Talks

I will talk about the generalization of Berry classes for quantum lattice spin systems. It defines invariants of topologically ordered states or families thereof. In particular, its equivariant version for 2d gapped states gives the zero-temperature Hall conductance and its various generalizations. I will also discuss the construction of chiral states realizing the topological order associated with a unitary rational vertex operator algebra for which these invariants are non-trivial

Zoom link:  https://pitp.zoom.us/j/99910103969?pwd=VlVHVGRiV29iVEFyTXZyR3ovMkRaQT09

The initial conditions of our universe appear to us in the form of a classical probability distribution that we probe with cosmological observations. In the current leading paradigm, this probability distribution arises from a quantum mechanical wavefunction of the universe. In this talk I will discuss how we can adapt flat space bootstrapping techniques to the quantum fluctuations in the early universe, in particular showing that the requirement of unitary time evolution, colloquially the conservation of probabilities, fixes the analytic structure of the wavefunction and of all the cosmological correlators it encodes.

Zoom link:  https://pitp.zoom.us/j/95812107239?pwd=bVZMcWdHTVM0Y0tFZGMxS2FCVGF0Zz09

Error-correcting codes were invented to correct errors on noisy communication channels. Quantum error correction (QEC), however, has a wider range of uses, including information transmission, quantum simulation/computation, and fault-tolerance. These invite us to rethink QEC, in particular, the role that quantum physics plays in terms of encoding and decoding. The fact that many quantum algorithms, especially near-term hybrid quantum-classical algorithms, only use limited types of local measurements on quantum states, leads to various new techniques called Quantum Error Mitigation (QEM). We examine the task of QEM from several perspectives. Using some intuitions built upon classical and quantum communication scenarios, we clarify some fundamental distinctions between QEC and QEM. We then discuss the implications of noise invertibility for QEM, and give an explicit construction called Drazin-inverse for non-invertible noise, which is trace-preserving while the commonly-used MoorePenrose pseudoinverse may not be. Finally, we study the consequences of having imperfect knowledge about system noise and derive conditions when noise can be reduced using QEM.

Zoom link:  https://pitp.zoom.us/j/91543402893?pwd=b09IS3VWNk5KZi8ya3gzSmRKRFJidz09

A well-established approach to solving interacting quantum systems is variational Monte Carlo. There is a lot of renewed interest in it since the introduction of neural networks as a highly expressive and unbiased variational ansatz. Similar to more traditional ansätze, neural networks struggle with solving frustrated quantum systems. A conjecture has been made that the cause of these difficulties lies in the sign structures of the ground state wavefunctions. Here, we will discuss these sign structures in more detail and try to analyze how complex they really are by establishing a connection to classical Ising models.

Zoom link:  https://pitp.zoom.us/j/99087954160?pwd=Vm5zWWRFbHBwVFR1RHZMc3ptem03QT09

When individuals in a social network learn about an unknown state from private signals and neighbors’ actions, the network structure often causes information loss. We consider rational agents and Gaussian signals in the canonical sequential social-learning problem and ask how the network changes the efficiency of signal aggregation. Rational actions in our model are a log-linear function of observations and admit a signal-counting interpretation of accuracy. This generates a fine-grained ranking of networks based on their aggregative efficiency index. Networks where agents observe multiple neighbors but not their common predecessors confound information, and we show confounding can make learning very inefficient. In a class of networks where agents move in generations and observe the previous generation, aggregative efficiency is a simple function of network parameters: increasing in observations and decreasing in confounding. Generations after the first contribute very little additional information due to confounding, even when generations are arbitrarily large.

Many social network phenomena such as norms and cascades depend not only on what agents believe but on what they believe other agents believe.   One important instantiation of agents’ beliefs about beliefs is knowledge commonly known by all agents.  However, current definitions that capture this idea such as common knowledge and common belief are too restrictive for use in understanding strategic coordination and cooperation in social network settings. In this talk, I will propose a relaxation of common belief called factional belief that is suitable for the analysis of social network phenomena.  I will then show how this definition can be used to analyze revolt games on sparse graphs.  In particular, I will show that for a certain natural class of revolt games, the degree sequence of a network almost entirely characterizes whether any equilibrium can often support a large revolt.  The proof is via an efficient algorithm for determining the same.  A key goal of this talk is to provide the background to start a conversation about where common knowledge (or its variants) can help us to reason about social network phenomena.

We characterize the optimal communication network in a firm with a modular production function, which we model as a network of decisions with a non-overlapping community structure. Optimal communication is characterized by two hierarchies that determine whom each agent receives information from and sends information to. Receiver rank depends only on module cohesion while sender rank also depends on decision-specific values of adaptation. When the hierarchies are the reverse of each other, optimal communication is bottom up in aggregate, and when they are the same, it has a core-periphery structure, in which the core contains the most cohesive modules.

Other peoples' experiences serve as primary sources of information about the potential payoffs to various available opportunities. Homophily in social networks affects both the quality and diversity of information to which people have access.On the one hand, homophily provides higher quality information since observing the experiences of another person is more informative as that person is more similar to the decision maker. On the other hand, homophily lowers the variety of actions about which people can learn when a group ends up herding on specific actions about which they have better information. This can lead to inefficiencies and inequalities across groups, as we show. Homophily lowers efficiency and increases inequality in sparse networks, while enhancing efficiency and decreasing inequality in denser networks. We characterize conditions under which groups herd on separate actions, and show how such homophily-induced herding driven by limited scope of information differs from standard forms of herding driven by cascading inferences.