Talks

We give a quantum speedup for solving the canonical semidefinite programming relaxation for binary quadratic optimization. The class of relaxations for combinatorial optimization has so far eluded quantum speedups. Our methods combine ideas from quantum Gibbs sampling and matrix exponent updates. A de-quantization of the algorithm also leads to a faster classical solver. For generic instances, our quantum solver gives a nearly quadratic speedup over state-of-the-art algorithms.
This is joint work with Fernando Brandao (Caltech) and Daniel Stilck Franca (QMATH, Copenhagen).

The asymptotic symmetry charge algebra of certain class of spacetimes could have a nontrivial central extension, which measures the non-equivariance of the charges of the large gauge transformations. The Cardy formula of the dual CFT has been famously used to derive black hole entropy. However, it remains obscure from the point of view of gravity why such a constant on the gravitational phase space could encode the information about the density of black hole micro-states, and what the degrees of freedom accounting for the black hole entropy truly are. I will discuss the ongoing efforts of understanding these questions in the covariant phase space formalism.

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.