Sofia Gonzalez Garcia, Perimeter Institute & University of Waterloo
Tensor Networks in a Nutshell
This seminar will be an introductory 'class' to Tensor Networks, so I will assume no previous knowledge on the subject. I aim to provide motivation for this powerful ansatz as well as some of its applications. I will introduce the main architectures (MPS, PEPS and MERA) and their characteristics. Throughout the seminar I will try to include part of the material I have produced for a 2017 PSI course taught by Guifre Vidal.
If time permits I will also briefly introduce my research on the subject, which is on 2D tensor networks contraction and its accuracy convergence.
The dark universe may host physics as rich and complex as the visible sector, but the only guaranteed window to the dark sector(s) is through gravity. If the dark matter has a dissipative self-interaction, dark gas can cool and collapse to form compact object whose mergers may be accessible to LIGO. The mass spectrum of the merging compact objects encodes fundamental physical information--a purely gravitational probe of dark matter microphysics.
In this talk, I will present our work to forward-model the gas collapse process in the "atomic dark matter" model, beginning with a retelling of the standard cosmological history including this new ingredient and culminating in a description of the fragmentation scale of the dark gas.
In recent years, the classification of fermionic symmetry protected topological phases has led to renewed interest in classical constructions of invariants in homotopy theory. In this talk, we focus on the description of Steenrod squares for triangulated spaces at the cochain level, introducing new formulas for the cup-i products and discussing their universality through an axiomatic approach. We also examine the interaction between Steenrod squares and the algebra structure in cohomology, providing a cochain level proof of the Cartan relation as requested by Kapustin. Time permitting, we will also study the Adem relation from this perspective.
In their seminal 1977 paper, Gibbons and Hawking (GH) audaciously applied concepts of quantum statistical mechanics to ensembles containing black holes, finding that a semiclassical saddle point approximation to the partition function recovers the laws of black hole thermodynamics. In the same paper they insouciantly applied the formalism to the case of boundary-less de Sitter space (dS), obtaining the expected temperature and entropy of the static patch. To what ensemble does the dS partition function apply? And why does the entropy of the dS static patch decrease upon addition of Killing energy? I’ll answer these questions, and then generalize the GH method to find the approximate partition function of a ball of space at any fixed proper volume. The result is the exponential of the Bekenstein-Hawking entropy of its boundary.