Talks

After briefly reviewing the dictionary between branes of Type IIB string theory and representations of the simplest quantum toroidal algebra, I will present a new class of brane setups which I call spiralling branes. Partition functions of these remarkable configurations reproduce K-theoretic vertex partition function, while on the algebraic side they correspond to Drinfeld twists of R-matrices. Time permitting, I will also discuss other applications of spiralling branes.

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Rich clusters of galaxies are the largest gravitational magnifiers in the Universe. One of the most interesting gravitational lensing phenomena arises when background galaxies overlap with the lensing caustics cast by the cluster lens, such that a portion of it is tremendously magnified by hundreds to even thousands fold. As a result, Nature’s most luminous classes of stars have been individually or collectively detected by space telescopes from cosmological distances. Quantitatively studying their behavior will enable us to probe an impressive hierarchy of fine mass structures inside the lens: from star-free sub-galactic cold dark matter halos, to intracluster stars, and to even minuscule dark matter clumps predicted in many of the particle physics models of the dark matter. I will talk about what we have theoretically understood about the extremely magnified stars, what latest observational advances there are, and what unique constraints on dark matter micro-structures can be derived.

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The asymptotic theory of quantum channel estimation has been well established, but in general noiseless and controllable ancilla is required for attaining the ultimate limit in the asymptotic regime. Little is known about the metrological performance without noiseless ancilla, which is more relevant in practical circumstances. In this work, we present a novel theoretical framework to address this problem, bridging quantum metrology and the asymptotic theory of quantum channels. Leveraging this framework, we prove sufficient conditions for achieving the Heisenberg limit with repeated application of the channel to estimate, both with and without applying interleaved unitary control operations. For the latter case, we design an algorithm to identify the control operation. Finally, we analyze several intriguing examples by our approach.

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Determining the long-range phase of matter of a strongly coupled system from its microscopic description has long been one of the central topics in physics. Simple microscopic systems often become strongly coupled at long range where we usually rely on clever approximations. Bootstrap is an alternative approach that uses positivity and equations of motion to make predictions in quantum many-body systems without making approximations. In this talk, I will show my recent work on using bootstrap to compute the ground state energy, local observables and gaps of a quantum many-body system in the thermodynamic limit with rigorous error bars.

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A cosmological network of axion strings in our Universe today may leave its imprint on the polarization pattern of the cosmic microwave background radiation through the phenomenon of axion-string-induced birefringence. I will explain how this signal arises, discuss how it depends on the properties of the string network and the axion-photon coupling, describe how existing measurements of anisotropic birefringence place constraints on axion strings, and discuss how the non-Gaussian nature of this signal could be leveraged in searches with future data.

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