Symmetry in quantum field theory and quantum gravity 1
2022-12-01 10:30 - 11:30 (America/New_York) | MA
Speaker: Daniel Harlow (MIT)
Title: Symmetry in quantum field theory and quantum gravity 1
Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence. These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact. Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields. These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).

Compactness and Anticompactness Principles in Set Theory
2022-12-02 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Member Seminar
Speaker: Alejandro Poveda
Title: Compactness and Anticompactness Principles in Set Theory
Abstract: Several fundamental properties in Topology, Algebra or Logic are expressed in terms of Compactness Principles.For instance, a natural algebraic question is the following: Suppose that G is an Abelian group whose all small subgroups are free – Is the group G free? If the answer is affirmative one says that compactness holds; otherwise, we say that compactness fails. Loosely speaking, a compactness principle is anything that fits the following slogan: Suppose that M is a mathematical structure (a group, a topological space, etc) such that all of its small substructures N have certain property $varphi$; then the ambient structure M has property $varphi$, as well. Oftentimes when these questions are posed for infinite sets the problem becomes purely set-theoretical and axiom-sensitive. In this talk I will survey the most paradigmatic instances of compactness and present some related results of mine. If time permits, I will hint the proof of a recent result (joint with Rinot and Sinapova) showing that stationary reflection and the failure of the Singular Cardinal Hypothesis can co-exist. These are instances of two antagonist set-theoretic principles: the first is a compactness principle while the second is an anti-compactness one. This result solves a question by M. Magidor from 1982.

Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
2022-12-05 09:00 - 10:30 | Virtual
Quantum Matter Seminar
Speaker: Junkai Dong (Harvard University)
Title: Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
Abstract: Motivated by the higher Chern bands of twisted graphene multilayers, we consider flat bands with arbitrary Chern number C with ideal quantum geometry. While C>1 bands differ from Landau levels, we show that these bands host exact fractional Chern insulator (FCI) ground states for short range interactions. We show how to decompose ideal higher Chern bands into separate ideal bands with Chern number 1 that are intertwined through translation and rotation symmetry. The decomposed bands admit an SU(C) action that combines real space and momentum space translations. Remarkably, they also allow for analytic construction of exact many-body ground states, such as generalized quantum Hall ferromagnets and FCIs, including flavor-singlet Halperin states and Laughlin ferromagnets in the limit of short-range interactions. In this limit, the SU(C) action is promoted to a symmetry on the ground state subspace. While flavor singlet states are translation symmetric, the flavor ferromagnets correspond to translation broken states and admit charged skyrmion excitations corresponding to a spatially varying density wave pattern. We confirm our analytic predictions with numerical simulations of ideal bands of twisted chiral multilayers of graphene, and discuss consequences for experimentally accessible systems such as monolayer graphene twisted relative to a Bernal bilayer.

IIB Explored - Dualities, Bordisms, and the Swampland
2022-12-05 11:00 - 12:00 | Jefferson 356
Swampland Seminar
Location: Jefferson Physical Laboratory, Seminar room J356
Speaker: Markus Dierigl (LMU Munich)
Title: IIB Explored – Dualities, Bordisms, and the Swampland
Abstract: In this talk I will discuss the application of the Cobordism Conjecture to type IIB supergravity with non-trivial duality bundle. Calculating the relevant bordism groups we find that they are highly non-trivial and would predict the presence of various global symmetries in the underlying theory. Since quantum gravity theories do not allow for global symmetries, we discuss which defects need to be included to break them completely. Interestingly, we find many backgrounds that are well-known in the F-theory literature, such as [p,q]-7-branes, non-Higgsable clusters, as well as S-folds and their generalizations to higher codimensions. Further including worldsheet reflections, predicts the existence of a new non-supersymmetric 7-brane with interesting properties and applications, which I will discuss in more detail.

Neutrino Masses from Generalized Symmetry Breaking
2022-12-06 09:00 - 10:30 | Virtual
Quantum Matter Seminar
Speaker: Sungwoo Hong (U Chicago & KAIST)
Title: Neutrino Masses from Generalized Symmetry Breaking
Abstract: We explore generalized global symmetries in theories of physics beyond the Standard Model. Theories of Z′ bosons generically contain ‘non-invertible’ chiral symmetries, whose presence indicates a natural paradigm to break this symmetry by an exponentially small amount in an ultraviolet completion. For example, in models of gauged lepton family difference such as the phenomenologically well-motivated U(1)Lμ−Lτ, there is a non-invertible lepton number symmetry which protects neutrino masses. We embed these theories in gauged non-Abelian horizontal lepton symmetries, e.g. U(1)Lμ−Lτ⊂SU(3)H, where the generalized symmetries are broken nonperturbatively by the existence of lepton family magnetic monopoles. In such theories, either Majorana or Dirac neutrino masses may be generated through quantum gauge theory effects from the charged lepton Yukawas e.g. yν∼yτexp(−Sinst). These theories require no bevy of new fields nor ad hoc additional global symmetries, but are instead simple, natural, and predictive: the discovery of a lepton family Z′ at low energies will reveal the scale at which Lμ−Lτ emerges from a larger gauge symmetry.

Controlling Quantum Matter with Quantum Cavity Fields
2022-12-07 10:00 - 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Topological Quantum Matter Seminar
Speaker: Vasil Rokaj (Harvard)
Title: Controlling Quantum Matter with Quantum Cavity Fields
Abstract: Cavity modification of material properties and phenomena is a novel research field motivated by the advances in strong light-matter interactions [1]. For condensed matter systems it has been demonstrated experimentally that the transport properties of 2D materials can be modified via coupling to vacuum fields [2,3]. While in polaritonic chemistry it has been shown that ground state chemical properties can be controlled with cavity fields [4]. In the first part of my talk, I will present how the quantized cavity field can alter the conduction properties of a condensed matter system by focusing on the paradigmatic Sommerfeld model of the free electron gas [5]. The exact analytic solution of the Sommerfeld model in the cavity will be presented as well as its fundamental properties. Then, in the second part of the talk, I will focus on a many-particle system of cold ions in a harmonic trap coupled to the cavity field. I will show how this system couples collectively to the cavity and that hybrid states between light and matter, known as polaritons, emerge. The formation of polaritons leads to the modification of the properties of the cold ions and enhances the localization of the many-body wave function [6]. Connections to experiments will be discussed as well.
[1] F. Garcia-Vidal, C. Ciuti, T. W. Ebbesen, Science, 373, 178 (2021)
[2] G. L. Paravicini-Bagliani et al., Nat. Phys. 15, 186-190 (2019)
[3] F. Appugliese et al., Science 375 (6584), 1030-1034 (2022)
[4] T. W. Ebbesen, Acc. Chem. Res. 49, 11, 2403–2412 (2016)
[5] V. Rokaj, M. Ruggenthaler, F. G. Eich, A. Rubio, Phys. Rev. Research 4, 013012 (2022)
[6] V. Rokaj, S.I. Mistakidis, H.R. Sadeghpour, arXiv:2207.03436 (2022)

How do Transformers reason? First principles via automata, semigroups, and circuits
2022-12-07 14:00 - 15:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
New Technologies in Mathematics Seminar
Speaker: Cyril Zhang, Microsoft Research
Title: How do Transformers reason? First principles via automata, semigroups, and circuits
Abstract: The current “Transformer era” of deep learning is marked by the emergence of combinatorial and algorithmic reasoning capabilities in large sequence models, leading to dramatic advances in natural language understanding, program synthesis, and theorem proving. What is the nature of these models’ internal representations (i.e. how do they represent the states and computational steps of the algorithms they execute)? How can we understand and mitigate their weaknesses, given that they resist interpretation? In this work, we present some insights (and many further mysteries) through the lens of automata and their algebraic structure.
Specifically, we investigate the apparent mismatch between recurrent models of computation (automata & Turing machines) and Transformers (which are typically shallow and non-recurrent). Using tools from circuit complexity and semigroup theory, we characterize shortcut solutions, whereby a shallow Transformer with only o(T) layers can exactly replicate T computational steps of an automaton. We show that Transformers can efficiently represent these shortcuts in theory; furthermore, in synthetic experiments, standard training successfully finds these shortcuts. We demonstrate that shortcuts can lead to statistical brittleness, and discuss mitigations.
Joint work with Bingbin Liu, Jordan Ash, Surbhi Goel, and Akshay Krishnamurthy.

Fourier quasicrystals and stable polynomials
2022-12-07 15:30 - 16:30 | 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.
