Talks

 3d mirror symmetry relates the geometry of dual pairs of algebraic symplectic stack and has served in as

a guiding principle for developments in representation theory. However, due to the lack of definitions, thus far only part of the subject has been mathematically accessible. In this talk, I will explain joint work with Ben Gammage and Aaron Mazel-Gee on formulation of abelian 3d mirror symmetry as an equivalence between a pair of 2-categories constructed from the algebraic and symplectic geometry, respectively, of Gale dual toric cotangent stacks.

In the simplest case, our theorem provides a spectral description of the 2-category of spherical functors -- i.e., perverse schobers on the affine line with singularities at the origin. We expect that our results can be extended from toric cotangent stacks to hypertoric varieties, which would provide a categorification of previous results on Koszul duality for hypertoric categories $\mathcal{O}$.

Zoom Link: https://pitp.zoom.us/j/95205675729?pwd=OXRSTlhiQUxQYm5lLzVLYTE1Z0FLdz09

Recent advances in quantum simulation experiments have paved the way for a new perspective on strongly correlated quantum many-body systems. Digital as well as analog quantum simulation platforms are capable of preparing desired quantum states, and various experiments are starting to explore non-equilibrium many-body dynamics in previously inaccessible regimes in terms of system sizes and time scales. State-of-the art quantum simulators provide single-site resolved quantum projective measurements of the state. Depending on the platform, measurements in different local bases are possible. The question emerges which observables are best suited to study such quantum many-body systems.

In this talk, I will cover two different approaches to make the most use of these possibilities. In the first part, I will discuss the use of machine learning techniques to study the thermalization behavior of an interacting quantum system. A neural network is trained to distinguish non-equilibrium from thermal equilibrium data, and the network performance serves as a probe for the thermalization behavior of the system. We apply this method to numerically simulated data, as well experimental snapshots of ultracold atoms taken with a quantum gas microscope. 

In the second part of this talk, I will present a scheme to perform adaptive quantum state tomography using active learning. Based on an initial, small set of measurements, the active learning algorithm iteratively proposes the basis configurations which will yield the maximum information gain. We apply this scheme to GHZ states of a few qubits as well as ground states of one-dimensional lattice gauge theories and show an improvement in accuracy over random basis configurations.

We study D dimensional pure Einstein gravity theory in a region of spacetime bounded by a generic null boundary. We show besides the graviton modes propagating in the bulk, the system is described by boundary degrees of freedom labeled by D surface charges associated with nontrivial diffeomorphisms at the boundary. We establish that the system admits a natural thermodynamical description. Using standard surface charge analysis and covariant phase space method, we formulate  laws of null surface thermodynamics which are local equations over an arbitrary null surface. This thermodynamical system is generally an open system and can be closed only when there is no flux of gravitons through the null surface. Our analysis  extends the usual black hole thermodynamics to a universal feature of any area element on a generic null surface in a generic diffeomorphism invariant theory of gravity. 

Zoom Link: https://pitp.zoom.us/j/91590041045?pwd=UXpWY3JEd0QwK2hXanBzSkdPRC94UT09

I will discuss the detailed process by which slow contraction smooths and flattens the universe using an improved numerical relativity code that accepts initial conditions with non-perturbative deviations from homogeneity and isotropy along two independent spatial directions. Contrary to common descriptions of the early universe, I will show that the geometry first rapidly converges to an inhomogeneous, spatially-curved, and anisotropic ultralocal state in which all spatial gradient contributions to the equations of motion decrease as an exponential in time to negligible values. This is followed by a second stage in which the geometry converges to a homogeneous, spatially flat, and isotropic spacetime. In particular, the decay appears to follow the same history whether the entire spacetime or only parts of it are smoothed by the end of slow contraction.

Zoom Link: https://pitp.zoom.us/j/95441238892?pwd=TUh4Mjh1MHJ6TDNCL0V1NUk5WWFZQT09

What is the global symmetry of Nature? In the absence of gravity, the most obvious answer to this question is given by special relativity and is associated with the Poincare transformations. As was noted a long time ago, the free Maxwell equations have a wider symmetry group - the 15 parameters conformal invariance, containing in addition to ten Poincare generators, four special conformal transformations, and dilatations. Dilatations change the length of the rulers, while special conformal transformation can bend the lines but do not alter the angles between them. Could it be that the symmetry of all interactions is conformal? We will show that the answer to this question is "yes". The essential feature of the theory is the anomaly-free extension of the spontaneously broken conformal symmetry to curved space-time. We discuss how the effective Lagrangian respecting this special Weyl symmetry can be used for the description of particle phenomenology and cosmology.

Euclidean wormholes are exotic types of gravitational solutions that we still don't understand completely. In the first part of the talk, I will analyze asymptotically AdS wormhole solutions from a gravitational point of view. By studying correlation functions of local and non-local operators, the universal properties that any putative holographic dual should exhibit, become manifest. In the second part, I will describe some concrete field theoretic models (both effective and microscopic) that share these properties.

Superradiant instabilities may create clouds of ultralight bosons around black holes, forming so-called “gravitational atoms.” It was recently shown that the presence of a binary companion can induce resonant transitions between a cloud's bound states. When these transitions backreact on the binary's orbit, they lead to qualitatively distinct signatures in the gravitational waveform that can dominate the overall behavior of the inspiral. In this talk, I will show that the interaction with the companion can also trigger transitions from bound to unbound states of the cloud---a process which I will refer to as ``ionization,'' in analogy with the photoelectric effect in atomic physics. Here, too, there is a type of resonance with a similarly distinct signature, which may ultimately be used to detect any dark ultralight bosons that exist in our universe.

Zoom Link: https://pitp.zoom.us/j/97300299361?pwd=azhmVTR5VmpPQ1hwbkVHTUsrOGlJZz09

The field of quantum information provides fundamental insight into central open questions in quantum thermodynamics and quantum many-body physics, such as the characterization of the influence of quantum effects on the flow of energy and information. These insights have inspired new methods for cooling physical systems at the quantum scale using tools from quantum information processing. These protocols not only provide an essentially different way to cool, but also go beyond conventional cooling techniques, bringing important applications for quantum technologies. In this talk, I will first review the basic ideas of algorithmic cooling and give analytical results for the achievable cooling limits for the conventional heat-bath version. Then, I will show how the limits can be circumvented by using quantum correlations. In one algorithm I take advantage of correlations that can be created during the rethermalization step with the heat-bath and in another I use correlations present in the initial state induced by the internal interactions of the system. Finally, I will present a recently fully characterized quantum property of quantum many-body systems, in which entanglement in low-energy eigenstates can obstruct local outgoing energy flows.

Monitored quantum circuits (MRCs) exhibit a measurement-induced phase transition between area-law and volume-law entanglement scaling. In this talk, I will argue that MRCs with a conserved charge additionally exhibit two distinct volume-law entangled phases that cannot be characterized by equilibrium notions of symmetry-breaking or topological order, but rather by the non-equilibrium dynamics and steady-state distribution of charge fluctuations. These include a charge-fuzzy phase in which charge information is rapidly scrambled leading to slowly decaying spatial fluctuations of charge in the steady state, and a charge-sharp phase in which measurements collapse quantum fluctuations of charge without destroying the volume-law entanglement of neutral degrees of freedom. I will present some statistical mechanics and effective field theory approaches to such charge-sharpening transitions.

Zoom Link: https://pitp.zoom.us/meeting/register/tJcqc-ihqzMvHdW-YBm7mYd_XP9Amhypv5vO

Causality is fundamental to science, but it appears in several different forms. One is relativistic causality, which is tied to a space-time structure and forbids signalling outside the future. On the other hand, causality can be defined operationally using causal models by considering the flow of information within a network of physical systems and interventions on them. From both a foundational and practical viewpoint, it is useful to establish the class of causal models that can coexist with relativistic principles such as no superluminal signalling, noting that causation and signalling are not equivalent. We develop such a general framework that allows these different notions of causality to be independently defined and for connections between them to be established. The framework first provides an operational way to model causation in the presence of cyclic, fine-tuned and non-classical causal influences. We then consider how a causal model can be embedded in a space-time structure and propose a mathematical condition (compatibility) for ensuring that the embedded causal model does not allow signalling outside the space-time future. We identify several distinct classes of causal loops that can arise in our framework, showing that compatibility with a space-time can rule out only some of them. We then demonstrate the mathematical possibility of causal loops embedded in Minkowski space-time that can be operationally detected through interventions, without leading to superluminal signalling. Our framework provides conditions for preventing superluminal signalling within arbitrary (possibly cyclic) causal models and also allows us to model causation in post-quantum theories admitting jamming correlations. Applying our framework to such scenarios, we show that post-quantumjamming can indeed lead to superluminal  signalling contrary to previous claims. Finally, this work introduces a new causal modelling concept of ``higher-order affects relations'' and several related technical results, which have applications for causal discovery in fined-tuned causal models.

Deligne tensor categories are defined as an interpolation of the categories of representations of groups GL_n, O_n, Sp_{2n} or S_n to the complex values of the parameter n. One can extend many classical representation-theoretic notions and constructions to this context. These complex rank analogs of classical objects provide insights into their stable behavior patterns as n goes to infinity.
I will talk about some of my results on Harish-Chandra bimodules in Deligne categories. It is known that in the classical case simple Harish-Chandra bimodules admit a classification in terms of W-orbits of certain pairs of weights. However, the notion of weight is not well-defined in the setting of Deligne categories. I will explain how in complex rank the above-mentioned classification translates to a condition on the corresponding (left and right) central characters.
Another interesting phenomenon arising in complex rank is that there are two ways to define Harish-Chandra bimodules. That is, one can either require that the center acts locally finitely on a bimodule M or that M has a finite K-type. The two conditions are known to be equivalent for a semi-simple Lie algebra in the classical setting, however, in Deligne categories that is no longer the case. I will talk about a way to construct examples of Harish-Chandra bimodules of finite K-type using the ultraproduct realization of Deligne categories.

Zoom Link: https://pitp.zoom.us/j/93951304913?pwd=WVk1Uk54ODkyT3ZIT2ljdkwxc202Zz09