Talks

We will begin by reviewing the work of Kazhdan and Lusztig, who established an equivalence between certain affine Lie algebra representations and quantum group representations. It can be thought of as a logarithmic version of the CS-WZW correspondence. In a joint work with Lin Chen, we used factorization algebras to establish an extended version of this equivalence. We will explain the main structure of the proof, and draw some connections with Kazhdan and Lusztig's original proof. The key idea is that of Kac-Moody localization, a parametrized version of factorization homology. Time permitting, we will also explain how this idea plays a role in the recently announced proof (by Gaitsgory et al.) of the de Rham geometric Langlands conjecture.

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Zoom link https://pitp.zoom.us/j/98932564942?pwd=WWdMLzI5WktkZnMrQmplU0J3Mk43dz09

Obtaining a description of cosmology is a central open problem in holography. Studying simple models can help us gain insight on the generic properties of holographic cosmologies. In this talk I will describe the construction of entangled microstates of a pair of holographic CFTs whose dual semiclassical description includes big bang-big crunch AdS cosmologies in spaces without boundaries. The cosmology is supported by inhomogeneous heavy matter and it partially purifies the bulk entanglement of two auxiliary AdS spacetimes. In generic settings, the cosmology is an entanglement island contained in the entanglement wedge of one of the two CFTs. I will then describe the properties of the non-isometric bulk-to-boundary encoding map and comment on an explicit, state-dependent boundary representation of operators acting on the cosmology. Finally, if time allows, I will argue for a non-isometric to approximately-isometric transition of the encoding of "simple" cosmological states as a function of the bulk entanglement, with tensor network toy models of the setup as a guide.

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Zoom link https://pitp.zoom.us/j/93483219872?pwd=TGpJVVlaNDVGWTN5ZHpkTHp6a2hTZz09

In this talk, we will discuss some mathematical models that address the release of wolbachia-infected mosquito to replace or suppress the wild Aedes mosquito. In particular, we will present some results on the effect of temperature and quiescent eggs over the technique.