I will introduce the QAOA and discuss some recent developments. These might include the application of the QAOA to the Sherrington-Kirkpatrick model, landscape independence, and the odd behavior when starting in a good place.
Classical simulation algorithms provide a rigorous ground for investigating quantum resources responsible for quantum speedup. In my talk, I will consider one such algorithm provided by Lambda polytopes. These polytopes are defined to be the polar dual of the stabilizer polytopes and can be used to provide a hidden variable model for finite-dimensional quantum theory. This hidden variable model can be turned into a classical algorithm that can simulate any quantum computation. The efficiency of this algorithm depends on the combinatorial structure of the polytope. In general, which subset of the vertices gives rise to efficient simulation is an open problem. I will describe some of the known classes of vertices and available methods for studying this polytope.
The language of integrable systems is widely applicable to string theory. One context where it is useful is the Seiberg-Witten theory, describing low-energy dynamics of confined 4d N=2 supersymmetric gauge theories: the families of complex curves with differentials, playing a central role in this description, appeared to be spectral curves, solving the integrable systems of interacting particles. Moreover, the spectrum of stable BPS particles appears from the consideration of hyperkahler structures on the phase spaces of integrable systems. And the full partition functions of instantons, regularized by Omega-background, solve deuatonomized systems of particles.
In my talk, I will explain correspondence unifying to some extent two latter ones. It relates discrete dynamics of so-called cluster integrable systems and partition functions of 5d N=1 supersymmetric gauge theories, or more generally of topological stings on corresponding local Calabi-Yau manifolds. Based on the simplest non-trivial example, I will show how both "equations" and "solutions" sides of correspondence naturally appear in the simple statistical models of dimers and "melting crystals" made out of them.
A dark energy-like component in the early universe, known as early dark energy (EDE), is a proposed solution to the Hubble tension. In this talk, I will describe how a frequentist profile likelihood yields important complementary information compared to a Bayesian MCMC analysis. While in an MCMC analysis, the EDE model is clearly disfavoured by Cosmic Microwave Background and large-scale structure data, a profile likelihood analysis prefers consistently larger amounts of EDE and with that a Hubble constant consistent with the SH0ES measurement for the same data sets. The difference between MCMC and profile likelihood can be explained by prior volume effects in the MCMC analysis. I will discuss how frequentist and Bayesian methods can give important complementary information in the context of beyond-LCDM models.
Optimal extraction of the non-Gaussian information encoded in the Large-Scale Structure (LSS) of the universe lies at the forefront of modern precision cosmology. In this talk, I will discuss recent efforts to achieve this task using the Wavelet Scattering Transform (WST), which subjects an input field to a layer of non-linear transformations that are sensitive to non-Gaussianity in spatial density distributions through a generated set of WST coefficients. In order to assess its applicability in the context of LSS surveys, I will present the first WST application to actual galaxy observations, through a WST re-analysis of the BOSS DR12 CMASS dataset. After laying out the procedure on how to capture all necessary layers of realism for an application on data obtained from a spectroscopic survey, I will show results for the marginalized posterior probability distributions of 5 cosmological parameters obtained from a WST likelihood analysis of the CMASS data. The WST is found to deliver a substantial improvement in the values of the predicted 1σ errors compared to the regular galaxy power spectrum, both in the case of flat and uninformative priors and also when a Big Bang Nucleosynthesis prior is applied to the value of ω_b. Finally, I will discuss ongoing follow-up work towards applying this estimator to the next generation of spectroscopic observations to be obtained by the DESI and Euclid surveys.