Search Talks

We have great certainty on how gravity works around our solar system: General Relativity (GR) has been found to be very accurate at these small scales. On large scales though, we still have a considerable lack of understanding about the evolution of the universe, and its constituents. While the LCDM model is in good agreement with cosmological data, this might change in the future. For this reason, we need to test GR on these scales.

There are a number of proposals on how to characterize deviations from GR on larges scales, by parametrizing different cosmological evolutions of the universe - the PPF, EFT and EA approaches. The objective is to use experimental data to constrain these parameters, and thus identify the most accurate cosmological model. In this talk I will show an alternative, systematic and general, parametrization method, in which we construct the most general quadratic action for linear cosmological perturbations, given some field content and gauge symmetries. I will show the example of linearly diffeomorphism-invariant scalar-tensor theories, in which case the parametrization encompasses well-known theories such as Horndeski and Beyond Horndeski. The method can straightforwardly be applied to any gravity theory with any fields and gauge symmetries.

Questions of nonlinear stability in global AdS space have recently received a significant amount of attention, both as an interesting problem in mathematical general relativity and nonlinear dynamics, and in relation to thermalization studies within the AdS/CFT paradigm. Working with nonlinear perturbation theory (the main technique available for analytic studies in this area) requires a thorough understanding of the properties of linearized AdS fields'

mode functions, which are the fundamental building blocks in perturbative treatments of nonlinearities. While complicated explicit expressions for these mode functions are available in the literature, they hide a good deal of the elegant underlying structure dictated by the AdS symmetries. Extending the mode functions in the flat embedding space (in which the AdS space can be realized as a hyperboloid) results in families of homogeneous polynomials, on which the AdS isometries act in a straightforward manner. This suggests a simple proof of important selection rules in nonlinear perturbation theory.

Studies of multiplet structures of the mode functions furthermore reveal a relation to the Higgs oscillator, a well-known quantum-mechanical superintegrable system. This AdS connection leads to an explicit construction of the hidden symmetry generators for the Higgs oscillator, a long-standing problem in mathematical quantum mechanics.

We discuss how to formulate a quantum field theory of dark energy interacting with dark matter. We show that the proposals based on the assumption that dark matter is made up of heavy particles with masses which are very sensitive to the value of dark energy are strongly constrained. Quintessence-generated long range forces and radiative stability of the quintessence potential require that such dark matter and dark energy are completely decoupled. However, if dark energy and a fraction of dark matter are very light axions, they can have significant mixings which are radiatively stable and perfectly consistent with quantum field theory. Such models can naturally occur in multi-axion realizations of monodromies. The mixings yield interesting signatures which are observable and are within current cosmological limits but could be constrained further by future observations.

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.

I will discuss the stability and breakdown of the topological classification of gapped ground states of non-interacting fermions, the tenfold way, in the presence of quartic fermion-fermion interactions.  In our approach [1], the effects of interactions on the boundary gapless modes are encoded in terms of boundary dynamical masses. Breakdown of the non-interacting topological classification occurs when the quantum nonlinear sigma models for the boundary dynamical masses favor quantum disordered phases.  The non-interacting topological classification $Z$ in odd spatial dimensions is unstable and reduces to $Z_N$ that can be identified explicitly for any dimension and any defining symmetries.
[1] T. Morimoto, A. Furusaki, and C. Mudry, Phys. Rev. B 91, 235111 (2015).

I will discuss how we constrain properties of the universe using two
tracers of large scale structure measured by the BOSS (Baryon
Oscillations Spectroscopic Experiment): galaxies and Lyman-alpha
forest. I will show recent results from baryonic acoustic oscillations
measured in both tracers and discuss cosmological implications. I
will briefly mention other measurements and consider forecasts for
quasar-forest bispectrum to constrain primordial non-Gaussianity.

Topological factorization homology is an invariant of manifolds which enjoys a hybrid of the structures in topological field theory, and in singular homology.  These invariants are especially interesting when we restrict attention to the factorization homology of surfaces, with coefficients in braided tensor categories.  In this talk, I would like to explain a technique, related to Beck monadicity, which allows us to compute these abstractly defined categories, as modules for explicitly computable, and in many cases well-known, algebras.

The algebras produced in this way for the annulus and punctured torus are the so-called ``reflection equation algebra" and "quantum differential equation algebra", respectively.  When we close up punctures, a variation on the our formalism naturally reproduces the framework of quantum Hamiltonian reduction, and leads to simultaneous deformations of categories D(g/G) of character sheaves on g, on the one hand, and categories QC(Ch_G(T^2)), of quasi-coherent sheaves on the character variety of T^2, on the other.  We call these deformations "quantum character varieties", and they form the two-dimensional part of a four dimensional TFT related to Kapustin-Witten's geometric Langlands TFT, or "topologically twisted N=4 SYM".

I will review recent progress on theory of many-body localization, mostly focusing on properties of the many-body localized phase itself.

I will discuss explicit construction of effective Hamiltonians governing the dynamics of conserved quantities.  The analysis reveals several inequivalent length scales in the system, some of which do not appear to diverge on the approach to the thermalized phase.

Experimental protocols to measure these length scales will also be discussed.

Numerical results suggest that the quantum Hall effect at {\nu} = 5/2 is described by the Pfaffian or anti-Pfaffian state in the absence of disorder and Landau level mixing. Those states are incompatible with the observed transport properties of GaAs heterostructures, where disorder and Landau level mixing are strong. We show that the recent proposal of a PH-Pfaffian topological order by Son is consistent with all experiments. The absence of the particle-hole symmetry at {\nu} =

5/2 is not an obstacle to the existence of the PH-Pfaffian order since the order is robust to symmetry breaking.