Title: A universal sum over topologies in 3d gravity
Abstract: A careful analysis of the sum over topologies in 2d gravity led to an averaged form of the holographic correspondence: pure 2d gravity is dual to random matrix theory rather than to a single Hamiltonian. In this talk, I go one dimension higher and study the sum over topologies in 3d gravity and its relation to the statistical interpretation of the boundary theory. I formulate a statistical version of the conformal bootstrap that organizes universal properties of CFT data, namely typicality and crossing symmetry. I then identify a set of surgery moves on bulk manifolds that directly reflect these properties. These moves generate non-handlebodies, produce only hyperbolic manifolds, and do not generate all hyperbolic manifolds. This indicates a large range of possible choices for which manifolds may be included in the gravitational path integral, reflecting a broad class of ensembles consistent with crossing symmetry and typicality. Based on work with Alexandre Belin, Scott Collier, Lorenz Eberhardt and Boris Post (arXiv:2601.07906).
Tittle: RANDOM WALK ON THE RANDOM GRAPH
Abstract: pick a random graph on n points by flipping a fair coin for each possible edge. Now do it again, independently. What's the chance the two graphs you get are isomorphic? Small? How small? When n= 100, less than 10^(-1300). Now, let n = infinity. Pick two graphs at random. the chance that they are isomorphic is one (!). this is THE random graph. I will illustrate its strange properties by studying random walk. This is a typical problem of probability in the presence of a random geometry. I will introduce 'Hardy's inequalities' for trees to get where we need to go. This is joint work with Sourav Chatterjee and Laurent Miclo.
Title: Semiclassical analysis of finite cut-off JT gravity on a disk
Abstract: In this talk I will present the computation of the partition function of finite cut-off JT gravity (with positive, zero or negative curvature) defined on a disk and coupled to conformal matter with central charge c. The analysis is done in a regime where c is a large negative number, while the magnitude of the cosmological constant scales linearly with |c| and the length of the boundary of the disk is kept finite. In this regime, the gravitational path integral is dominated by a smooth geometry corresponding to a saddle point of the action. By systematically taking into account the quantum fluctuations about this saddle point, one can obtain a perturbative expansion of the partition function in powers of 1/|c|. I will present the results for the leading and the first subleading terms in this expansion.
Speaker: Wayne W. Weng
Title: A single geometry from an all-genus expansion in quantum gravity
Abstract: In this talk, I will discuss an instance in quantum gravity where a topological expansion resums into an effective description on a single geometry. The original theory whose gravitational path integral we study is JT quantum gravity with one asymptotic boundary at nonperturbatively low temperatures. The effective theory we derive is a deformation of JT gravity by a highly quantum and nonlocal interaction for the dilaton, evaluated only on a disk topology. This emergent description addresses a strongly quantum gravitational regime where all genera contribute at the same order, successfully capturing the doubly nonperturbative physics of the original theory.
Students can begin to submit major/minor changes effective Fall Semester.
Title: Holography for Mathematicians
Title: Holography for Mathematicians
Title: Dynamics of Reeb vector fields in three dimensions
Abstract: We review various recent results on the existence and properties of periodic orbits of Reeb vector fields in three dimensions. The results we will discuss can be proved using spectral invariants in embedded contact homology. Many of these results can also be proved using a new, simplified version of these invariants, called "elementary spectral invariants". The elementary spectral invariants are defined as a max-min energy of pseudoholomorphic curves satisfying certain constraints, inspired by a construction of McDuff-Siegel.
In the first lecture we will introduce the results on Reeb dynamics that we will be discussing. In the second lecture we will state the axiomatic properties of the elementary spectral invariants and explain how these can be used to obtain results on Reeb dynamics. In the third lecture we will describe the construction of elementary spectral invariants.
Lecture 1: Recent results in three-dimensional Reeb dynamics
Title: Holography for Mathematicians
Title: Dynamics of Reeb vector fields in three dimensions
Abstract: We review various recent results on the existence and properties of periodic orbits of Reeb vector fields in three dimensions. The results we will discuss can be proved using spectral invariants in embedded contact homology. Many of these results can also be proved using a new, simplified version of these invariants, called "elementary spectral invariants". The elementary spectral invariants are defined as a max-min energy of pseudoholomorphic curves satisfying certain constraints, inspired by a construction of McDuff-Siegel.
In the first lecture we will introduce the results on Reeb dynamics that we will be discussing. In the second lecture we will state the axiomatic properties of the elementary spectral invariants and explain how these can be used to obtain results on Reeb dynamics. In the third lecture we will describe the construction of elementary spectral invariants.
Lecture 2: Elementary spectral invariants and applications
Title: Dynamics of Reeb vector fields in three dimensions
Abstract: We review various recent results on the existence and properties of periodic orbits of Reeb vector fields in three dimensions. The results we will discuss can be proved using spectral invariants in embedded contact homology. Many of these results can also be proved using a new, simplified version of these invariants, called "elementary spectral invariants". The elementary spectral invariants are defined as a max-min energy of pseudoholomorphic curves satisfying certain constraints, inspired by a construction of McDuff-Siegel.
In the first lecture we will introduce the results on Reeb dynamics that we will be discussing. In the second lecture we will state the axiomatic properties of the elementary spectral invariants and explain how these can be used to obtain results on Reeb dynamics. In the third lecture we will describe the construction of elementary spectral invariants.
Lecture 3: Construction of elementary spectral invariants
Last day students can process a withdrawal from individual courses(es) via SOLAR. "W" (withdrawal) will be recorded on transcript.
Last day to submit a Section/Credit Change Form to Office of Registrar. Changes must be processed by 4:00 PM. After this date petition is required and "W" (withdrawal) will be recorded on transcript.
Last day students can select Grade/Pass/No Credit (GPNC). Non-petionable.