Search Talks

Cosmic microwave background (CMB) experiments, which currently provide some of the most powerful cosmological data sets, will become much more constraining in the near future. While these measurements promise to teach us more about the nature of dark energy, inflation and neutrino physics, increased precision will require special attention dedicated to the data analysis. In this talk I will focus on the gravitational lensing of the CMB and some of its implications. By introducing a novel analysis technique, applying it to the Planck satellite data and commenting on improvements which will be possible with a CMB Stage 4 experiment, I will first show how we can utilize CMB gravitational lensing to probe self-consistency of the CMB data sets. Then I will overview how gravitational lensing induces non-Gaussian covariances between the CMB data and how these covariances affect constraints on the cosmological parameters.

Teleportation, Superdense coding, Quantum Zeno effect, Looking ahead to Week 3 (classical vs. quantum state space & connection to Q. Zeno effect) - link to orginal teleportation paper.

Factorization spaces (introduced by Beilinson and Drinfeld as "factorization monoids") are non-linear analogues of factorization algebras. They can be constructed using algebro-geometric methods, and can be linearised to produce examples of factorization algebras, whose properties can be studied using the geometry of the underlying spaces. In this talk, we will recall the definition of a factorization space, and introduce the notion of a module over a factorization space, which is a non-linear analogue of a module over a factorization algebra. As an example and an application, we will introduce a moduli space of principal G-bundles with parabolic structures, and discuss how it can be linearised to recover modules of the factorization algebra associated to the affine Lie algebra corresponding to a reductive algebraic group G.

This is based on my joint work with Yaping Yang. In this talk, we use the equivariant elliptic cohomology theory to study the elliptic quantum groups.  We define a sheafified elliptic quantum group for any symmetric Kac-Moody Lie algebra. This definition is naturally obtained using the cohomological Hall algebra associated to the equivariant elliptic cohomology. After taking suitable rational sections, the sheafified elliptic quantum group becomes a quantum algebra consisting of the elliptic Drinfeld currents. The Drinfeld currents satisfy the relations of the elliptic quantum group studied by Felder and Gautam-Toledano Laredo. We show the elliptic quantum group acts on the equivariant elliptic cohomology of Nakajima quiver varieties.

In particular, the sheafified elliptic quantum group is an algebra object in a certain monoidal category of sheaves on the colored Hilbert scheme of an elliptic curve. This monoidal structure is related to Mirkovic’s refinement of the factorization structure on semi-infinite affine Grassmannian over an elliptic curve. If time permits, I will also talk about a work in progress, joint with Mirkovic and Yang, towards a construction of a double loop Grassmannian and vertex representations of the toroidal algebra, which in turn is related to representations of the elliptic quantum groups