Talks

Measurements of the cosmic microwave background (CMB) have proven to be a powerful probe of the physics of our universe. CMB observations are helping to address fundamental questions, such as the nature of dark energy and dark matter, and are being used to probe the physics of inflation at energies a trillion times higher than the Large Hadron Collider. Recent measurements led to several exciting first detections, including CMB lensing, massive galaxy clusters, the large-scale velocity field, and the “B-mode” component of the polarization field. These results have been enabled by the development of superconducting detectors and optics instrumentation, but we are now approaching the limits of current telescope facilities. Continuing advances in CMB research require greater sensitivity through major gains in optical throughput.

The CCAT-prime extreme field-of-view submillimeter telescope on Cerro Chajnantor will meet this challenge. The six-meter aperture telescope is designed to observe between 350um - 3mm and is capable of mapping the CMB roughly 10x faster than current observatories, making it a potential platform for the next generation “Stage IV” CMB survey. The first light instrument will take advantage of the unique CCAT-prime capabilities and site to characterize the large-scale velocity field and CMB polarization. In addition, CCAT-prime will enable spectroscopic intensity mapping of [CII] from early stars and galaxies during reionization and low-redshift galactic ecology. The intensity mapping measurements can be cross-correlated with upcoming neutral hydrogen surveys, and this combination may eventually characterize primordial non-Gaussianities beyond the reach of CMB measurements to provide new insights into the high-energy physics of inflation.

This talk applies effective field theory to the back-reaction of sources with finite size but infinite mass. The main tool for calculating back-reaction is a general relation between a source's effective action and the boundary conditions of `bulk’ fields in the near-source limit. As applied to the Maxwell (or Einstein) fields for point sources this boundary condition reproduces standard Gauss’ Law expressions, but the same arguments imply source-dependent boundary conditions for the Schrodinger (or Dirac) field of an orbiting particle. As applied to the quantum mechanics of a particle interacting with a source through an inverse-square potential EFTs remove the guess-work from the (well-known) ambiguities in the determination of boundary conditions at the origin, and provides a simple interpretation of the classical renormalization effects that are known to arise in this case. EFT arguments show why the RG evolution associated with this classical renormalization is likely universal for a great many types of point sources. The EFT boundary conditions also modify how finite-size effects alter bound-state orbits in the Coulomb problem, and in particular give them a non-standard dependence on the mass of the orbiting particle. It is argued that this might provide a solution to the `proton-radius puzzle’, in which experiments seem to indicate a different proton radius depending on whether or not it is measured using electrons or muons.

Motivated by the question about reconstructing a Conformal field theory from the data of a subfactor of finite index, Jones studied the continuous limit of the periodic quantum spin chain which Thompson group acts on. Based on planar algebras, the topological axiomatization of subfactors, we will illustrate the idea of the correspondence between the skein theory of planar algebras and presentation of Thompson groups.

The affine Grassmannian is the analog of the Grassmannian for the loop group. They are very important objects in mathematical physics and the Geometric Langlands program. In this talk, I will explain my recent work on the central degeneration of semi-infinite orbits, Iwahori orbits and Mirkovic-Vilonen cycles in the affine Grassmannian. I will also use lots of convex polytopes to illustrate my results. In addition, I will explain the connections between my work and other parts of geometric representation theory and combinatorial algebraic geometry.