Scientific Series

According to the standard model of cosmology 96% of the matter and energy in the universe is invisible. The dark matter particles comprising the invisible material have so far not been detected in laboratory and astrophysical experiments.  The dark energy responsible for the acceleration of the universe is still a controversial issue. A modified gravity theory is presented that can potentially fit current cosmological and astrophysical data. The black holes and their shadows predicted by MOG can differ from the predictions of Einstein gravity.

Fast radio bursts (FRBs) are bright, broadband, non-repeating, millisecond flashes of unknown astronomical origin. The dispersion of these bursts by intervening plasma suggests that the sources of the 16 bursts reported to date= are at 0.2<z<1. I will discuss the possibility of using dispersion, instead of redshift, to study the large-scale structure of the Universe in three dimensions. Like redshift, which is distorted by peculiar velocities, dispersion is an imperfect proxy for distance as it is distorted by inhomogeneities in the electron density. These dispersion-space distortions are calculable and actually greatly enhance the signal. The clustering signal in dispersion space could be detected in a survey of 10 000 FRBs, as is expected to be produced by the CHIME telescope over three years.

The greatest uncertainty in whether this technique will be successful is the unknown nature of FRB sources. A new observation tells us more about the environment of a source than ever before through the polarization and scattering properties of a burst. More observations of this type, along with observations that identify host galaxies, will soon tell whether FRBs will provide a new probe of structure.

Let $S$ be a surface, $G$ a semi-simple group of type B, C or D. I will explain why the moduli space of framed local systems $A_{G,S}$ defined by Fock and Goncharov has the structure of a cluster variety, and fits inside a larger structure called a cluster ensemble. This was previously known only in type A. This gives a more direct proof of results of Fock and Goncharov for the symplectic and spin groups, and also allows one to quantize higher Teichmuller space in these cases. If time permits, I hope to talk about applications to counting tensor invariants of finite dimensional representations of these groups.

Quantum adiabatic optimization (QAO) slowly varies an initial Hamiltonian with an easy-to-prepare ground-state to a final Hamiltonian whose ground-state encodes the solution to some optimization problem. Currently, little is known about the performance of QAO relative to classical optimization algorithms as we still lack strong analytic tools for analyzing its performance. In this talk, I will unify the problem of bounding the runtime of one such class of Hamiltonians -- so-called stoquastic Hamiltonians -- with questions about functions on graphs, heat diffusion, and classical sub-stochastic processes. I will introduce new tools for bounding the spectral gap of stoquastic Hamiltonians and, by exploiting heat diffusion, show that one of these techniques also provides an optimal and previously unknown gap bound for particular classes of graphs. Using this intuition and combining heat diffusion with classical sub-stochastic processes, I will offer a classical adiabatic algorithm that exhibits behavior typically considered "quantum", such as tunneling.

In the rst part of this talk I will give a brief introduction to the variational class of continuous
matrix product states (cMPS). Then I will present a time evolution algorithm for cMPS with periodic
boundary conditions. In the second part, I will explain how to apply this method to simulate
atomtronic circuits. In particular, I will show results for persistent currents in an interacting bose
gas rotating in a ring shaped trap in the presence of an arti cial U(1) gauge potential.

The BPS spectrum of d=4 N=2 field theories in general contains not only hyper and vector-multipelts but also short multiplets of particles with arbitrarily high spin. These BPS states of higher spin reveal quite a peculiar behavior, so sometimes they are called "wild"

states. In this talk we would try to discuss a small refinement of the asymptotic study (spectral network technique) of tt* equations arising in an effective theory on 2d defects in N=2 4d SYM theory capturing spin information and apply it to study some properties of wild BPS spectra.

The vacuum energy changes when cosmological phase transitions take place, or in environments with high temperatures or chemical potentials.  The propagation of primordial gravity waves is affected through the trace anomaly, and eras where the vacuum energy dominates can lead tofeatures in the gravity wave spectrum.  High density phases of QCD in neutron stars, where the vacuum is rearranged, are also a novel probe:  The mass-radius relationships for neutron stars is sensitive to the equation of state appearing in the Einstein equations, which may depend on new dynamics associated with vacuum energy.  Such observations could potentially rule out large classes of explanations for the smallness of the currently observed cosmological constant.

In this talk I derive the evolution equations for two scalar fields with non-canonical field space metric up to third order in perturbation theory, employing the covariant formalism. These equations can be used to calculate the local bi- and trispectra of the non-minimal ekpyrotic model. Remarkably, the nearly scale-invariant entropy perturbations have vanishing bi- and trispectra during the ekpyrotic phase. However, an efficient conversion process to curvature perturbations induces local non-Gaussianity parameters f_NL and g_NL at levels that should be detectable by near-future observations.
In the second part of the talk I construct a new kind of cosmological model – conflation. The universe undergoes accelerated expansion, but with crucial differences compared to ordinary inflation. In particular, the potential energy is negative, which is of interest for supergravity and string theory where both negative potentials and the required scalar-tensor couplings are rather natural. A distinguishing feature of the model is that it does not amplify adiabatic scalar and tensor fluctuations, and in particular does not lead to eternal inflation and the associated infinities.

I discuss a new proposal for nonperturbatively defining chiral gauge theories, something that has resisted previous attempts. The proposal is a well defined field theoretic framework that contains mirror fermions with very soft form factors, which allows them to decouple, as well as ordinary fermions with conventional couplings.  The construction makes use of an extra dimension, which localizes chiral zeromodes on the boundaries, and a four dimensional gauge field extended into the bulk via classical gradient flow.  After explaining how this setup works, I consider open questions concerning the flow of topological gauge configurations, as well as possible exotic phenomenology in the Standard Model lurking at the low energy frontier.

We introduce the spectrum bifurcation renormalization group (SBRG) as an improvement of the excited-state real space renormalization group (RSRG-X) for qubit models. Starting from a disordered many-body Hamiltonian in the full many-body localized (MBL) phase, the SBRG flows to the MBL fixed-point Hamiltonian, and generates the local integrals of motion and the matrix product state representations for all eigenstates. The method is applicable to both spin and fermion models with arbitrary interaction strength on any lattice in all dimensions, as long as the models are in the full MBL phase. As a Hilbert-space preserving RG, the SBRG also generates an entanglement holographic mapping, which duals the MBL state to a fragmented holographic space.