15/06/2023 (DG Seminar)
Speaker: Frank Ferrari
Title: Random Disks of Constant Curvature: the conformal gauge story
Abstract: Two-dimensional quantum gravity models fall in three classes: Liouville gravity, for which the geometry is wildly random in the bulk; topological gravity, for which the geometries, having constant curvature and geodesic boundaries, have a finite number of moduli; and an intermediate class of models, which has attracted a lot of attention recently, for which the metrics have constant curvature but the boundaries can fluctuate wildly. These so-called Jackiw-Teitelboim theories, mainly in negative curvature, have been intensively studied in the physics literature in recent years. They build a bridge between several different problems, from strongly coupled electron systems in condensed matter theory to quantum black hole models. They are analysed using a variety of techniques, including matrix models, Mirzakhani/Eynard recursion relations, integration over Diff(S1)/PSL(2,R), etc.
14/06/2023
Speaker: Frank Ferrari
Title: Random Disks of Constant Curvature: the conformal gauge story
Abstract: We describe a first-principle approach to JT quantum gravity at finite cut-off using conformal gauge. The cases of positive, zero or negative curvatures can be studied in parallel. The picture that emerges is very different from the usual perspective used in the literature, that focuses on a gently fluctuating boundary. This appears to be a minisuperspace approximation. Our results superficially kill the Schwarzian model, but it raises from the dead in a completely unexpected way and is shown to be relevant even in zero and positive curvature! New consistent ``Hilbert-Liouville'' models, governing the dynamics of the boundary conformal factor, are constructed. We also explain that the gauge theoretic description of the model is unstable and utterly unable to reproduce the full-fledged quantum gravity theory.
31/05/2023
Speaker: Razvan Gurau
Title: The conformal limit of the SYK model
Abstract: I will briefly discuss the melonic CFTs which arise in the large N limit of the SYK model and higher dimensional tensor field theories
17/05/2023
Speaker: Hannes Keppler
Title: Chaos in the SYK model (continuation)
Abstract: I will review some arguments in the literature and explain in which sense the Sachdev-Ye-Kitaev (SYK) model displays chaotic behavior and how this made the model interesting for AdS-CFT holography. This statement relies on the behavior of certain Out-of-time-order-Correlations, and I will show how they capture some aspects of chaos. After introducing the SYK model - a model of N interacting Majorana Fermions -, I will review properties and arguments that indicate a holographic relation to Black Hole systems, as this relation sparked a lot of research on this model in previous years.
10/05/2023
Speaker: Hannes Keppler
Title: Chaos in the SYK model
Abstract: I will review some arguments in the literature and explain in which sense the Sachdev-Ye-Kitaev (SYK) model displays chaotic behavior and how this made the model interesting for AdS-CFT holography. This statement relies on the behavior of certain Out-of-time-order-Correlations, and I will show how they capture some aspects of chaos. After introducing the SYK model - a model of N interacting Majorana Fermions -, I will review properties and arguments that indicate a holographic relation to Black Hole systems, as this relation sparked a lot of research on this model in previous years.
03/05/2023
Speaker: Björn Friedrich
Title: Black holes and (quantum) chaos
Abstract: The connection between black holes, the information paradox and chaos will be reviewed.
22/02/2023
Speaker: Alexander Thomas
Title: Coadjoint orbits of the Virasoro group
Abstract: The dual Virasoro algebra has a surprising description in terms of differential operators of degree 2, so-called Hill operators, which in turn describe projective structures on the circle. In this correspondence, coadjoint orbits are equivalent to the (extended) monodromy of the projective structure. Passing to matrix-valued differential operators of order 1, we get another approach called the Drinfeld-Sokolov reduction.
15/02/2023
Speaker: Carlos Perez-Sanchez
Title: Topological recursion and selected random matrix tools in JT-gravity
Abstract: Before addressing the main result of this talk, due to Saad-Shenker-Stanford (SSS), I will give a pedagogical introduction to several facets of random matrices. Also, I will remind what topological recursion (TR) computes for us from two approaches: On the one hand, following the historical path, sketching Mirzakhani's TR for the Weil-Petersson volumes. On the other hand, with slightly more detail, TR will be presented in the rather modern language of Airy structures (the Kontsevich-Soibelman approach). The main result of SSS is a restatement of the partition function of JT-gravity in terms of matrix ensembles, whose correlation functions are computed using TR.
08/02/2023
Speaker: Peter Smillie
Title: Diff(S¹) and Teichmüller Spaces
Abstract: We prove that the natural Kähler structure on Diff(S¹)/SL(2,R), viewed as a coadjoint orbit, is the same as the Ahlfors-Bers / Weil-Petersson Kähler structure on universal Teichmüller space, pulled back via the natural inclusion.
01/02/2023
Speaker: Bjoern Friedrich
Title: The Hilbert space of 2d topological gravity
Abstract: Evaluating the partition function for a gravitational system, including the change of topology, is known to be highly challenging. For a theory of topological surfaces, Marolf and Maxfield were able to compute the partition function exactly and found surprising results. The presence of wormholes and baby universes (i.e. topology change) leads to the surprising fact that many states in the space of physical states are null states. Hence, after taking the quotient, the Hilbert space turns out the be much smaller than expected. In this seminar, I'll report on the results of Marolf and Maxfield to show how 2d gravity can be an inspiring toy model in physics and mathematics.
25/01/2023
Speaker: Sebastian Nill
Title: Duistermaat-Heckman Localization
Abstract: Given a circle action on a compact manifold with isolated fixed points, the integral of an equivariant differential form localizes to a finite sum over the fixed points. We will discuss a proof of this Atiyah-Bott-Berline-Vergne localization formula via Witten's trick and specialize it to the Duistermaat-Heckman localization formula in the context of symplectic manifolds equipped with an Hamiltonian circle action. In the following talk, an infinite-dimensional analogue will compute the partition function of the Schwarzian theory.
07/12/2022
Speaker: Donald Youmans
Title: The Virasoro Group, its Coadjoint Orbits and the Schwarzian Theory II
Abstract: We will continue the discussion of coadjoint orbits of the Virasoro group. In particular, we will derive explicit expressions for a point in the orbit, for the Kostant-Kirillov-Souriau symplectic form and its Poisson bracket.
30/11/2022
Speaker: Donald Youmans
Title: The Virasoro group, its Coadjoint Orbits and the Schwarzian Theory I
Abstract: In this talk we will introduce the Virasoro group and discuss its coadjoint orbits. In particular, we will show that the partition function of the Schwarzian theory is given by an orbital integral of the moment map of rigid rotations acting on the orbit.
23/11/2022
Speaker: Valdo Tatitscheff
Title: Quantum Black Holes and the SYK model II
Abstract: We will take up the discussion of quantum black holes with glimpses of holography, information recovery and chaos. Then, I will introduce the Sachdev-Ye-Kitaev (SYK) model and present some of its properties at large N: the melonic expansion at weak coupling, the effective conformal action at low energy with the Schwarzian action as leading-order correction, out-of-time ordered correlators and quantum chaos. Eventually, I will outline how the SYK model relates to JT gravity.
16/11/2022
Speaker: Valdo Tatitscheff
Title: Quantum Black Holes and the SYK model I
Abstract: My goal will be to motivate the study of the Sachdev–Ye–Kitaev (SYK) model by reviewing some aspects of the marriage between black hole solutions of general relativity and quantum physics. In particular, black holes generally lose energy in the form of Hawking radiation, which leads to the black hole information problem. In order for a quantum system to possibly describe a black hole, it needs to satisfy some fundamental properties such as having finitely-many degrees of freedom and being chaotic, which are two properties that the SYK model displays.
09/11/2022
Speaker: Donald Youmans
Title: From JT Gravity to the Schwarzian Theory
Abstract: In this talk we will describe how the study of JT gravity (in Euclidean signature) on a disk, with boundary conditions motivated by black hole physics, yields the Schwarzian theory on the boundary. The Schwarzian theory recovers the equations of motion for the dilaton restricted to the boundary and thus provides an effective theory of JT gravity (near the boundary). We will discuss JT gravity with the appropriate boundary conditions in second and first order formulation; the former is the traditional point of view as a theory of gravity, the latter allows a generalization to study the model in terms of a two-dimensional gauge theory.
02/11/2022
Speaker: Donald Youmans
Title: Near Horizon Geometry of (extremal) Black Holes and JT Gravity
Abstract: In this talk we will review the near horizon geometry of a 4d charged black hole. This geometry turns out to be the geometry of AdS_2 x S^2 and is universally described by an effective model - 2d JT gravity. Motivated by this, we start the analysis of JT gravity. Imposing suitable Dirichlet boundary conditions on the metric leads to the study of the Schwarzian theory on the boundary.