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This course uses quantum electrodynamics (QED) as a vehicle for covering several more advanced topics within quantum field theory, and so is aimed at graduate students that already have had an introductory course on quantum field theory. Among the topics hoped to be covered are: gauge invariance for massless spin-1 particles from special relativity and quantum mechanics; Ward identities; photon scattering and loops; UV and IR divergences and why they are handled differently; effective theories and the renormalization group; anomalies.

I'll explain work in progress, joint with Miroslav Rapcak, on geometric constructions of vertex algebras associated to divisors in toric Calabi-Yau threefolds, in terms of moduli stacks of objects in certain exotic abelian subcategories of complexes of coherent sheaves on the underlying threefold. These vertex algebras were originally proposed by Gaiotto-Rapcak, and constructed mathematically in the example of affine space by Rapcak-Soibelman-Yang-Zhao, building on Schiffmann-Vasserot's proof of the AGT conjecture. We give a geometric explanation and generalization of the quivers with potential that feature in the latter results, and outline the analogous construction of vertex algebras in this setting.

Zoom link:  https://pitp.zoom.us/j/93749710253?pwd=Y3NUTHBXZ3FPQUdPU0E0d0ttVzFFdz09

I discuss novel symmetries of perturbation theory around rotating and non-rotating black holes in general relativity, and discuss their origins and implications for gravitational-wave astronomy. This is motivated by two special aspects of black hole perturbations in four dimensions: isospectrality of quasinormal modes and the vanishing of tidal Love numbers. There turn out to be off-shell symmetries underlying each of these phenomena. One is a duality, which on shell reproduces the famous Chandrasekhar duality and therefore underlies isospectrality, and can be thought of as an extension of electric-magnetic duality to black hole backgrounds. The other is a set of "ladder symmetries" relating modes of different angular momentum or spin, which imply the vanishing of Love numbers. This has a geometric origin in the conformal symmetry of low-frequency modes.

Zoom link:  https://pitp.zoom.us/j/93633894223?pwd=cEFRYno5WSt5NUJlOWJLdVZHWjE1QT09

In this talk I will explore perspectives of quantum entanglement in (1+1)-d systems in presence of defects. The talk consists of two parts. In the first part, I will talk about the ground state entanglement entropy for 1d quantum spin chains with defects, using the transverse field Ising model and the three-state Potts model as examples. In the second part, I will describe the field theoretical replica trick approach to study entanglement entropy in such systems. This talk consists of some reviews about existing work, as well as work in progress with Linnea Grans-Samuelsson, Ananda Roy, Hubert Saleur, and Yifan Wang.

Zoom link: https://pitp.zoom.us/j/93049110080?pwd=QmpneGs2QlpZMlBROUlvU3VzaGtsZz09

This course uses quantum electrodynamics (QED) as a vehicle for covering several more advanced topics within quantum field theory, and so is aimed at graduate students that already have had an introductory course on quantum field theory. Among the topics hoped to be covered are: gauge invariance for massless spin-1 particles from special relativity and quantum mechanics; Ward identities; photon scattering and loops; UV and IR divergences and why they are handled differently; effective theories and the renormalization group; anomalies.

Celestial holography posits a duality between a theory of quantum gravity in asymptotically flat spacetime and a "celestial" conformal field theory that lives on its co-dimension two boundary. By studying soft theorems of scattering amplitudes in the bulk it was shown that there exist infinite towers of corresponding soft currents in cCFT and their algebra was calculated. In this talk I will consider a bulk theory of Yang-Mills coupled to a massive scalar and show, via soft limits, that the corresponding boundary algebra admits a level proportional to the strength of the background. I will comment on some other aspects of this deformation as well as potentially important subtleties we have encountered with our method of computing celestial amplitudes.

Zoom link:  https://pitp.zoom.us/j/95423960414?pwd=RVoxc1FRRGRmL2RIMXJpbXFKZVBFdz09

The polarization measurements of particles produced in heavy-ion collisions allow us to study amazing phenomena such as, the collective rotation of the nuclear medium, quark spin-alignment with the global angular momenta, local vs global polarization effects and their evolution when there are drastic changes in the properties of the hot, dense and whirly medium. Recently, measurements by the STAR collaboration at RHIC and the HADES collaboration at GSI, show the rising of Lambda and anti-Lambda global polarization with decreasing collision energy and what seems to be a differentiated peak with a sharp decrease at a lower bound in collision energy. In this talk I will report on our recent work where we predict this differentiated peak behavior using a core-corona model, so that measuring the polarization of hyperons becomes a tool to learn about strangeness availability in the medium created in heavy-ion collisions for different initial conditions. I will also present a few new developments we have made to probe the strong magnetic field produced early after the collision with primordial photons and mention other relevant signals that we are working on in order to learn about the critical end-point in the QCD phase diagram.

Zoom link:  https://pitp.zoom.us/j/95896792626?pwd=QlovbE5EWEJBSDdOZjUyK2MxYktmQT09