Fourier quasicrystals and stable polynomials
2022-12-07 15:30 - 16:30 (America/New_York) | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Probability Seminar
Note location change: Science Center Room 300H
Speaker: Lior Alon (MIT)
Title: Fourier quasicrystals and stable polynomials
Abstract: The Poisson summation formula says that the countable sum of exp(int), over all integers n, vanishes as long as t is not an integer multiple of 2 pi. Can we find a non-periodic discrete set A, such that the sum of exp(iat), over a in A, vanishes for all t outside of a discrete set? The surprising answer is yes. Yves Meyer called the atomic measure supported on such a set a crystalline measure. Crystalline measures provide another surprising connection between physics (quasicrystals) and number theory (the zeros of the Zeta and L functions under GRH). A recent work of Pavel Kurasov and Peter Sarnak provided a construction of crystalline measures with ‘good’ convergence (Fourier quasicrystals) using stable polynomials, a family of multivariate polynomials that were previously used in proving the Lee-Yang circle theorem and the Kadison-Singer conjecture. After providing the needed background, I will discuss a recent work in progress with Cynthia Vinzant on the classification of these Kurasov-Sarnak measures and their supporting sets. We prove that these sets have well-defined gap distributions. We show that each Kurasov-Sarnak measure decomposes according to the irreducible decomposition of its associated polynomial, and the measures associated with each irreducible factor is either supported on an arithmetic progression, or its support has a bounded intersection with any arithmetic progression. Finally, we construct random Kurasov-Sarnak measures with gap distribution as close as we want to the eigenvalues spacing of a random unitary matrix.
Based on joint work with Pravesh Kothari.

A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter
2022-12-08 09:30 - 10:30 | Virtual
General Relativity Seminar

Speaker: Allen Fang (Princeton)
Title: A new proof for the nonlinear stability of slowly-rotating Kerr-de Sitter
Abstract: The nonlinear stability of the slowly-rotating Kerr-de Sitter family was first proven by Hintz and Vasy in 2016 using microlocal techniques. In my talk, I will present a novel proof of the nonlinear stability of slowly-rotating Kerr-de Sitter spacetimes that avoids frequency-space techniques outside of a neighborhood of the trapped set. The proof uses vector field techniques to uncover a spectral gap corresponding to exponential decay at the level of the linearized equation. The exponential decay of solutions to the linearized problem is then used in a bootstrap proof to conclude nonlinear stability.

Self-organization of motile cells by quorum-sensing or chemotactic interactions
2022-12-08 13:00 - 14:00 | MA
Active Matter Seminar

Speaker: Julien Tailleur (MIT)
Title: Self-organization of motile cells by quorum-sensing or chemotactic interactions
Abstract: Equilibrium statistical mechanics tells us how to control the self-assembly of passive materials by tuning the competition between energy and entropy to achieve desired states of organization. Out of equilibrium, no such principles apply and self-organization principles are scarce. Active matter describes systems in which individual units dissipate energy to exert forces on their environment. Dissipation and injection of energy are then disconnected at the microscopic scale, hence driving the system strongly out of thermal equilibrium. This leads to a phenomenology markedly different from that of equilibrium systems, such as the emergence of dense phases in the absence of cohesive attractive forces, but it also leaves us without guiding principles to understand the self-organization of active matter. In this talk, I will review the progress which has been made over the past ten years to control the organization of self-propelled agents using motility control, either externally or through interactions. I will show that generic principles apply and illustrate the theoretical developments presented in the talk using recent experiments on the motility-induced self-organization of bacterial mixtures.

Non-Invertible Symmetries from Holography and Branes
2022-12-12 09:00 - 10:30 | Virtual
Quantum Matter Seminar
Speaker: Federico Bonetti (Oxford)
Title: Non-Invertible Symmetries from Holography and Branes
Abstract: The notion of global symmetry in quantum field theory (QFT) has witnessed dramatic generalizations in the past few years. One of the most exciting developments has been the identification of 4d QFTs possessing non-invertible symmetries, i.e. global symmetries whose generators exhibit fusion rules that are not group-like. In this talk, I will discuss realizations of non-invertible symmetries in string theory and holography. As a concrete case study, I will consider the Klebanov-Strassler setup for holographic confinement in Type IIB string theory. The global symmetries of the holographic 4d QFT (both invertible and non-invertible) can be accessed by studying the topological couplings of the low-energy effective action of the dual 5d supergravity theory. Moreover, non-invertible symmetry defects can be realized in terms of D-branes. The D-brane picture captures non-trivial aspects of the fusion of non-invertible symmetry defects, and of their action on extended operators of the 4d QFT.

Phase Fluctuations in Two-Dimensional Superconductors and Pseudogap Phenomenon
2022-12-20 09:00 - 10:30 | Virtual
Quantum Matter Seminar
Speaker: Yang Qi (Fudan)
Title: Phase Fluctuations in Two-Dimensional Superconductors and Pseudogap Phenomenon
Abstract: We study the phase fluctuations in the normal state of a general two-dimensional (2d) superconducting system with s-wave pairing. The effect of phase fluctuations of the pairing fields can be dealt with perturbatively using disorder averaging, after we treat the local superconducting order parameter as a static disordered background. It is then confirmed that the phase fluctuations above the 2d Berenzinskii-Kosterlitz-Thouless (BKT) transition give birth to the pseudogap phenomenon, leading to a significant broadening of the single-particle spectral functions. Quantitatively, the broadening of the spectral weights at the BCS gap is characterized by the ratio of the superconducting coherence length and the spatial correlation length of the superconducting pairing order parameter. Our results are tested on the attractive-U fermion Hubbard model on the square lattice, using unbiased determinant quantum Monte Carlo method and stochastic analytic continuation. We also apply our method to 2d superconductors with d-wave pairing and observe that the phase fluctuations may lead to Fermi-arc phenomenon above the BKT transition.

Reflections on Parity Breaking
2023-01-24 13:15 - 14:45 | Virtual
Quantum Matter Seminar
Speakers: Jacob McNamara (Caltech) and Matthew Reece (Harvard)
Title: Reflections on Parity Breaking
Abstract: One approach to the Strong CP Problem (known as Nelson-Barr models) is to assume that parity is a gauge symmetry, which is spontaneously broken in the world around us. In this talk, we will describe the formal meaning of parity as a gauge symmetry, and argue that the domain walls formed from spontaneous parity breaking are exactly stable. This stability can be understood as the result of an unusual sort of conserved charge, which has features in common with both gauge charges and global charges. We will explain how these charges are compatible with the expected absence of global symmetries in quantum gravity, as well as their relationship with the Swampland Cobordism Conjecture.

Testing spacetime geometry with images of supermassive compact objects: Current status and the future
2023-01-26 09:30 - 10:30 | Virtual
General Relativity Seminar
Speaker: Prashant Kocherlakota (BHI)
Title: Testing spacetime geometry with images of supermassive compact objects: Current status and the future
Abstract: Astrophysical black holes (BHs) are expected to be described by the Kerr solution of the Einstein equations. Several frameworks have recently been developed to parametrically deform the Kerr metric in significantly different ways, to enable formulations of tests of the no-hair theorems. Testing the viability status of alternative models – such as non-Kerr BHs from general relativity, BHs from alternative theories, wormholes, and other exotic objects – as descriptors of astrophysical objects has been of longstanding interest. The Event Horizon Telescope (EHT) recently imaged Sagittarius A* (Sgr A*), the supermassive compact object at the center of the Galaxy, making such tests possible. In such tests, the shadow critical curve (or simply shadow boundary), defined on the observer’s image plane, has gained prominence as the observable of interest. We will discuss how the EHT is able to extract information regarding the shadow of Sgr A* and the status of associated tests of the spacetime geometry in the strong-field regime. Future imaging measurements expect to detect the so-called photon ring, a strong-gravitational lensing feature that appears in the close vicinity of the critical curve, which houses higher-order images of the emission source. Time permitting, we will also discuss how these can be used to set up more stringent tests of the spacetime metric and gravity in the future.

Group Invariant States as Many-Body Scars
2023-01-30 09:30 - 10:30 | Virtual
Quantum Matter Seminar
Title: Group Invariant States as Many-Body Scars
Speaker: Igor R. Klebanov (Princeton University)
Abstract: Quantum many-body scars have been an active area of research in Condensed Matter Physics for several years. In some many-body systems, the Hilbert space breaks up into a large ergodic sector and a much smaller scar subspace. It has been suggested [K. Pakrouski et al., Phys. Rev. Lett. 125 (2020) 230602] that the two sectors may be distinguished by their transformation properties under a large group whose rank grows with the system size (this group is not a symmetry of the Hamiltonian). The scars are invariant under this group, while all other states are not. We begin by reviewing some many-body systems where group singlet states have special properties: the matrix quantum mechanics and fermionic tensor models. We continue on to appropriately deformed versions of the SU(2) Hubbard model and show that the scar subsector is invariant under a large group, which acts on the lattice sites. More generally, we apply this idea to lattice systems with N sites that contain M Majorana fermions per site. The Hilbert space may be decomposed under the action of the SO(N)xSO(M) group, and the scars are the SO(N) singlets. For any even M, there are two families of scars. One of them, which we call the eta-states, is symmetric under the group O(N) that includes a reflection. The other, the zeta-states, has the SO(N) invariance only. For M=4, where our construction reduces to a deformed SU(2) Hubbard chain with local interactions, the former family are the N+1 eta-pairing states, while the latter are the N+1 states of maximum spin. For M=6, we exhibit explicit formulae for the scar states and calculate the bipartite entanglement entropy analytically. For large N, it grows logarithmically with the region size. In general, the energies of the scars within each family are not equidistant. For M>6 we also find that, with local Hamiltonians, the scars typically have certain degeneracies. The latter part of the talk is based on the recent paper “Majorana Scars as Group Singlets” by Zimo Sun, Fedor Popov, Igor Klebanov and Kiryl Pakrouski, arXiv:2212.11914

Swampland program, extra dimensions and supersymmetry breaking
2023-01-30 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Swampland Seminar
Speaker: Ignatios Antoniadis (LPTHE Paris)

Title: Swampland program, extra dimensions and supersymmetry breaking

Abstract: I will argue on the possibility that the smallness of some physical parameters signal a universe corresponding to a large distance corner in the string landscape of vacua. Such parameters can be the scales of dark energy and supersymmetry breaking, leading to a generalisation of the dark dimension proposal. I will discuss the theoretical framework and some of its main physical implications to particle physics and cosmology.

AI and Theorem Proving
2023-01-31 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Mike Douglas
Title: AI and Theorem Proving
Abstract: We survey interactive theorem proving and the Lean theorem prover, and the use of AI and large language models to improve this technology. We hope to start a discussion on projects we can do at the CMSA.

Near extremal de Sitter black holes and JT gravity
2023-02-02 09:30 - 10:30 | Virtual
General Relativity Seminar
Speaker: Chiara Toldo (Harvard)
Title: Near extremal de Sitter black holes and JT gravity
Abstract: In this talk I will explore the thermodynamic response near extremality of charged black holes in four-dimensional Einstein-Maxwell theory with a positive cosmological constant. The latter exhibit three different extremal limits, dubbed cold, Nariai and ultracold configurations, with different near-horizon geometries. For each of these three cases I will analyze small deformations away from extremality, and construct the effective two-dimensional theory, obtained by dimensional reduction, that captures these features. The ultracold case in particular shows an interesting interplay between the entropy variation and charge variation, realizing a different symmetry breaking with respect to the other two near-extremal limits.

Neural Optimal Stopping Boundary
2023-02-02 12:30 - 13:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Max Reppen (Boston University)
Title: Neural Optimal Stopping Boundary
Abstract: A method based on deep artificial neural networks and empirical risk minimization is developed to calculate the boundary separating the stopping and continuation regions in optimal stopping. The algorithm parameterizes the stopping boundary as the graph of a function and introduces relaxed stopping rules based on fuzzy boundaries to facilitate efficient optimization. Several financial instruments, some in high dimensions, are analyzed through this method, demonstrating its effectiveness. The existence of the stopping boundary is also proved under natural structural assumptions.

Interacting Active Matter
2023-02-02 13:00 - 14:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Active Matter Seminar

Speaker: Amin Doostmohammadi, Niels Bohr Institute, University of Copenhagen
Title: Interacting Active Matter
Abstract: I will focus on the interaction between different active matter systems. In particular, I will describe recent experimental and modeling results that reveal how interaction forces between adhesive cells generate activity in the cell layer and lead to a potentially new mode of phase segregation. I will then discuss mechanics of how cells use finger-like protrusions, known as filopodia, to interact with their surrounding medium. First, I will present experimental and theoretical results of active mirror-symmetry breaking in subcellular skeleton of filopodia that allows for rotation, helicity, and buckling of these cellular fingers in a wide variety of cells ranging from epithelial, mesenchymal, cancerous and stem cells. I will then describe in-vivo experiments together with theoretical modeling showing how during embryo development specialized active cells probe and modify other cell layers and integrate within an active epithelium.

Third Annual Yip Lecture
2023-02-02 19:00 - 20:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Andrew Strominger will give the Third Annual Yip Lecture on February 2, 2023.
Time: 7:00-8:00 pm ET
Location: Harvard Science Center Hall A

Title: Black Holes: The Most Mysterious Objects in the Universe
Abstract: In the last decade black holes have come to center stage in both theoretical and observational science. Theoretically, they were shown a half-century ago by Stephen Hawking and others to obey a precise but still-mysterious set of laws which imply they are paradoxically both the simplest and most complex objects in the universe. Compelling progress on this paradox has occurred recently. Observationally, they have finally and dramatically been seen in the sky, including at LIGO and the Event Horizon Telescope. Future prospects for progress on both fronts hinge on emergent symmetries occurring near the black holes. An elementary presentation of aspects of these topics and their interplay will be given.
Andrew Strominger is the Gwill E. York Professor of Physics and a senior faculty member at the Black Hole Initiative at Harvard University.
Introduction: Peter Galison (Harvard Physics & Black Hole Initiative)
Moderator: Daniel Kapec (Harvard CMSA)
The Yip Lecture takes place thanks to the support of Dr. Shing-Yiu Yip.

The previous Yip Lecture featured Avi Loeb (Harvard), who spoke on Extraterrestrial Life.

Fracton orders in hyperbolic space and its excitations with fractal mobility
2023-02-03 10:30 - 11:30 | Virtual
Quantum Matter Seminar
Speaker: Han Yan (Rice U)
Title: Fracton orders in hyperbolic space and its excitations with fractal mobility
Abstract: Unlike ordinary topological quantum phases, fracton orders are intimately dependent on the underlying lattice geometry. In this work, we study a generalization of the X-cube model, on lattices embedded in a stack of hyperbolic planes. We demonstrate that for certain hyperbolic lattice tesselations, this model hosts a new kind of subdimensional particle, treeons, which can only move on a fractal-shaped subset of the lattice. Such an excitation only appears on hyperbolic geometries; on flat spaces, treeons become either a lineon or a planeon. Additionally, we find intriguingly that for certain hyperbolic tessellations, a fracton can be created by a membrane operator (as in the X-cube model) or by a fractal-shaped operator within the hyperbolic plane. Our work shows that there are still plenty of exotic behaviors from fracton order to be explored, especially when the embedding geometry is curved.
Reference: H. Yan, K. Slage, A. H. Nevidomskyy, arXiv:2211.15829

Motivic Geometry of Two-Loop Feynman Integrals
2023-02-07 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Chuck Doran
Title: Motivic Geometry of Two-Loop Feynman Integrals
Abstract: We study the geometry and Hodge theory of the cubic hypersurfaces attached to two-loop Feynman integrals for generic physical parameters. We show that the Hodge structure attached to planar two-loop Feynman graphs decomposes into a mixed Tate piece and a variation of Hodge structure from families of hyperelliptic curves, elliptic curves, or rational curves depending on the space-time dimension. We give more precise results for two-loop graphs with a small number of edges. In particular, we recover a result of Spencer Bloch that in the well-known double box example there is an underlying family of elliptic curves, and we give a concrete description of these elliptic curves. We show that the motive for the “non-planar” two-loop tardigrade graph is that of a family of K3 surfaces of generic Picard number 11. Lastly, we show that generic members of the multi-scoop ice cream cone family of graph hypersurfaces correspond to pairs of multi-loop sunset Calabi-Yau varieties. Our geometric realization of these motives permits us in many cases to derive in full the homogeneous differential operators for the corresponding Feynman integrals. This is joint work with Andrew Harder and Pierre Vanhove.

From spin glasses to Boolean circuits lower bounds - Algorithmic barriers from the overlap gap property
2023-02-08 12:30 - 13:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: David Gamarnik (MIT)
Title: From spin glasses to Boolean circuits lower bounds. Algorithmic barriers from the overlap gap property
Abstract: Many decision and optimization problems over random structures exhibit an apparent gap between the existentially optimal values and algorithmically achievable values. Examples include the problem of finding a largest independent set in a random graph, the problem of finding a near ground state in a spin glass model, the problem of finding a satisfying assignment in a random constraint satisfaction problem, and many many more. Unfortunately, at the same time no formal computational hardness results exist which explains this persistent algorithmic gap.
In the talk we will describe a new approach for establishing an algorithmic intractability for these problems called the overlap gap property. Originating in statistical physics theory of spin glasses, this is a simple to describe property which a) emerges in most models known to exhibit an apparent algorithmic hardness; b) is consistent with the hardness/tractability phase transition for many models analyzed to the day; and, importantly, c) allows to mathematically rigorously rule out a large class of algorithms as potential contenders, specifically the algorithms which exhibit a form of stability/noise insensitivity.
We will specifically show how to use this property to obtain stronger (stretched exponential) than the state of the art (quasi-polynomial) lower bounds on the size of constant depth Boolean circuits for solving the two of the aforementioned problems: the problem of finding a large independent set in a sparse random graph, and the problem of finding a near ground state of a p-spin model.
Joint work with Aukosh Jagannath and Alex Wein

Bakry-Emery theory and renormalisation
2023-02-08 15:30 - 16:30 | Hybrid
Probability Seminar
Speaker: Roland Bauerschmidt (Cambridge)

Title: Bakry-Emery theory and renormalisation
Abstract: I will discuss an approach to log-Sobolev inequalities that
combines the Bakry-Emery theory with renormalisation and present several
applications. These include log-Sobolev inequalities with polynomial
dependence for critical Ising models on Z^d when d>4 and singular SPDEs
with uniform dependence of the log-Sobolev constant on both the
regularisation and the volume. The talk is based on joint works with
Thierry Bodineau and Benoit Dagallier.

Quasinormal modes and Ruelle resonances: mathematician's perspective
2023-02-09 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Maciej Zworski, UC Berkeley
Title: Quasinormal modes and Ruelle resonances: mathematician’s perspective
Abstract: Quasinormal modes of gravitational waves and Ruelle resonances in hyperbolic classical dynamics share many general properties and can be considered “scattering resonances”: they appear in expansions of correlations, as poles of Green functions and are associated to trapping of trajectories (and are both notoriously hard to observe in nature, unlike, say, quantum resonances in chemistry or scattering poles in acoustical scattering). I will present a mathematical perspective that also includes zeros of the Riemann zeta function (scattering resonances for the Hamiltonian given by the Laplacian on the modular surface) and stresses the importance of different kinds of trapping phenomena, resulting, for instance, in fractal counting laws for resonances.

Special Lectures on Machine Learning and Protein Folding
2023-02-09 15:30 - 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
The CMSA hosted a series of three 90-minute lectures on the subject of machine learning for protein folding.
Thursday Feb. 9, Thursday Feb. 16, & Thursday March 9, 2023, 3:30-5:00 pm ET
Location: G10, CMSA, 20 Garden Street, Cambridge MA 02138 & via Zoom

Speaker: Nazim Bouatta, Harvard Medical School
Abstract: AlphaFold2, a neural network-based model which predicts protein structures from amino acid sequences, is revolutionizing the field of structural biology. This lecture series, given by a leader of the OpenFold project which created an open-source version of AlphaFold2, will explain the protein structure problem and the detailed workings of these models, along with many new results and directions for future research.
Thursday, Feb. 9, 2023

Thursday, Feb. 9, 2023
3:30–5:00 pm ET
Lecture 1: Machine learning for protein structure prediction, Part 1: Algorithm space
A brief intro to protein biology. AlphaFold2 impacts on experimental structural biology. Co-evolutionary approaches. Space of ‘algorithms’ for protein structure prediction. Proteins as images (CNNs for protein structure prediction). End-to-end differentiable approaches. Attention and long-range dependencies. AlphaFold2 in a nutshell.

Thursday, Feb. 16, 2023
3:30–5:00 pm ET
Lecture 2: Machine learning for protein structure prediction, Part 2: AlphaFold2 architecture
Turning the co-evolutionary principle into an algorithm: EvoFormer. Structure module and symmetry principles (equivariance and invariance). OpenFold: retraining AlphaFold2 and insights into its learning mechanisms and capacity for generalization. Applications of variants of AlphaFold2 beyond protein structure prediction: AlphaFold Multimer for protein complexes, RNA structure prediction.

Thursday, March 9, 2023
3:30–5:00 pm ET
Lecture 3: Machine learning for protein structure prediction, Part 3: AlphaFold2 limitations and insights learned from OpenFold
Limitations of AlphaFold2 and evolutionary ML pipelines. OpenFold: retraining AlphaFold2 yields new insights into its capacity for generalization.

Biography: Nazim Bouatta received his doctoral training in high-energy theoretical physics, and transitioned to systems biology at Harvard Medical School, where he received training in cellular and molecular biology in the group of Prof. Judy Lieberman. He is currently a Senior Research Fellow in the Laboratory of Systems Pharmacology led by Prof. Peter Sorger at Harvard Medical School, and an affiliate of the Department of Systems Biology at Columbia, in the group of Prof. Mohammed AlQuraishi. He is interested in applying machine learning, physics, and mathematics to biology at multiple scales. He recently co-supervised the OpenFold project, an optimized, trainable, and completely open-source version of AlphaFold2. OpenFold has paved the way for many breakthroughs in biology, including the release of the ESM Metagenomic Atlas containing over 600 million predicted protein structures.

Chair: Michael Douglas (Harvard CMSA)
Moderators: Farzan Vafa & Sergiy Verstyuk (Harvard CMSA)

Lecture 1: Machine learning for protein structure prediction, Part 1: Algorithm space

Lecture 2: Machine learning for protein structure prediction, Part 2: AlphaFold2 architecture

Lecture 3: Machine learning for protein structure prediction, Part 3: AlphaFold2 limitations and insights learned from OpenFold

Non-invertible Symmetry Enforced Gaplessness
2023-02-10 10:30 - 11:30 | Virtual
Quantum Matter Seminar
Speaker: Ho Tat Lam (MIT)
Title: Non-invertible Symmetry Enforced Gaplessness
Abstract: Quantum systems in 3+1-dimensions that are invariant under gauging a one-form symmetry enjoy novel non-invertible duality symmetries encoded by topological defects. These symmetries are renormalization group invariants which constrain infrared dynamics. We show that such non-invertible symmetries often forbid a symmetry-preserving vacuum state with a gapped spectrum, leaving only two possibilities for the infrared dynamics: a gapless state or spontaneous breaking of the non-invertible symmetries. These non-invertible symmetries are realized in lattice gauge theories, which serve to illustrate our results.

Parity and Cobordism
2023-02-13 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Swampland Seminar
Speaker: Jake McNamara (Caltech)

Title: Parity and Cobordism

Abstract: The swampland cobordism conjecture provides a convenient way to discuss conserved charges associated with the topology of spacetime. However, much of the power of the cobordism conjecture comes from a mathematical black box: the Adams spectral sequence. In this talk, I will give physical meaning to this black box through a concrete example: domain walls arising from the spontaneously breaking of parity symmetry, which arise in particle physics in Nelson-Barr models. I will argue that parity domain walls are exactly stable, and interpret this stability as the result of an unusual type of gauge symmetry that can only occur in gravitational theories.

Complete Calabi-Yau metrics: Recent progress and open problems
2023-02-13 12:30 - 13:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Tristan Collins, MIT
Title: Complete Calabi-Yau metrics: Recent progress and open problems
Abstract: Complete Calabi-Yau metrics are fundamental objects in Kahler geometry arising as singularity models or “bubbles” in degenerations of compact Calabi-Yau manifolds. The existence of these metrics and their relationship with algebraic geometry are the subjects of several long standing conjectures due to Yau and Tian-Yau. I will describe some recent progress towards the question of existence, and explain some future directions, highlighting connections with notions of algebro-geometric stability.

Dynamics of active nematic defects on cones
2023-02-14 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Farzan Vafa
Title: Dynamics of active nematic defects on cones
Abstract: In the first part of the talk, we investigate the ground-state configurations of two-dimensional liquid crystals with p-fold rotational symmetry (p-atics) on cones. The cone apex develops an effective topological charge, which in analogy to electrostatics, leads to defect absorption and emission at the cone apex as the deficit angle of the cone is varied. We find three types of ground-state configurations as a function of cone angle, which is determined by charged defects screening the effective apex charge: (i) for sharp cones, all of the +1/p defects are absorbed by the apex; (ii) at intermediate cone angles, some of the +1/p defects are absorbed by the apex and the rest lie equally spaced along a concentric ring on the flank; and (iii) for nearly flat cones, all of the +1/p defects lie equally spaced along a concentric ring on the flank. We check these results with numerical simulations for a set of commensurate cone angles and find excellent agreement. In the second part of the talk, we investigate the dynamics of an active nematic on a cone, and via simulations find long-time circular orbits of either one or two flank defects, with transitions between these states mediated by the apex via defect absorption, emission, or defect pair creation.

Manifold Fitting: An Invitation to Statistics
2023-02-15 15:30 - 16:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Probability Seminar
Speaker: Zhigang Yao (Harvard CMSA/National University of Singapore)

Title: Manifold Fitting: An Invitation to Statistics
Abstract: This manifold fitting problem can go back to H. Whitney’s work in the early 1930s (Whitney (1992)), and finally has been answered in recent years by C. Fefferman’s works (Fefferman, 2006, 2005). The solution to the Whitney extension problem leads to new insights for data interpolation and inspires the formulation of the Geometric Whitney Problems (Fefferman et al. (2020, 2021a)): Assume that we are given a set $Y subset mathbb{R}^D$. When can we construct a smooth $d$-dimensional submanifold $widehat{M} subset mathbb{R}^D$ to approximate $Y$, and how well can $widehat{M}$ estimate $Y$ in terms of distance and smoothness? To address these problems, various mathematical approaches have been proposed (see Fefferman et al. (2016, 2018, 2021b)). However, many of these methods rely on restrictive assumptions, making extending them to efficient and workable algorithms challenging. As the manifold hypothesis (non-Euclidean structure exploration) continues to be a foundational element in statistics, the manifold fitting Problem, merits further exploration and discussion within the modern statistical community. The talk will be partially based on a recent work Yao and Xia (2019) along with some on-going progress. Relevant reference: https://arxiv.org/abs/1909.10228

Towards programmable living materials and quantitative models of active matter
2023-02-16 13:00 - 14:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Active Matter Seminar

Speaker: Jörn Dunkel, MIT
Title: Towards programmable living materials and quantitative models of active matter
Abstract: Over the last two decades, major progress has been made in understanding the self-organization principles of active matter. A wide variety of experimental model systems, from self-driven colloids to active elastic materials, has been established, and an extensive theoretical framework has been developed to explain many of the experimentally observed non-equilibrium pattern formation phenomena. Two key challenges for the coming years will be to translate this foundational knowledge into functional active materials, and to identify quantitative mathematical models that can inform and guide the design and production of such materials. Here, I will describe joint efforts with our experimental collaborators to realize self-growing bacterial materials [1], and to implement computational model inference schemes for active and living systems dynamics [2,3].
[1] Nature 608: 324, 2022
[2] PNAS 120: e2206994120, 2023
[3] eLife 10: e68679, 2021

Quasinormal Modes from Penrose Limits
2023-02-16 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Kwinten Fransen (UC Santa Barbara)
Title: Quasinormal Modes from Penrose Limits
Abstract: In this talk, I will explain how to describe quasinormal modes with large real frequencies using Penrose limits. To do so, I first recall relevant aspects of the Penrose limit, and its resulting plane wave spacetimes, as well as quasinormal modes to subsequently tie these together. Having established the main principle, I will illustrate the usefulness of this point of view with the geometric realization of the emergent symmetry algebra underlying the quasinormal modes in the large real frequency limit and present its application to the astrophysically important example of Kerr black holes. Based on arXiv:2301.06999.

Quantum Spin Lakes: NISQ-Era Spin Liquids from Non-Equilibrium Dynamics
2023-02-17 10:00 - 11:30 | Virtual
Quantum Matter Seminar
Speaker: Rahul Sahay (Harvard)
Title: Quantum Spin Lakes: NISQ-Era Spin Liquids from Non-Equilibrium Dynamics
Abstract: While many-body quantum systems can in principle host exotic quantum spin liquid (QSL) states, realizing them as ground states in experiments can be prohibitively difficult. In this talk, we show how non-equilibrium dynamics can provide a streamlined route toward creating QSLs. In particular, we show how a simple Hamiltonian parameter sweep can dynamically project out condensed anyons from a family of initial product states (e.g. dynamically “un-Higgs”), yielding a QSL-like state. We christen such states “quantum spin lakes” which, while not thermodynamically large QSLs, enable their study in NISQ-era quantum simulators. Indeed, we show that this mechanism sheds light on recent experimental and numerical observations of the dynamical state preparation of the ruby lattice spin liquid in Rydberg atom arrays. Time permitting, we will discuss how our theory motivates a tree tensor network-based numerical tool—reliant on our theory—that quantitatively reproduces the experimental data two orders of magnitude faster than conventional brute-force simulation methods. Finally, we will highlight that even spin liquid states that are unstable in equilibrium—namely, 2 + 1D U(1) spin liquid states—can be robustly prepared by non-equilibrium dynamics.

Hints of Flat Space Holography
2023-02-21 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Dan Kapec
Title: Hints of Flat Space Holography
Abstract: Despite our detailed understanding of holography in Anti-de Sitter space, flat space holography remains somewhat mysterious. “Celestial CFT” is a formalism which attempts to recast quantum gravity in (d+2)-dimensional asymptotically flat spacetimes in terms of a d-dimensional Euclidean conformal field theory residing at the conformal boundary. I will discuss certain universal aspects of this correspondence. As in Anti-de Sitter space, bulk gravitons produce a boundary stress tensor, and bulk gluons furnish boundary-conserved currents. I will also show that continuous spaces of vacua in the bulk map directly onto the conformal manifold of the boundary CFT. This correspondence provides a new perspective on the role of the BMS group in flat space holography and offers a new interpretation of the antisymmetric double-soft gluon theorem in terms of the curvature of an infinite-dimensional vacuum manifold.

The Black Hole Information Paradox: A Resolution on the Horizon?
2023-02-22 12:30 - 13:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Netta Engelhardt (MIT)
Title: The Black Hole Information Paradox: A Resolution on the Horizon?
Abstract: The black hole information paradox — whether information escapes an evaporating black hole or not — remains one of the most longstanding mysteries of theoretical physics. The apparent conflict between validity of semiclassical gravity at low energies and unitarity of quantum mechanics has long been expected to find its resolution in a complete quantum theory of gravity. Recent developments in the holographic dictionary, and in particular its application to entanglement and complexity, however, have shown that a semiclassical analysis of gravitational physics can reproduce a hallmark feature of unitary evolution. I will describe this recent progress and discuss some promising indications of a full resolution of the information paradox.
