Talks

The cosmic microwave background radiation has been an indispensable tool for learning about the origins and evolution of our Observable Universe. Satellites and ground based experiments measuring the temperature and polarization anisotropies with ever increasing angular resolution and sensitivity have established the standard cosmological model, LCDM, and constrained or ruled out a huge variety of theoretical models of the early Universe. Most of this cosmological information has thus far been derived from the primary CMB, anisotropies largely sourced during the epoch of recombination some 380,000 years after the Big Bang. However, experiments are achieving the sensitivity and resolution necessary to access a whole new treasure-trove of cosmological information: secondary temperature and polarization anisotropies induced by photons scattering from mass (CMB lensing) and free electrons (the Sunyaev Zel'dovich effect). Unlike the primary CMB, where cosmological information is contained in the pattern of fluctuations in statistically isotropic temperature/polarization anisotropies, the secondary CMB encodes cosmological information in the statistical anisotropies of non-gaussian temperature/polarization fields on the sky. In this talk, I will describe the possibilities for future CMB experiments, in concert with large galaxy surveys, to reconstruct the cosmological information contained in the statistics of the secondary CMB anisotropies. In particular, I will describe the information that can be reconstructed from kinetic/polarized Sunyaev Zel'dovich effect, CMB lensing, and the moving lens effect. I speculate on what we might learn from future measurements, and conclude by discussing several projects in progress.

I will review the geometric approach to the description of Coulomb branches and Chern-Simons terms of gauge theories coming from compactifications of M-theory on elliptically fibered Calabi-Yau threefolds. Mathematically, this involves finding all the crepant resolutions of a given Weierstrass model and understanding the network of flops connecting them together with computing certain topological invariants. I will further check that the uplifted theory in 6d is anomaly-free using Green-Schwartz mechanism. I will give examples on the theory with semi-simple gauge groups such as SU(2)xG2, which plays a major role in the classification of 6d superconformal theories, and SU(2)xSU(3), which describes the non-abelian sector of the standard model.

We study correlations in fermionic systems with long-range interactions in thermal equilibrium. We prove an upper-bound on the correlation decay between anti-commut-ing operators based on long-range Lieb-Robinson type bounds. Our result shows that correlations between such operators in fermionic long-range systems of spatial dimension $D$ with at most two-site interactions decaying algebraically with the distance with an exponent $\alpha \geq 2\,D$, decay at least algebraically with an exponent arbitrarily close to $\alpha$. Our bound is asymptotically tight, which we demonstrate by numerically analysing density-density correlations in a 1D quadratic (free, exactly solvable) model, the Kitaev chain with long-range interactions. Away from the quantum critical point correlations in this model are found to decay asymptotically as slowly as our bound permits.