Speaker:   Shihang He

Abstract:  
We prove the Riemannian positive mass theorem up to dimension 19, building on a combination of torical symmetrization and the singularity blow-up technique, together with the generic regularity theory for area-minimizing hypersurfaces developed by Chodosh, Mantoulidis, Schulze and Wang. This is a joint work with Yuchen Bi, Tianze Hao, Yuguang Shi and Jintian Zhu.

Title:   The quantum energy outflux emerging from a collapsing shell    

Abstract:   When a compact object collapses to form a black hole, quantum field theory predicts the emission of an energy outflux to future null infinity, which later relaxes to Hawking radiation.
Within the semiclassical framework, we derive a simple, closed form, analytical expression for the energy outflux emitted from a spherical thin null shell collapsing to form a black hole. In particular, this energy outflux vanishes (quadratically in r-2M) as the shell approaches the horizon. This result refutes claims that the Hawking energy outflux originates from the collapsing body, showing instead that it develops in a broad strong-field region. Additionally, this vanishing implies that semiclassical backreaction cannot prevent or significantly affect the classical process of gravitational collapse and horizon formation (as sometimes claimed).

This talk is based on the joint work arXiv:2503.00622 with Amos Ori.

Speaker:   Dan Petersen

Abstract:  
This is a report of joint work with Bergström-Diaconu-Westerland and Miller-Patzt-Randal-Williams. There is a "recipe" due to Conrey-Farmer-Keating-Rubinstein-Snaith which allows for precise predictions for the asymptotics of moments of many different families of L-functions. We consider the family of all L-functions attached to hyperelliptic curves over some fixed finite field. One can relate this problem to understanding the homology of the hyperelliptic mapping class group with symplectic coefficients. With Bergström-Diaconu-Westerland we compute the stable homology groups of the hyperelliptic mapping class group with these coefficients, together with their structure as Galois representations. With Miller-Patzt-Randal-Williams we prove a uniform range for homological stability with these coefficients. Together, these results imply the CFKRS predictions for all moments in the function field case, for all sufficiently large (but fixed) q.

Speaker:   Dzmitry Dudko

Abstract:  
TBA

For more information, please visit: https://scgp.stonybrook.edu/archives/45381

Speaker:   Andy Lucas
Title:   High-temperature self-correction in Lee-LDPC codes
Abstract:   I will describe our ongoing work on the search for quantum memory in the presence of very high noise rates. We have found a promising candidate for such a code to be a Lee-LDPC code -- these are quantum codes with few-body interactions of low Pauli weight on q-dimensional qudits, with large q. Our ongoing work suggests the existence of simple quantum codes that have very high thresholds against small weight bit/shift errors.

Speaker:   Yimu Bao
Title:   Non-linear sigma model for the surface code with coherent errors
Abstract:   In this talk, I consider decoding in the square-lattice surface code with the simplest type of coherent error — single-qubit unitary rotations which create electric anyon excitations. I will derive a non-linear sigma model that governs the decoding in this setting. The sigma model predicts distinct phase diagrams for the optimal decoder, which assumes the knowledge of coherent rotation angles, and the suboptimal decoder that only has imperfect knowledge. Our theory hints at a possible decodable phase up to the maximally coherent rotation angle. We examine the predictions from the sigma model on the decoding fidelity and other physical observables using extensive numerical simulations. I will also discuss how the target space of the sigma model changes when the syndromes live on a non-bipartite lattice.

Speaker:   Tim Hsieh
Title:   A unified framework for locally stable phases
Abstract:   We propose a unifying framework for characterizing pure and mixed-state phases of matter across equilibrium, non-equilibrium, and metastable regimes. We introduce the concept of locally stable states, defined by the operational property that any local operation (including post-selection) can be reversed by a local channel. We prove that local stability is equivalent to a state being short-range correlated—defined by the decay of both correlations and conditional mutual information. We demonstrate that these properties are invariant under locally reversible channels, thus defining locally stable phases. Furthermore, we prove that local stability implies both the decay of various nonlinear correlators and the decay of correlations in the canonical purification, thus bridging the gap between mixed and pure states. Along the way, we establish two results which may be of independent interest: we show that post-selection on locally stable / short-range correlated states can be implemented via local channels and that quantum Markov chains can be characterized by the local computability of nonlinear observables.

Speaker:   Cenke Xu
Title:   Theory and experiment of strong-weak SSB
Abstract:   We discuss recent theoretical and experimental progress of the strong-weak spontaneous symmetry breaking driven by dephasing or measurement. Theoretically we demonstrate that SW-SSB is tightly connected with the emergence of indistinguishability, decodabilidy, and hydrodynamics. We also discuss experimental observation of both the SW-SSB phase and SW-SSB transition, realized in fermi-gas microscope.

Speaker:   Dan Cristofaro-Gardiner

Abstract:  
TBA

Speaker:   Andreas Ludwig
Title:   Non-perturbative monotonicity theorems for RG flow in systems with broken translational symmetry due to measurements
Abstract:   Very general monotonicity theorems exist for translationally invariant systems, identifying quanitities that decrease upon renormalization group (RG) flow: Zamolodchikov's "c-theorem" in 2D (1986), the "F-theorem" in 3D, Cardy's "a-theorem" in 4D (1988), and the "g-theorem" for boundaries (Affleck+Ludwig, 1991). No such monotonicity theorems have been identified for RG flows occurring in systems where translational symmetry is broken by generic spatially uncorrelated quenched randomness, e.g., from "impurity-type" disorder. Here we present two non-perturbative monotonicity theorems in systems where translational symmetry is broken by the randomness of measurement outcomes. The quantities that decrease under RG flow appear directly in the Shannon Entropy of the measurement record. [R.A.Patil, A.W.W.Ludwig, arXiv:2507.07959]

Speaker:   Romain Vasseur
Title:   Measurement-induced entanglement in CFTs
Abstract:   Local measurements can radically reshape patterns of many-body entanglement, especially in long-range entangled quantum-critical states. Yet, analytical results addressing the effects of measurements on many-body states remain scarce, and measurements are often approximated as forcing specific measurement outcomes. In this talk, I will discuss measurement-induced entanglement (MIE) in Tomonaga-Luttinger liquids, a broad family of 1+1d quantum critical states described at low energies by compact free boson conformal field theories (CFT). Measuring the local charge operator, I will show that the MIE is entirely universal, conformally invariant, and can be computed exactly using a replica trick. I will also discuss recent work on the full distribution of MIE, and comment on the general description of measurements in quantum field theories.

Speaker:   Meng Cheng
Title:   Entanglement negativity in decohered topological phases
Abstract:   I will discuss two computations of entanglement negativity: one for general decohered Abelian topological phases within a continuum field-theory framework, and the other for decohered G-graded string-net models. In both cases, we find that the topological correction is given by the logarithm of the total quantum dimension associated with the modular strong one-form symmetry, while the topological mutual information captures the non-modular sector. I will also comment on a discrepancy between the field-theory and lattice results.

Speaker:   Xueda Wen
Title:   Higher topological structures in local purifications
Abstract:   In this talk, I will show that local purifications of density matrix in one-dimensional many-body gapped systems give rise to higher topological structures, going beyond conventional vector bundles. When there is an obstruction of finding local purifications that are globally continuous over the parameter space, the data of local purifications organize into an equivariant gerbe (or equivariant higher line-bundle) structure. Physically, this means there will be a topological pump along the 1d system.

Observance
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Speaker:   Yizhi You
Title:   LSM in open quatum system: A spacetime duality view
Abstract:   Quantum anomalies strongly constrain many-body dynamics. A prime example is the Lieb-Schultz-Mattis (LSM) theorem, which links microscopic symmetry and filling to either gaplessness or degeneracy. Here, we ask how LSM constraints shape dynamical signatures and temporal correlations in open quantum systems. Using a spacetime duality, we show that the time trajectory of a $d$-dimensional repeated quantum channel with a mixed anomaly between strong $S$ and weak $G$ symmetry can be mapped to a $(d{+}1)$-dimensional mixed-state symmetry-protected topological (mSPT) phase. In this correspondence, the channel’s initial and steady states are identified with boundary states of the higher-dimensional mSPT in the presence of bulk measurements. We further introduce the twisted Renyi-$N$ correlator (TRNC) as a probe of temporal correlations in the channel and demonstrate that it is dual to the mSPT strange correlator, providing a direct bulk-boundary route to diagnose long-range temporal order implied by the LSM anomaly. Notably, we identify the Liouvillian singular spectrum, rather than the Liouvillian spectrum itself, as a more precise diagnostic of quantum anomalies, and show that it is dual to the entanglement spectrum of the mSPT.

Speaker:   Peter Abbamonte
Title:   Quantum geometric bounds in ionic and covalent insulators measured with inelastic x-ray scattering
Abstract:   Widespread interest in topological phases of matter has recently raised awareness of the importance of quantum geometry in solids. The topology of an electronic energy band is quantified by its Berry curvature, which is the imaginary part of a more general quantity called the quantum geometric tensor, T. Its real part, the quantum metric, characterizes electronic polarization fluctuations and is a measure of the delocalization of valence electrons in a material. These fluctuations can be expressed in terms of the quantum weight, K(q), which is proportional to the quantum Fisher information, a measure of the number of entangled degrees of freedom per unit volume in a quantum system. These relationships imply a deep connection between quantum geometry, entanglement, and the nature of chemical bonding in solids.
In this talk, I will present an experimental investigation of these ideas using inelastic x-ray scattering (IXS) from two prototypical insulators, covalently bonded diamond and ionically bonded LiF. Extracting the quantum weight from the IXS data demonstrates that, in diamond, the delocalization of electronic information extends over multiple unit cells, while in LiF it is confined within a single unit cell. In both cases, the quantum weight lies within fundamental bounds recently postulated for insulating states of matter [1,2]. Our results align with the intuitive understanding of covalent and ionic bonding, and demonstrate that energy-loss scattering provides a quantitative probe of wave function geometry in solids.
[1] Y. Onishi, L. Fu, PRX 14, 011052 (2024)
[2] D. Balut, M. D. Collins, B. Bradlyn, P. Abbamonte, arXiv:2601.19054

Speaker:   Itamar Kimchi
Title:   Global topology from local lattice defects
Abstract:   Defects are always present in solid state materials and effectively in many artificial quantum systems without translation symmetry. I will present our group’s recent theoretical results showing how quantum-entangled or topological systems can enable local defects to produce surprising global effects.

Speaker:   Adam Nahum
Title:   Bayesian critical points in classical lattice models
Abstract:   The Boltzmann distribution encodes our subjective knowledge of the configuration in a classical lattice model, given only its Hamiltonian. If we acquire further information about the configuration from local measurements then our knowledge is updated according to Bayes' theorem. I will argue that the resulting statistical ensembles (conditioned on measurements) show various interesting phase transitions, and will comment on some alternative interpretations of these transitions.

TITLE: Information Lattice Learning

ABSTRACT: Drawing on group-theoretic and information-theoretic foundations, we propose information lattice learning (ILL) as a general framework to learn rules of a signal (e.g., an image or a probability distribution). In our definition, a rule is a coarsened signal used to help us gain one interpretable insight about the original signal. To make full sense of what might govern the signal’s intrinsic structure, we seek multiple disentangled rules arranged in a hierarchy, called a lattice. Compared to representation/rule-learning models optimized for a specific task (e.g., classification), ILL focuses on explainability: it is designed to mimic human experiential learning and discover rules akin to those humans can distill and comprehend. We will detail the mathematical foundations and algorithms of ILL, and illustrate how it addresses the fundamental question “what makes X an X” by creating rule-based explanations designed to help humans understand. Our focus is on explaining X rather than (re)generating it. We show ILL’s efficacy and interpretability on benchmarks and assessments, as well as a demonstration of ILL-enhanced classifiers achieving human-level digit recognition using only one or a few MNIST training examples (1–10 per class).  We present applications in knowledge discovery, using ILL to distill music theory from scores and chemical laws from molecules and further revealing connections between them. We close with some early work on understanding the principles that govern scattering amplitudes in Super Yang-Mills theory, rather than just predicting them.

BIOGRAPHY:
Lav R. Varshney is the Della Pietra Infinity Professor and inaugural director of the AI Innovation Institute at Stony Brook University. He is co-founder and CEO of Kocree, Inc., a startup company building novel human-controllable AI for discovery and creativity, and chief scientist of Ensaras, Inc., a startup company focused on AI and wastewater treatment. He holds appointments at RAND Corporation and at Brookhaven National Laboratory. He was previously on the faculty of the University of Illinois Urbana-Champaign, a visiting scholar at Northwestern's Kellogg School of Management, a principal research scientist at Salesforce Research AI, and a research staff member at IBM Research. He is a former White House staffer, having served on the National Security Council staff as a White House Fellow, where he contributed to national AI and wireless communications policy. His research interests include information theory and artificial intelligence. He received his B.S. degree from Cornell University and his S.M. and Ph.D. degrees from the Massachusetts Institute of Technology.

Speaker:   Etienne Granet
Title:   Spectral functions on a quantum computer through system-environment interaction
Abstract:   Spectral functions are experimentally measurable quantities that provide key insights into the band structure of materials. Their computation on quantum computers poses a number of technical difficulties and typically comes with a large sampling overhead. I will introduce a new approach to measure spectral functions on quantum computers based on modelisation of system-environment interaction and on the use of fermionic quantum Fourier transforms, that provides a significant reduction of sampling overhead and runtime compared to standard approaches. I will present an implementation on Quantinuum's System Model H2 trapped-ion system.

Speaker:   Carolyn Zhang
Title:   Strongly symmetric lindbladians: constraints from LSM anomalies and locality
Abstract:   We will show how LSM anomalies appear naturally in the context of Lindbladian dynamics with strong finite symmetries. We will also show how the Lovasz local lemma can be applied to a broad class of strongly symmetric Lindbladians to enforce long range correlations & long mixing time.

Speaker:   Yichen Xu
Title:   Error thresholds of toric codes with transversal logical gates
Abstract:   The threshold theorem promises a path to fault-tolerant quantum computation by suppressing logical errors, provided the physical error rate is below a critical threshold. While transversal gates offer an efficient method for implementing logical operations, they risk spreading errors and potentially lowering this threshold compared to a static quantum memory. To date, most available threshold estimates for transversal circuits have been obtained empirically and are limited to specific, sub-optimal decoders. In this work, we generalize the statistical mechanical mapping from static quantum memories to logical circuits with transversal gates. This generalization enables rigorous, decoder-independent error thresholds to be established for fault-tolerant logical computation. We first demonstrate this framework for two toric code blocks undergoing a transversal CNOT (tCNOT) gate, quantifying the impact of two independent error-spreading mechanisms: the spread of physical bit-flip errors and the spread of syndrome errors. In the former case, the stat-mech model is a 2D random Ashkin-Teller model. We use Monte Carlo simulation and finite-size scaling to show that the tCNOT gate reduces the optimal bit-flip error threshold to $p=0.080$, a $26\%$ decrease from the toric code memory threshold $p=0.109$. The case of syndrome errors coexisting with bit-flip errors is mapped to a 3D random 4-body Ising model with a plane defect, yielding a conservative threshold estimate of $p\geq 0.028$---a modest $15\%$ reduction from the memory threshold $p=0.033$. Going beyond the tCNOT gate, we derive stat-mech models for all transversal Clifford gates of the toric code, including the fold-transversal Hadamard and $S$ gates, showing that each gate manifests as a distinct permutation defect of the Ising spins. We further generalize the framework to arbitrary CSS codes with transversal Clifford gates, proving that each transversal gate modifies the stat-mech model only locally in time. Our work opens the door to rigorous threshold analysis of entire fault-tolerant logical circuits via classical statistical mechanics.

Speaker:   Hongyi Liu

Abstract:  
Poincare-Einstein metrics are a natural class of complete Einstein metrics with negative Einstein constant, though their construction is often difficult. In this talk, I will discuss four-dimensional conformally Kahler Poincare-Einstein metrics. In this setting, the conformally Kahler structure reduces the Einstein equation to a single nonlinear elliptic equation of Toda type, yielding an infinite-dimensional, nonperturbative construction of Poincare-Einstein metrics. I will then explain how the same framework extends to metrics with various cusp ends and how it can be used to study degenerations of Poincare-Einstein metrics. This provides a unified analytic perspective on several noncompact Einstein geometries through elliptic boundary value problems. This is joint work with Mingyang Li.

Speaker:   Nat Tantivasadakarn
Title:   Coupled-layer construction of quantum product codes
Abstract:   I will show how a class of quantum LDPC codes called product codes admit a coupled-layer construction by taking a stack of one code and condensing a set of excitations in the pattern given by the checks of the other code. The construction accommodates both classical and quantum CSS input codes, unifies known physical mechanisms for constructing higher dimensional topological phases via anyon condensation, and naturally extends to non-topological codes.

Speaker:   Ruben Verresen
Title:   Realizing, using, and decohering S3 topological order
Abstract:   As the smallest non-abelian group, S3 gauge theory provides the minimal example of a topological phase of matter beyond stabilizer Hamiltonians. I will discuss a recent experimental realization of this phase of matter, where anyon braiding and fusion was demonstrated to provide a universal topological gate-set. On the theory side, I will highlight what happens when one tries to decohere such phases with non-abelian anyon noise.

Speaker:   Tom Iadecola
Title:   Squeezing many-body scar states with weak measurements
Abstract:   Quantum many-body scar states provide a mechanism for coherent dynamics in nonintegrable systems and offer a platform for quantum enhanced sensing that is robust to certain interactions. In this talk I will describe how postselected weak measurements can be used to filter the dynamics of non-scarred initial states onto the scarred eigenstates, even in the absence of exact analytical knowledge of those states. The mechanism, a form of squeezing, is robust to fluctuations off of the optimal quantum trajectory, with the degree of postselection determining the amount of squeezing achieved at late times.

Speaker:   Alex Kamenev
Title:   Rare events in open quantum systems
Abstract:   I will discuss probability of a large quantum fluctuation (a rare event) in stationary states of driven open systems. Contrary to its equilibrium counterpart, this quantity appears to be a non-analytic function of the parameters, specifying the rare event. The formal reason for this phenomenon is related to the existence of more than one instanton solution, leading to the same observable rare event.

Speaker:   Jong Yeon Lee
Title:   Defining non-equilibrium phases of matter
Abstract:   In this talk, I will present recent works that establish a systematic framework to study mixed-state phases of matter. This is achieved by identifying three information-theoretic quantities that can play the role analogous to the spectral gap in the study of quantum phases of matter. These three conditions correspond to (i) local recoverability, (ii) no long-range correlations, and (iii) spatial uniformity. States obeying them exactly are fixed points, while only approximately are phases of matter away from fixed points. I will discuss how approximate versions of these conditions provide robust topological data.

Speaker:   Yi-Zhuang You
Title:   Measurement-based quantum diffusion model
Abstract:   Generative diffusion models learn to reverse an entropy-increasing noise process to synthesize data. I will show how this idea lifts to quantum mechanics, with randomized weak measurements playing the role of noise. The forward process is a measurement-induced stochastic diffusion of pure states; the reverse process is a unitary flow driven by a learned state-dependent Hamiltonian. The key ingredient is a crossed matching scheme that trains the reverse flow from forward measurement data, yielding a data-driven protocol for preparing complex quantum states, with applications to algorithmic cooling and quantum error correction.

Speaker:   Dan Mao
Title:   Symmetries enforced by local constraints
Abstract:   In this talk, I will revisit the trimer model, a natural generalization of the dimer model. While the classical trimer model was studied more than two decades ago, key features of the Hilbert space spanned by fully packed trimer covering have remained unnoticed. I will demonstrate that the interplay of local constraints, lattice geometry, and finite on-site degrees of freedom gives rise to an exact global symmetry within this Hilbert space, which is robust under any local moves. Curiously, the charged operator is string-like, whose charge is shape dependent.

Speaker:   Bowen Shi
Title:   Topological mixed states from entangled ground states: a holographic matching of pure and mixed entanglement bootstrap
Abstract:   Identifying fixed-point wavefunctions and their equivalence classes via entanglement structure is central to the entanglement bootstrap program for gapped phases. In recent work on mixed-state phases (with Tai-Hsuan Yang and Jong Yeon Lee), we provided a definition of mixed-state fixed points based on three fixed-point conditions, or axioms. In this talk, I show how topological mixed-state fixed points can be systematically generated from pure-state fixed points in one higher dimension. The essence of the argument is a holographic matching between the “pure” and “mixed” versions of the entanglement bootstrap axioms. We further derive several curious emergent properties of the mixed-state fixed points so constructed, some of which I conjecture to be general.

Speaker:   Michael Barz

Abstract:  
In characteristic 0, one of the most powerful tools for understanding linear ODEs is the Riemann--Hilbert correspondence. Around 1970, Cartier found a partial analogue of the Riemann--Hilbert correspondence in *positive* characteristic, now called Cartier descent. Unfortunately, Cartier descent does not apply to all ODEs, but only to those for which a certain invariant (called p-curvature) vanishes. Generalizations of Cartier descent which work when the p-curvature is nonzero are typically called non-abelian Hodge theorems in positive characteristic, as they end up being closely related to non-abelian Hodge theory over the complex numbers.

In this talk, we will explain a new non-abelian Hodge theorem for curves in positive characteristic, applying to connections with *logarithmic* singularities. Our work extends earlier results of Groechenig and de Cataldo--Zhang. Our key technical tool is a logarithmic variant of Carlos Simpson's de Rham stack, which may be of independent interest.

Speaker:   Chao-Ming Jian
Title:   Symmetry classification of dynamical quantum matter and decoding problems
Abstract:   In this talk, I will introduce the ten-fold symmetry classification for fermionic dynamical systems subject to both unitary evolution and measurements. I will demonstrate how symmetry classes govern the universal long-distance entanglement dynamics and the possible non-equilibrium topologies. I will then present a duality between fermionic dynamical systems with measurements and the decoding of surface codes with coherent errors, which enables the symmetry classification of the decoding problems. In particular, I will show that for surface codes on both square and honeycomb lattices, the corresponding decoding problems fall into symmetry classes D and DIII. These symmetry classes govern the general structure of the allowed phases and transitions in the decodability phase diagram, as well as continuum descriptions of the related systems. Finally, I will discuss concrete microscopic coherent error models that give rise to a variety of decodability transitions in the surface codes. These transitions are dual to measurement-induced phase transitions of distinct universality classes in dynamical Majorana systems.