Talks

Hidden-variables theories account for quantum mechanics in terms of a particular 'equilibrium' distribution of underlying parameters corresponding to the Born rule. A natural question to ask is whether the theory is stable under small perturbations away from equilibrium. We compare and contrast two examples: de Broglie's 1927 pilot-wave theory and Bohm's 1952 reformulation thereof. It is well established that in de Broglie's dynamics initial deviations from equilibrium will relax. We show that this is not the case for Bohm's dynamics: initial deviations from equilibrium do not relax and in fact grow with time. On this basis we argue that Bohm's dynamics is untenable as a physical theory (while de Broglie's dynamics remains a viable candidate). We advocate stability as a general selection criterion for hidden-variables theories.

All physical constraints of the conformal bootstrap in principle arise by applying linear functionals to the conformal bootstrap equation. An important goal of the bootstrap program is to identify a suitable basis for the space of functionals -- one that would allow us to solve crossing analytically. In my talk, I will describe two particularly convenient choices of the basis for the 1D conformal bootstrap. The two bases manifest the crossing symmetry of the four-point function of a generalized free boson and generalized free fermion respectively. I will use the bases to study small deformations of the two theories. Assuming no new operators appear in the OPE, the generalized free fermion allows no small deformation, and the generalized free boson allows a one-parameter deformation, which coincides with the AdS_2 four-point contact interaction at the leading order. Time allowing, I will discuss the connection of this work to the conformal bootstrap a la Polyakov.

Large scale structure surveys are one of our primary tools for answering open questions in cosmology like: What is the physics behind dark energy? Is gravity well described by general relativity on cosmological scales, or does that description need to be extended? In order to take full advantage of the information contained in survey data, however, we must ensure that we understand our data’s sensitivity to new physics and that our analyses are not biased by systematics. In my talk I’ll describe work I have been doing in this aim for the Dark Energy Survey (DES). I’ll begin with an introduction to how we can use data from surveys like the DES to test LCDM, including approaches to constraining extensions to general relativity with cosmological data. I’ll use that discussion to motivate a so-called growth-geometry split analysis, a consistency test of LCDM that works by comparing constraints from probes of structure growth and expansion history, and will discuss the status of such an analysis applied to DES data. I’ll also give an overview of the blinding strategy planned for future multi-probe DES cosmology analyses.

I'll discuss an ongoing project of mine with Dinakar Muthiah and Oded Yacobi, which is based on ideas of Kreiman-Lakshmibai-Magyar-Weyman.  It is aimed at developing a "nice" standard monomial theory for the affine Grassmannian in type A, where "nice" means hopefully close in spirit to Hodge's classical standard monomial theory for finite dimensional Grassmannians.