Talks

We are interested in Cantor sets in the complex plane and their quasiconformal equivalence classes. Especially, we consider generalized Cantor sets which are defined by sequences in $(0, 1)^{\mathbb N}$. In this talk, we present some recent progress on the research.

In this talk, we will explore what low-energy experiments on gravitationally mediated entanglement (GME) can reveal about the quantum nature of gravity. We will analyze the key assumptions necessary to interpret GME experiments as evidence for quantum aspects of the gravitational interaction and examine how these assumptions influence our conclusions. Additionally, we will discuss possible modifications to experimental designs aimed at minimizing dependence on assumptions. Then we will discuss what these experiments in different regimes can and cannot probe about gravity’s quantum nature.

Motivated by the frame independence of the Bekenstein-Hawking black hole entropy, and the possibility of it being fundamentally entanglement entropy, I will present a spacetime definition for the entanglement entropy of free quantum fields. This definition is a spectral formulation, conducive to frame independent regularization. I will then go on to show an example calculation in Rindler spacetime, and comment on more general applications.

This study presents the modeling of the gravitational wave (GW) bias parameter by bridging a connection between simulated GW sources and galaxies in low redshift galaxy surveys 2MPZ and WISExSCOS (WISC). We study this connection by creating a mock GW catalog, populating galaxy surveys with binary black holes (BBHs) for different scenarios of the GW host-galaxy probability as a function of the galaxy stellar mass. We probe the observable consequences of this connection by exploring the spatial clustering of the GW sources in terms of the GW bias parameter. We consider a phenomenological broken power law model for the host-galaxy probability function, with a potential turnover M_K at high stellar mass (10^{11} solar mass in the fiducial model) where the star formation efficiency begins to drop. We vary the parameters of the GW host-galaxy probability function and find that generically the GW bias increases as M_K increases (and gets suppressed as M_K decreases). The change in the GW bias parameter shows a maximum change of about 30% for different scenarios explored in this work in comparison to the galaxy bias. Future measurements of the GW bias can help constrain M_K and the slopes of the host-galaxy probability function and thus offer insights into the underlying astrophysical processes.

Complementarity is a phenomenon explaining several core features of quantum theory, such as the well-known uncertainty principle. Roughly speaking, two objects are said to be complementary if being certain about one of them necessarily forbids useful knowledge about the other. Two quantum measurements that do not commute form an example of complementary measurements, and this phenomenon can also be defined for ensembles of states. Although a key quantum feature, it is unclear whether complementarity can be understood more operationally, as a necessary resource in some quantum information task. Here we show this is the case, and relates to a task which we term unambiguous exclusion. As well as giving complementarity a clear operational definition, this also uncovers the foundational underpinning of unambiguous exclusion tasks for the first time.

In this talk will discuss a method to define Fenchel-Nielsen coordinates for representations of surface groups to SL(3,C). This both generalises and unifies the previous generalisations for PSL(2,C) by Kourouniotis and Tan, for SL(3,R) by Goldman and Zhang and for SU(2,1) by Parker and Platis.
 

For a punctured surface S and a split reductive algebraic group G such as SL_n or PGL_n, Fock and Goncharov (and Shen) consider two types of moduli spaces parametrizing G-local systems on S together with certain data at punctures. These moduli spaces yield versions of higher Teichmüller spaces, and are equipped with special coordinate charts, making them birational to cluster varieties. Fock and Goncharov’s duality conjectures predict the existence of a canonical basis of the algebra of regular functions on one of these spaces, enumerated by the tropical integer points of the other space. I will give an introductory overview of this topic, briefly explain recent developments involving quantum topology and mirror symmetry of log Calabi-Yau varieties, and present some open problems if time allows.