Scientific Series

Computing has had many fundamental platform shifts in its history, and each came shrouded with mystery, hype, and dazzling potential: Alan Turing's universal machines, Doug Engelbart's Dynamic Knowledge Repository, J.C.R. Licklider's Intergalactic Network, the development of the internet, and all the waves of personal computers. More recently, Web 1.0, Web 2.0, and now Web 3.0 have all been heralded with barely-working demos and baffling hype, only to quietly install and broadly distribute fundamental improvements to our everyday life, to our work, and to our society. Each time the smoke cleared, our civilization had been transformed.

Right now, there are fundamental improvements being designed, built, and deployed in the web 3.0 landscape. These improvements and the applications they enable have the potential to transform our lives, our societies, and our civilization yet again. Some of those changes have started to happen, but the vast majority loom in the horizon. To understand the potential changes to our future, we must first understand what the technologies are, what properties they have, and what applications and actions they enable. After looking at the pieces concretely, both in theory and in practice, we can then put the puzzle of the future back together.

This colloquium will explore:

- What web 3.0 is, and its key technologies
- Decentralized Web systems, and their applications
- Blockchain systems, as a next generation platform for computing
- Cryptocurrencies, and the systems they enable
- Smart contracts and autonomous programs
- Cryptoeconomics and incentive structure engineering
- Open Services -- open source internet-wide utilities
- and a set of Open Problems in the field.

Using Monte Carlo methods we explore how well does the recent proposal for computing conformal dimensions, using a large charge expansion, work. We focus on the O(2) and the O(4) Wilson-Fisher fixed points as test cases. Since the traditional Monte Carlo approach suffers from a severe signal-to-noise ratio problem in the large charge sectors, we use worldline formulations that eliminate such problems. In particular we argue that the O(4) model can be simplified drastically by studying what we refer to as a "qubit" formulation. Such simpler  formulations of quantum field theories have become interesting recently from the perspective of quantum computing. Using our studies we confirm that the conformal dimensions of both conformal field theories with O(2) and O(4) symmetries obey a simple formula predicted by the large charge expansion. We also compute the two leading universal low energy constants in both cases , that play an important role in the large charge expansion.

The need for a time-shift invariant formulation of quantum theory arises from fundamental symmetry principles as well as heuristic cosmological considerations. Such a description then leaves open the question of how to reconcile global invariance with the perception of change, locally. By introducing relative time observables, we are able to make rigorous the Page-Wootters conditional probability formalism to show how local Heisenberg evolution is compatible with global invariance.

Wilson loops are important observables in gauge theory. In this talk, we study half-BPS Wilson loops of a large class of five dimensional supersymmetric quiver gauge theories with 8 supercharges. The Wilson loops are codimension 4 defects of the quiver gauge theory, and their interaction with self-dual instantons is captured by a 1d ADHM quantum mechanics. We compute the partition function as its Witten index. It turns out that we can understand the 5d physics in 3d gauge theory terms. This comes about from so-called gauge/vortex duality; namely, we study the vortices on the Higgs branch of the 5d theory, and reinterpret the physics from the point of view of the vortices. This perspective has an advantage: it has a dual description in terms of "deformed" Toda Theory on a cylinder, in the Coulomb gas formalism. We show that the gauge theory partition function is equal to a (chiral) correlator of the deformed Toda Theory, with stress tensor and higher spin operator insertions. We derive all the above results from type IIB string theory, compactified on a resolved ADE singularity X times a cylinder with punctures. The 5d quiver gauge theory arises as the low energy limit of a system of D5 branes wrapping various two-cycles of X, the Wilson loops are D1 branes, and the duality to Toda theory emerges after introducing additional D3 branes.

Embezzlement of entanglement is the (impossible) task of producing an entangled state from a product state via a local change of basis, when a suitable catalytic entangled state is available.  The possibility to approximate this task was first observed by van Dam and Hayden in 2002.  Since then, the phenomenon is found to play crucial roles in many aspects of quantum information theory.  In this colloquium, we will explain various methods to embezzlement entanglement and explore applications (such as an extension to approximately violate other conservation laws, a Bell inequality that cannot be violated maximally with finite amount of entanglement, consequences for resource theories, and the quantum reverse Shannon theorem).

Trisections were introduced by Gay and Kirby in 2013 as a way to study 4-manifolds. They are similar in spirit to a common tool in a lower dimension: Heegaard splittings of 3-manifolds. In both cases, one understands a manifold by examining the ways that standard building blocks can be put together. They both also have the advantage of changing problems about manifolds into problems about diagrams of curves on surfaces. This talk will be a relaxed introduction to these decompositions.

We discover an infinite hierarchical web of the products of supersymmetric generators sustained by the superconformal Virasoro algebra. This hierarchy structure forms the mathematical foundation underpinning the explicit derivation of the character for the self-symmetric Ramond highest weight $c/24$. To consistently fit these exact results into the modular-invariant torus partition function, we advocate a necessary augmentation of the representation theory in the original Friedan--Qiu--Shenker construction via symmetrizing the ground-state manifold associated with the $c/24$ Verma module. Under the newly-proposed scheme, we invoke a quantum-interference mechanism between the two independent Ishibashi states to construct the boundary Cardy states for the whole family of the $\mathcal{N}=1$ superconformal minimal series, based on which the extra fusion channels are unveiled through the obtained Verlinde formula. Our work thus provides the first complete solution to this thirty-year-old question.

Black hole (more generally, horizon) thermodynamics is a window into quantum gravity. Can horizon thermodynamics---and ultimately quantum gravity---be quasi-localized? A special case is the static patch of de Sitter spacetime, known since the work of Gibbons and Hawking to admit a thermodynamic equilibrium interpretation. It turns out this interpretation requires that a negative temperature is assigned to the state. I'll discuss this example, and its generalization to all causal diamonds in maximally symmetric spacetimes. This story includes a Smarr formula and first law of causal diamonds, analogous to those of black hole mechanics. I’ll connect this first law to the statement that generalized entropy in a small diamond is maximized in the vacuum at fixed volume.

In 2012, Maulik proved a conjecture of Oblomkov-Shende relating: (1) the Hilbert schemes of a plane curve (alternatively, its compactified Jacobian), (2) the HOMFLY polynomials of the links of its singularities. We recast his theorem from the viewpoint of representation theory. For a split semisimple group G with Weyl group W, we state a stronger conjecture relating two virtual modules over Lusztig's graded affine Hecke algebra,  constructed from: (1) fibers of a parabolic Hitchin map, (2) generalized Bott-Samelson spaces attached to conjugacy classes in the braid group of W. In arbitrary type, we can establish an infinite family of cases where it holds. Time permitting, we'll indicate how the new conjecture relates to P = W phenomena in nonabelian Hodge theory.

The n-point correlation functions (n>2) of primordial fluctuations, known as primordial non-Gaussianities, encode rich information about the physical degrees of freedom and their interactions at inflation scale, and can be viewed as signals from a cosmological collider with huge energy. In this talk we introduce recent theoretical attempts to extract new physics at the inflation scale from primordial non-Gaussianities, including possible discovery channels, the background signals from the standard model, and signals from new physics such as heavy neutrinos, and a possible way to turn inflation into a Higgs collider.

The history of the baryonic (normal) matter in the universe is an excellent probe of the  formation of cosmic structures and the evolution of galaxies.  Over the last decade, considerable effort has gone into investigating the physics of baryonic material, particularly after the epoch of Cosmic Dawn: signalling the birth of the earliest stars and 
galaxies --- widely considered the ‘final frontier’ of observational cosmology today. The technique of (line) ‘intensity mapping’ (IM) has emerged as a powerful tool to explore this phase of the universe by measuring the integrated emission from sources over a broad range of frequencies. I will overview my current research on the mapping of atomic hydrogen over 12  billion years of cosmic time, based on a data-driven framework developed for interpreting current and future IM observations. I will then describe extensions of this approach which provide a comprehensive picture of molecular gas evolution, and interpret results from ongoing observations. This opens up the exciting potential of constraining fundamental physics from Cosmic Dawn.

Tensor models exhibit a melonic large $N$ limit: this is a non trivial family of Feynman graphs that can be explicitly summed in many situations. In $d$ dimensions, they give rise to a new family of conformal field theories and provide interesting examples of the renormalization group flow from a free theory in the UV to a melonic large $N$ CFT in the IR. 

We consider here a bosonic tensor model in rank three and $d<4$ dimensions. After giving a short introduction to tensor models, I will present the renormalization group flow of the model. At leading order in $1/N$ but non perturbatively in the coupling constants, we found a real and infrared fixed point.