jordan decomposition" of loops which is made precise by an equivariant localization result.  We also discuss an Atiyah-Segal completion theorem which relates completed periodic cyclic homology to Betti cohomology.

Albert Einstein predicted a century ago the existence of gravitational waves – ripples in the fabric of spacetime moving at the speed of light. It was believed that these ripples were so faint that no experiment would ever be precise enough to detect them. But in September 2015, LIGO did exactly that. The teams working with the Laser Interferometer Gravitational-wave Observatory (LIGO) detectors in Louisiana and Washington measured a loud gravitational wave signal as it traveled through the Earth after a billion-year journey from the violent merger of two black holes.

Since that first detection, scientists have measured many more gravitational waves, including a signal produced by colliding neutron stars captured by LIGO and the Virgo detector in Europe in 2017. That cataclysm also generated electromagnetic waves – light – detected by numerous other telescopes, and helped scientists understand how gold is created in deep space.

In a special public lecture webcast at Perimeter Institute on October 23, 2019, Gabriela González will provide a first-hand account of LIGO’s century-in-the-making breakthrough, and explain observations made as recently as this year. González, a professor of physics and astronomy at Louisiana State University and former spokesperson of the LIGO collaboration, will take the audience on a journey to some of the universe’s most violent places, and explain how such distant events can lead to a very bright future here on Earth.

There is a profound lack of diversity in science labs and classrooms, which has a negative impact on productivity. Scientific research demonstrates that diverse groups are more creative and better able to solve problems. Though the perception is that things are improving, NSERC’s recently released report shows that attrition rates in Canadian STEM fields are higher for women than for men at all career stages and that the percentage of women has not changed substantially in the last 15 years. Racialized and Indigenous people are also underrepresented at Canadian universities. This seminar will explore the scientific research surrounding EDI in hiring, writing reference letters, reviewing grants, and managing trainees. Also included are tips and tricks for incorporating EDI into grant applications.

Many free-fermion topological phases can be diagnosed by analyzing a suitable collection of symmetry data. While the Fu-Kane parity criterion for topological insulators is an early example, the systematic generalization to cover all possible crystalline symmetries and their associated topological phases has only recently been achieved. Interestingly, a key step in the generalization is to recognize the importance of understanding the entanglement-free product states: once these trivial phases are completely mapped, the topological ones are naturally exposed as the “remainders.” In this talk, we will first introduce the theory of symmetry indicators for topological (crystalline) insulators and semimetals, and then discuss how it can be generalized to cover superconductors.

The AdS/CFT correspondence provides a remarkably useful tool
for asking questions in quantum gravity, as it formulates a theory of
quantum gravity in terms of an ordinary non-gravitational quantum field
theory.  Fruitfully exploiting this correspondence therefore requires
understanding how to translate the language of CFT into gravity; a key
insight that has emerged over the past decade is that the entanglement
structure of the CFT must be intimately tied to the emergence of the
gravitational dual (when a classical geometric picture even exists).  In
my talk, I'll review what is currently known about this emergence
(so-called bulk reconstruction), and then discuss some recent results on
precisely how the entanglement of the CFT fixes the geometry on the
gravitational side.  I'll conclude with some open directions, notably
how the result I'll present is amenable to incorporating quantum
corrections.

Making use of modern multi-core computers (and multi-machine supercomputers) in Python can be achieved in a few different ways.  I will present the built-in Python “multiprocessing” module approach, which tends to work well and relatively painlessly for “naturally parallel” (aka “embarrassingly parallel”) problems. I’ll show what is required to use this approach, including how to submit jobs to the Slurm batch system on Symmetry.