Talks

The moduli of Higgs bundles and the Hitchin fibration are central to many thriving research areas, such as mirror symmetry, non-abelian Hodge theory and the geometric Langlands program.  A group-theoretic or multiplicative version was introduced by Frenkel and Ngo in 2011 to give a geometric interpretation of orbital integrals and trace formulas from automorphic representation theory. Since then, there is an ongoing program to replicate the theory of Higgs bundles for the multiplicative case. One notable development is the study of multiplicative affine Springer fibers. Like the usual ones, they are local analogues of multiplicative Hitchin fibers. In this talk, I discuss my work in continuing this program and providing a multiplicative version of Z. Yun's global Springer theory. This involves the study of parabolic multiplicative Higgs bundles and affine Springer fibers. 

Group field theory (GFT) is a background independent approach to quantum gravity in which the quanta represent "building blocks of space". It has been successfully applied to the cosmological setting and shown to have the potential for rich phenomenology. In this talk we will explore a novel proposal to construct operators in GFT based on symmetries of the action, which can then be identified with respective classically conserved currents. This construction relies on a relational coordinate system spanned by four massless scalar fields. As the classical currents are related to the components of the metric, the expectation values of the new GFT operators can be interpreted as giving rise to an effective metric originating directly from the quantum theory. We proceed to investigate the implications of this proposition for a flat homogeneous universe and its perturbations.

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Zoom link https://pitp.zoom.us/j/98843634192?pwd=OWs1SEdiWnIyYmlSbTh3bU9MaDBDdz09

In this talk I will present our 3+1 formulation of the Four-Derivative scalar-tensor theory of gravity with a modified puncture gauge that proves to be well-posed. Then I will show the results from Binary Black Hole evolutions that we have obtained from the implementation of these equations with GRFolres, the extension for modified gravity of our numerical relativity code GRChombo.

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Zoom link https://pitp.zoom.us/j/96339156414?pwd=ajhWb1hQNFRYalRpUEd3ajhYdTFldz09

Several years ago, Nayak and Else argued that Symmetry Protected Topological phases in d dimensions can be classified using non-on-site actions of the symmetry group in d-1 dimensions. Such non-on-site actions can have an “anomaly”, in the sense that the symmetry action cannot be consistently localized. This anomaly is similar but distinct from ’t Hooft anomaly in QFT. Nayak and Else assumed that the symmetry group is finite and the non-on-site action is given by a finite-depth local unitary circuit. I will explain how to generalize the construction of the anomaly index in two directions: to Lie groups as well as to arbitrary actions which preserve locality. For simplicity, I will only discuss the one-dimensional case. One can prove that a nonzero anomaly index prohibits any invariant 1d Hamiltonian from having invariant ground states. This is similar to ’t Hooft anomaly matching in QFT. Lieb-Schultz-Mattis-type theorems arise as a special case where the symmetry group involves translations. This is joint work with Nikita Sopenko.

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Zoom link https://pitp.zoom.us/j/95661517248?pwd=SkMxUFJWTG56SG9hVlNiNS9yeEVrQT09