Scientific Series

Higher spin symmetries are gauge symmetries sourced by massless particles with spin greater than two. When coupled with diffeomorphism, they give rise to higher spin gravity. After a review on higher spin gravity, I will discuss its holography and its embedding in the string theory. Finally I will talk about some applications of higher spin symmetry, both in string theory and in QFT. 

The discrete time-translation symmetry of a periodically-driven (Floquet) system allows for the existence of novel, nonequilibrium interacting phases of matter. A well-known example is the discrete time crystal, a phase characterized by the spontaneous breaking of this time-translation symmetry. In this talk, I will show that the presence of *multiple* time-translational symmetries, realized by quasiperiodically driving a system with two or more incommensurate frequencies, leads to a panoply of novel non-equilibrium phases of matter, both spontaneous symmetry breaking ("discrete time quasi-crystals") and topological. In order to stabilize such phases, I will outline rigorous mathematical results establishing slow heating of systems driven quasiperiodically at high frequencies. As a byproduct, I will introduce the notion of many-body localization (MBL) in quasiperiodically driven systems.

I will describe an example in which ER=EPR can be understood as a worldsheet string duality, by finding the Lorentzian continuation of the FZZ duality. The result is that string perturbation theory around the thermofield double state in a disconnected spacetime with a condensate of entangled folded strings is equivalent to string theory in a connected two sided black hole spacetime. Important ingredients are the Lorentzian interpretation of time winding vertex operators, and string theory with target space Schwinger-Keldysh contours. I will also discuss a related conjecture in AdS3-Rindler.

The core Python language is not particularly powerful or fast for numerical computing.  Fortunately, there is a large "numerical python" library, "numpy", that is a standard part of any Python-using scientist's toolkit.  I will present numpy, the associated "scientific python" library, "scipy", and the popular "matplotlib" plotting library.

I will talk about compact hyperkahler manifolds, which generalize the famous K3 surface to the higher dimensions. Given a compact simple hyperkahler manifold $M$, I will describe how the structure of cohomology algebra H*(M) is related with the so(b_2+2) Lie algebra action and the second cohomology group. I will explain how this is applied to the generalization of Kuga-Satake construction which allows us to assign for K3-type Hodge structure a Hodge structure of weight one (i.e. complex torus).

Advanced LIGO and Advanced Virgo are currently in the middle of their third observing run, and releasing open public event alerts for the first time. The LIGO-Virgo collaboration has issued 29 un-retracted candidate event alerts as of September 20th, 2019, potentially adding dozens more known compact binary object mergers to the eleven confident LIGO-Virgo detections from the first two Advanced-era observing runs. I’ll review novel LIGO-Virgo results to date, and discuss the challenges of extracting interesting new physics from noisy detector data. Finally, I'll summarize future prospects for astrophysics, cosmology, and tests of general relativity with gravitational waves, and the roadmap to future gravitational wave detectors on Earth and in space.

Hypermassive neutron stars (HMNS) can be briefly formed after a binary neutron star merger and are likely to be highly deformed and strongly oscillating. These oscillations may be seen as modulation of the associated short gamma-ray burst and could provide observational evidence for the HMNS phase. I will discuss the prospects for their detection and the important physical information that can be gained by their observation.

In this talk, I will describe some of the recent progress on computing holographic correlators using analytic bootstrap techniques combined with supersymmetric localization.  From taking a certain flat space limit of the holographic correlators, one can obtain scattering amplitudes of gravitons in string theory, and one can then reproduce some of the known results for these scattering amplitudes.  I will focus mostly on the case of the 4d {\cal N} = 4 super-Yang-Mills theory, but I will also mention related work in the 3d ABJM theory.

 Python is a widely used programming language for scientific
computing, data analysis, and machine learning. This tutorial will
feature an introduction for those with little or no background.

Non minimal couplings of scalar fields to gravity are a generic feature of Lagrangian formulations of gravity. Although challenging to probe at low energies and small curvature, such couplings can play a crucial role in cosmological setups. We focus on their impact in the production of scalar dark matter and its interplay with inflationary physics. We show how the standard non-thermal production mechanism of scalar dark matter, the misalignment mechanism, is modified, and explore how alternative scenarios like production from inflationary fluctuations become viable. We study potentially observable features of these scenarios, such as the enhancement of dark matter substructure at small scales and the generation of an isocurvature component in the fluctuations of the CMB.

A massive U(1)' gauge boson known as a “dark photon” or A', has long been proposed as a potential explanation for the muon g − 2 anomaly. Recently, experimental results have excluded this possibility for a dark photon decaying visibly and invisibly. I revisit this idea and consider a model where A' couples to inelastic dark matter, leading to a semi-visible decay mode. I show that for large mass splittings between the dark sector states this decay mode is enhanced, weakening the invisibly decaying dark photon bounds. As a consequence, A' resolves the g −2 anomaly in a region of parameter space the thermal dark matter component of the Universe is readily explained.

The category of coherent sheaves on an interesting variety X has an extremely annoying property: does not have enough projectives, so it cannot be equivalent to the category of modules over an algebra. However, if you pass to the derived category, this defect can be fixed in many interesting cases, by finding a tilting generator: that is, a vector bundle T such that any coherent sheaf can be resolved by a complex consisting of sums of copies of T, and Ext^i(T,T)=0 for all i>0. If A=End(T), then we obtain an equivalence of derived categories between finitely generated A-modules and Coh(X). This provides a bridge between representation theory and algebraic geometry. This bridge was largely built for us by Bezrukavnikov and Kaledin, but they did not make it very easy for the rest of us to cross it; in particular, while both ends of the bridge are in characteristic 0, the middle is in characteristic p. I’ll talk about how recent input from work in 3d field theory by Braverman, Finkelberg and Nakajima allows us in certain cases to reroute this bridge and avoid characteristic p, while getting a more concrete understanding of the algebra A on the other side.