Talks

For a family of finite rate stabilizer codes, one can define two distinct error correction thresholds: the usual "block" threshold for the entire code, and the single-qubit threshold, where we only care about the stability of a single encoded qubit corresponding to a randomly chosen conjugate pair of logical X and Z operators.  Our main result is that in the case of erasures, for hyperbolic surface codes related to a {p,q} tiling of the hyperbolic plane, it is the latter threshold that coincides exactly with the infinite-graph edge percolation transition.  I will also discuss likely generalizations to more general codes and other error models. This is joint work with Nicolas Delfosse.

General relativity taught us that space time is dynamical and quantum theory posits that dynamical objects are quantum. Hence the Newtonian notion of space time as a passive stage where physics takes place needs to be replaced by a notion of quantum space time which is interacting with all other quantum matter fields.

I will present recent developments that aim at constructing quantum space time. In particular I will explain how  topological quantum field theories give rise to new quantum geometry realizations and how these serve as starting points  for the construction of a  dynamics  of quantum gravity, which is consistent over all scales.  Such a dynamics will then determine the properties of quantum space time.  

I discuss a string theoretic approach to integrable lattice models. This approach provides a unified perspective on various important notions in lattice models, and relates these notions to four-dimensional N = 1 supersymmetric field theories and their surface operators.  I explain how my construction connects to Costello's work and the Nekrasov-Shatashvili correspondence.

The properties of physical processes reflect themselves in the structure of the relevant observables. This idea has been largely exploited for the flat space  S-matrix, whose analytic structure is determined by locality and unitary, the two pillars which our current understanding of nature is based on. In this context, it  has been possible to find new mathematical structures whose properties turn out to be the ones we ascribe to scattering processes in flat-space, so that both  unitarity and locality can be viewed as emergent from some more fundamental structure. However, the S-matrix does certainly not exhaust all the physical information contained in a theory and thus an interesting question to ask is whether and how we can get a similar and deeper understanding of other observables.

In this talk I will report on some recent progress towards such a formulation for quantities such as the universe wave-function and late-time correlators. In particular, I will focus on the perturbative representations of such quantities, their analytic properties and their geometrical interpretation as volumes of certain new polytopes. I  will consider a specific toy model which allows to extend most of the discussion to other set-ups than the cosmological one, such as flat and AdS space-times.

Topological phases of matter serve as one of the most striking examples of the richness and novelty of quantum systems with many degrees of freedom.  In contrast to conventional matter, they are characterized by both non-local properties and non-classical notions such as entanglement.  I will discuss two broad categories of topological phases, distinguished by whether or not they possess fractionalized “anyon” excitations that are neither bosons nor fermions.  I will demonstrate that entanglement not only provides an understanding of such phases but also enables the transmutation between these two categories of topological phases. 

This talk concerns a family of special functions common to the study of quantum conformal blocks and hypergeometric solutions to q-KZB type equations.  In the first half, I will explain two methods for their construction -- as traces of intertwining operators between representations of quantum affine algebras and as certain theta hypergeometric integrals we term Felder-Varchenko functions.  I will then explain our proof by bosonization the first case of Etingof-Varchenko's conjecture that these constructions are related by a simple renormalization.

The second half of the talk will concern applications to affine Macdonald theory.  I will present refinements of the denominator and evaluation conjectures for affine Macdonald polynomials proposed by Etingof-Kirillov Jr.  I will then explain how to prove the first non-trivial cases of these conjectures by combining the methods of the first half and well-chosen applications of the elliptic beta integral.   The second half of this talk is joint work with E. Rains and A. Varchenko.