Scientific Series

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

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

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

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

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

During this colloquium, I will discuss my journey in looking for astronomical information hiding in the ancestral knowledge of my community. I will show concrete examples of my findings and encourage communities to engage in similar practice to provide content that could be used to teach indigenous Astronomy in classrooms. 

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Bio:

Laurie Rousseau-Nepton is a new faculty at the University of Toronto and the Dunlap Institute for Astronomy and Astrophysics. She comes with six years of experience working as a resident astronomer at the Canada-France-Hawaii Observatory supporting various instruments including wide-field cameras, high-resolution spectrographs, Fourier Transform Spectro-imager. She received her diploma from Université Laval by studying regions of star formation in spiral galaxies and helping with the development of two Fourier Transform Spectro-imagers, SpIOMM and SITELLE. She is now leading an international project called SIGNALS, the Star formation,Ionized Gas, and Nebular Abundances Legacy Survey, which sampled with the SITELLE instrument more than 50,000 of star-forming regions in 40 nearby galaxies to understand how the local environment affect the young star clusters characteristics.

This seminar will be divided in two segments: 1) New Instrumentation for Astronomy and 2) the SIGNAL-Survey of Star-forming regions in Nearby Galaxy.

1) Evolution of technologies and optics manufacturing technics are providing new interesting options for the design of astronomical instruments to increase precision and add new capabilities. In this presentation, I will discuss my new laboratory plan at the University of Toronto to include Micro-kinetic inductance detector arrays and meta-surface optics to a Fourier Transform Imaging spectrograph design. The goal is to reach high-spectral resolution (R:15,000 to 80,000) over a large field-of-view, while keeping high sensitivity.

2) SIGNALS stands for the Star formation, Ionized Gas, and Nebular Abundances Legacy Survey. Using a Fourier Transform Imaging Spectrograph SITELLE, at the Canada-France-Hawaii Telescope, we observed 40 nearby galaxies and covered over 50,000 star-forming regions in different environment at a spatial resolution from 0.5 to 40 pc. Covering several emission line spectral features including Halpha (at R: 5,000), the survey aims at characterizing the star-forming sites and their environments to produce the most complete and well resolved database on star formation.

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Zoom link https://pitp.zoom.us/j/94273599584?pwd=TUY3UFpVa20wbkJUcEdoTmlYUzlQUT09

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Bio:

Laurie Rousseau-Nepton is a new faculty at the University of Toronto and the Dunlap Institute for Astronomy and Astrophysics. She comes with six years of experience working as a resident astronomer at the Canada-France-Hawaii Observatory supporting various instruments including wide-field cameras, high-resolution spectrographs, Fourier Transform Spectro-imager. She received her diploma from Université Laval by studying regions of star formation in spiral galaxies and helping with the development of two Fourier Transform Spectro-imagers, SpIOMM and SITELLE. She is now leading an international project called SIGNALS, the Star formation, Ionized Gas, and Nebular Abundances Legacy Survey, which sampled with the SITELLE instrument more than 50,000 of star-forming regions in 40 nearby galaxies to understand how the local environment affect the young star clusters characteristics. 

I will review how protected correlation functions in certain SQFTs can be used to ``quantize'' phase spaces built from their spaces of vacua.

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Zoom link https://pitp.zoom.us/j/96543843231?pwd=U0d5d3EvVXJGT0VzR2JYUzBQVGJlUT09

The presence of many competing classical ground states in frustrated magnets implies that quantum fluctuations may stabilize quantum spin liquids (QSL), which are characterized by fractionalized excitations and emergent gauge fields. A paradigmatic example is the U(1) Dirac spin liquid (DSL), which at low-energies is described by emergent quantum electrodynamics in 2+1 dimensions (QED3), a strongly interacting field theory with conformal symmetry. While the DSL is believed to be intrinsically stable, its robustness against various other couplings has been largely unexplored and is a timely question, also given recent experiments on triangular-lattice rare-earth oxides. In this talk, using complementary perturbation theory and scaling arguments as well as results from numerical DMRG simulations, I will show that a symmetry-allowed coupling between (classical) finite-wavevector lattice distortions and monopole operators of the U(1) Dirac spin liquid generally induces a spin-Peierls instability towards a (confining) valence-bond solid state. Away from the limit of static distortions, I will argue that the phonon energy gap establishes a parameter regime where the spin liquid is expected to be stable.

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Zoom link https://pitp.zoom.us/j/96764903405?pwd=Y0gyU3hGSC9va0hzWnZRZFBOVmRCZz09

With rapid progress in simulation of strongly interacting quantum Hamiltonians, the challenge in characterizing unknown phases becomes a bottleneck for scientific progress. We demonstrate that a Quantum-Classical hybrid approach (QuCl) of mining the projective snapshots with interpretable classical machine learning, can unveil new signatures of seemingly featureless quantum states. The Kitaev-Heisenberg model on a honeycomb lattice with bond-dependent frustrated interactions presents an ideal system to test QuCl. The model hosts a wealth of quantum spin liquid states: gapped and gapless Z2 spin liquids, and a chiral spin liquid (CSL) phase in a small external magnetic field. Recently, various simulations have found a new intermediate gapless phase (IGP), sandwiched between the CSL and a partially polarized phase, launching a debate over its elusive nature. We reveal signatures of phases in the model by contrasting two phases pairwise using an interpretable neural network, the correlator convolutional neural network (CCNN). We train the CCNN with a labeled collection of sampled projective measurements and reveal signatures of each phase through regularization path analysis. We show that QuCl reproduces known features of established spin liquid phases and ordered phases. Most significantly, we identify a signature motif of the field-induced IGP in the spin channel perpendicular to the field direction, which we interpret as a signature of Friedel oscillations of gapless spinons forming a Fermi surface. Our predictions can guide future experimental searches for U(1) spin liquids.

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Zoom link: https://pitp.zoom.us/j/94233944575?pwd=OVljLzMrZzlKeUErNHZQRkEzMFRKUT09

A tower is an infinite sequence of deloopings of symmetric monoidal ever-higher categories. Towers are places where extended functorial field theories take values. Towers are a "deeper" version of commutative rings (as opposed to "higher rings" aka E∞-spectra). Notably, towers have their own opinions about Galois theory, and think that usual Galois groups are merely shallow approximations of deeper homotopical objects. In this talk, I will describe some steps in the construction and calculation of the deeper Galois group of a characteristic-zero field. In particular, I'll explain a homotopical version of the Kummer description of abelian extensions. This is joint work in progress with David Reutter.

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Zoom link: https://pitp.zoom.us/j/97950701035?pwd=Wk9FRSt2MkN3eWptTVltRVJncnFHdz09

The event horizon of a dynamical black hole is generically a non-smooth hypersurface. I shall describe the types of non-smooth structure that can arise on a horizon that is smooth at late time. This includes creases, corners and caustic points. I shall discuss ``perestroikas'' of these structures, in which they undergo a qualitative change at an instant of time. A crease perestroika gives an exact local description of the event horizon near the ``instant of merger'' of a generic black hole merger. Other crease perestroikas describe horizon nucleation or collapse of a hole in a toroidal horizon. I shall discuss the possibility that creases contribute to black hole entropy, and the implications of non-smoothness for higher derivative terms in black hole entropy. This talk is based on joint work with Maxime Gadioux.

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Zoom link: https://pitp.zoom.us/j/98839294408?pwd=cytNYThQaDV4Y2lob1REY0NyaTJNUT09