Talks

I will talk about some connections among the GKZ (introduced by Gelfand-Kapranov-Zelevinsky) hypergeometric series, orbifold singularities of the system, and chain integrals in some geometry.  The GKZ hypergeometric series appeared in some very interesting contexts including arithmetic geometry, enumerative geometry and mathematical physics in the last few decades. I will report some new geometric realizations and interpretations of them.

In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study local quantum many-body systems at low energies. 

In this talk, I will describe how a tensor network representation of a quantum many-body ground state also encodes, in a natural way, another quantum many-body state whose properties must be related to the ground state in a systematic way. One can apply this tensor network state correspondence to the multi-scale entanglement renormalization ansatz (MERA) representation of the ground state of a one dimensional (1D) quantum lattice system to obtain a quantum many-body state of a 2D hyperbolic quantum lattice, whose boundary is the original 1D lattice. I propose that this bulk/boundary correspondence could potentially be a candidate implementation of the holographic correspondence of String theory on a lattice using the MERA.

For the MERA representation of a critical ground state I will show how the critical properties can be obtained from the corresponding bulk state, in particular, illustrating how point-like boundary operators are identified with extended operators in the bulk. I will also describe the entanglement and correlations in the bulk state, present numerical results that illustrate that the bulk entanglement may depend on the boundary critical charge, and describe how the bulk state can be described in terms of "holographic screens". If the boundary state has a global symmetry, the corresponding bulk state has a local gauge symmetry (described by the same group). In fact, the bulk state decomposes in terms of spin networks as they appear in lattice gauge theory, where they describe the gauge-invariant sector of the theory (here, the bulk). This decomposition also reveals entanglement between gauge degrees of freedom in the bulk, which are dual to a global symmetry at the  boundary, and remaining bulk degrees of freedom which may potentially include gravitational degrees of freedom in a holographic interpretation of the MERA.

I discuss, from a quantum information perspective, recent proposals of Maldacena, Ryu, Takayanagi, van Raamsdonk, Swingle, and Susskind that spacetime is an emergent property of the quantum entanglement of an associated boundary quantum system. I review the idea that the informational principle of minimal complexity determines a dual holographic bulk spacetime from a minimal quantum circuit U preparing a given boundary state from a trivial reference state. I describe how this idea may be extended to determine the relationship between the fluctuations of the bulk holographic geometry and the fluctuations of the boundary low-energy subspace. In this way we obtain, for every quantum system, an Einstein-like equation of motion for what might be interpreted as a bulk gravity theory dual to the boundary system. If time permits I will comment on the link to Brownian quantum circuits and tensor networks. 

In my talk I will consider resurgence properties of Chern-Simons
theory on compact 3-manifolds. I will also describe what role
resurgence plays in the problem of categorification of Chern-Simons
theory, that is the problem of generalizing Khovanov homology of knots
to compact 3-manifolds.

Supposing there exists no new physics stabilizing the weak scale, the Standard Model Higgs potential exhibits a true vacuum at large field values, rendering the electroweak vacuum metastable (i.e., long lived relative to the age of the Universe). While this scenario need not preclude our current existence, it may not reconcile with a period of large(ish)-field inflation---large fluctuations in the Higgs field, induced by the inflationary energy density, can lead to the field locally sampling the unstable/true vacuum part of the potential, with potentially disastrous consequences. Evaluating the extent to which large-field inflation and the Higgs vacuum instability are incompatible requires understanding (i) how Higgs fluctuations evolve during inflation and (ii) the fate of large local fluctuations that sample the part of the potential beyond the barrier that separates the electroweak and true vacua. In this talk, I will discuss both of these aspects, and explain the implications for large-field inflation.

In this seminar, I will present two promising ways in which the cosmic microwave background (CMB) sheds light on critical uncertain physics and systematics of the large-scale structure.
       Shear calibration with CMB lensing (arXiv:1607.01761):
Realizing the full potential of upcoming weak lensing surveys requires an exquisite understanding of the errors in galaxy shape estimation. In particular, such errors lead to a multiplicative bias in the shear, degenerate with the matter density parameter and the amplitude of fluctuations. Its redshift-evolution can hide the true evolution of the growth of structure, which probes dark energy and possible modifications to general relativity. I will show that CMB lensing from a stage 4 experiment (CMB S4) can self-calibrate the shear for an LSST-like optical lensing experiment. This holds in the presence of photo-z errors and intrinsic alignment.
       Evidence for the kinematic Sunyaev-Zel'dovich (kSZ) effect (arXiv:1510.06442); cluster energetics:

Through the kSZ effect, the baryon momentum field is imprinted on the CMB. I will report significant evidence for the kSZ effect from ACTPol and peculiar velocities reconstructed from BOSS. I will present the prospects for constraining cluster gas profiles and energetics from the kSZ effect with SPT-3G, AdvACT and CMB S4. This will provide constraints for galaxy formation and feedback models.

I'll describe a family of algebras called shifted Yangians, which arise as deformation quantizations of certain spaces related to loop groups.  I'll also describe coproducts for these algebras, which are related to multiplication in the loop group.  Physically, this fits into the story of Coulomb branches associated to 3d N=4 quiver gauge theories, where the above multiplication maps arises by taking products of scattering matrices.