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: Random geometries in various quantum gravity approaches
Abstract: The gravitational path integral involves a sum over geometries weighted by the exponential of the gravitational action. In certain quantum gravity (QG) models, this sum admits a precise probabilistic interpretation, namely as the partition function of random geometries. This perspective allows one to apply tools from random geometry, such as random maps and matrix and tensor models, to the study of QG. In this talk, I will give an overview of the different models I have worked on, including random maps, random hyperbolic surfaces, and random tensor models, and discuss their applications to quantum gravity, with examples ranging from JT gravity to dynamical triangulations.
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
Title: Review of JT Gravity Part 1
Title: Review of JT Gravity Part 2
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.
Title: “On Finite Cut-Off Holography and JT Gravity”
Title: Review of JT Gravity Part 3
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