Talks

The Callan Rubakov Effect describes the interaction between (massless) fermions and a smooth monopole in 4d gauge theory. In this scenario, the fermions can probe the UV physics inside the monopole core which leads to interesting effects such as proton decay in GUT models. However, the monopole-fermion scattering appears to lead to out-states that are not in the perturbative Hilbert space. In this talk, we will review this issue and propose a new physical mechanism that resolves this long-standing confusion.

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Zoom link: https://pitp.zoom.us/j/93551249905?pwd=REJvOUtTMlh6RU0vRjZnRVdZckgyZz09

A consequence of the works of Costello and Lurie is that the Hochschild chain complex of a Calabi-Yau category admit the structure of a framed E_2 algebra (the genus zero operations). I will describe a new algebraic point of view on these operations which admits generalizations to the setting of relative Calabi-Yau structures, which do not seem to fit into the framework of TQFTs. In particular, we obtain a generalization of string topology to manifolds with boundary, as well as interesting operations on Hochschild homology of Fano varieties. Time permitting, I will explain some applications to quiver varieties. This is joint work with Christopher Brav.

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Zoom link: https://pitp.zoom.us/j/97363589637?pwd=T25YS0ZYQlBSWm5maXhQTklpSm50UT09

Fermi liquid theory is a cornerstone of condensed matter physics. I will show how to formulate Fermi liquid theory as an effective field theory. In this approach, the space of low-energy states of a Fermi liquid is identified with a coadjoint orbit of the group of canonical transformations. The method naturally leads to a nonlinear bosonized description of the Fermi liquid with nonlinear corrections fixed by the geometry of the Fermi surface. I will present that the resulting local effective field theory captures both linear and nonlinear effects in Landau’s Fermi liquid theory. The approach can be extended to encompass non-Fermi liquids, which correspond to strongly interacting fixed points obtained by deforming Fermi liquids with relevant interactions. I will also discuss how Berry curvature can be captured in the effective field theory approach.

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Zoom link: https://pitp.zoom.us/j/95381972217?pwd=Ni9iQ2hrUVNnWTJERDRmZk9GaW1jZz09

Weyl geometry is a natural extension of conformal geometry with Weyl covariance mediated by a Weyl connection. We generalize the Fefferman-Graham (FG) ambient construction for conformal manifolds to a corresponding construction for Weyl manifolds. We first introduce the Weyl-ambient metric motivated by the Weyl-Fefferman-Graham (WFG) gauge, which is a generalization of the FG gauge for asymptotically locally AdS (AlAdS) spacetimes. Then, the Weyl-ambient space as a pseudo-Riemannian geometry induces a codimension-2 Weyl geometry. Through the Weyl-ambient construction, we investigate Weyl-covariant quantities on the Weyl manifold and define Weyl-obstruction tensors. We show that Weyl-obstruction tensors appear as poles in the Fefferman-Graham expansion of the AlAdS bulk metric for even boundary dimensions. Under holographic renormalization, we demonstrate that Weyl-obstruction tensors can be used as the building blocks for the Weyl anomaly of the dual quantum field theory.

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Zoom link https://pitp.zoom.us/j/91781363979?pwd=NlhjTVlHTlhMSTcxYnk5eExkTWFqdz09

Unimodularity is a classical notion shows up in various fields like linear algebra, lattices, Poisson algebras, etc. In this talk, we focus on unimodular Hopf algebras and unimodular tensor categories. We will introduce unimodular module categories and use them to construct Frobenius algebras and unimodular tensor categories. These ideas will be illustrated with examples drawn from Hopf algebras.

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Zoom link https://pitp.zoom.us/j/98477599322?pwd=UDJmTklMTGxGODJZTm1Xc1VhL2tDdz09

One hundred years after Heisenberg’s Uncertainty Principle, the question of how to make simultaneous measurements of noncommuting observables lingers. I will survey one hundred years of measurement theory, which brings us to the point where we can formulate how to measure any set observables weakly and simultaneously and then concatenate such measurements continuously to determine what is a strong measurement of the same observables. The description of the measurements is independent of quantum states---this we call instrument autonomy---and even independent of Hilbert space---this we call the universal Instrument Manifold Program. But what space, if not Hilbert space? It’s a whole new world: the Kraus operators of an instrument live in a Lie-group manifold generated by the measured observables themselves. I will describe measuring position and momentum and measuring the three components of angular momentum, special cases where the instrument approaches asymptotically a phase-space boundary of the instrumental Lie-group manifold populated by coherent states; these special universal instruments structure any Hilbert space in which they are represented. In contrast, for almost all sets of observables other than these special cases, the universal instrument descends into chaos ... literally. This work was done with Christopher S. Jackson, whose genius and vision inform every aspect.

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Zoom link https://pitp.zoom.us/j/94135518267?pwd=T2JOL21VaEcrY05KeG1SYTVYdHhxdz09