Mathematical Aspects of Scattering Amplitudes Lecture
2024-04-30 13:00 - 14:00 (America/New_York) | Jefferson 453, 17 Oxford St, Cambridge, MA 02138, MA
Mathematical Aspects of Scattering Amplitudes Lecture
Speaker: Nima Arkani-Hamed, IAS
Title: Surfaceology and the Real World Part 2
(Note change of venue to Jefferson 453)

Mathematical Aspects of Scattering Amplitudes Lecture
2024-04-30 16:00 - 17:00 | Jefferson 453, 17 Oxford St, Cambridge, MA 02138, MA
Mathematical Aspects of Scattering Amplitudes Lecture
Speaker: Nima Arkani-Hamed, IAS
Title: Surfaceology and the Real World Part 3
(Note change of venue to Jefferson 453)

Mathematical Aspects of Scattering Amplitudes Lecture
2024-05-01 11:00 - 12:00 | Science Center 507, 1 Oxford Street, Cambridge, 02138
Mathematical Aspects of Scattering Amplitudes Lecture
Speaker: Jaroslav Trnka, University of California, Davis
Title: Loops of loops expansion in the Amplituhedron

Mathematical Aspects of Scattering Amplitudes Lecture
2024-05-01 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Aspects of Scattering Amplitudes Lecture
Speaker: Yu-tin Huang, National Taiwan University
Title: Loop in trees: Chambers in amplitudes and correlation functions

Mathematical Aspects of Scattering Amplitudes Lecture
2024-05-01 16:00 - 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Aspects of Scattering Amplitudes Lecture
Speaker: Livia Ferro, University of Hertfordshire
Title: Scattering Amplitudes from Null-cone Geometry

Mathematical Aspects of Scattering Amplitudes Lecture
2024-05-01 17:00 - 18:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Aspects of Scattering Amplitudes Lecture
Speaker: Stephan Stieberger, Max Planck Institute
Title: One-loop Double Copy Relation in String Theory and Twisted (Co)homology

Mathematical Aspects of Scattering Amplitudes Lecture
2024-05-02 11:00 - 12:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
Mathematical Aspects of Scattering Amplitudes Lecture
Speaker: Daniil Rudenko, U Chicago
Title: Introduction to Cluster Polylogarithms
Location: Harvard Science Center 310

Non-dispersive one-way signal amplification in sonic metamaterials
2024-05-02 13:30 - 14:30 | Jefferson 256, 17 Oxford Street, Cambridge, MA, 02138, United States
Active Matter Seminar
Speaker: Jayson Paulose, University of Oregon
Title: Control of parametric amplification in space-time modulated mechanical metamaterials
Abstract: Active mechanical metamaterials harbor acoustic signal processing functionalities that are impossible to achieve in passive structures. Amplifying an elastic wave as it passes through the material is a prominent example, with potential applications in acoustic signal processing and loss mitigation. The fundamental mechanism for signal amplification of this kind is the parametric amplifier–an oscillator whose stiffness is periodically modulated in time, which can inject energy into mechanical oscillations. Typically, parametric amplification occurs at distinct modulation frequencies that are trivially related to the resonance modes of the unmodulated system, which restricts its utility for amplifying signals with complex spatial or spectral structure. In this talk, I’ll show how spatial variation of the modulation phase in parametric oscillator networks enables amplification phenomena that are far richer than those achievable by uncoupled and uncoordinated parametric amplifiers. Examples include turning off parametric resonances for particular vibrational modes in small assemblies [1], and achieving nonreciprocal broadband amplification in periodic arrays [2]. The existence of parametric resonances is tied to the internal symmetries inherent to mechanical systems as well as the symmetries obeyed by the parametric variation in space and time, through an exact theoretical framework that augments the standard Floquet analysis of space-time modulated systems.

[1] Melkani and Paulose, arXiv:2310.08734
[2] Kruss and Paulose, PRApplied17, 024020 (2022)

Symmetry Colloquia - Global Categorical Symmetries
2024-05-02 14:00 - 14:50 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Symmetry Colloquia – Global Categorical Symmetries
May 2, 2024
Location: Room G-10, CMSA, 20 Garden Street, Cambridge MA 02138
Speaker: Clay Còrdova, University of Chicago
Title: Particle-Soliton Degeneracies from Spontaneously Broken Non-Invertible Symmetry
Abstract: We study non-invertible topological symmetry operators in massive quantum field theories in (1+1) dimensions. In phases where this symmetry is spontaneously broken we show that the particle spectrum often has degeneracies dictated by the non-invertible symmetry and we deduce a procedure to determine the allowed multiplets. These degeneracies are robust predictions and do not require integrability or other special features of renormalization group flows. We exhibit these conclusions in examples where the spectrum is known, recovering soliton and particle degeneracies. For instance, the Tricritical Ising model deformed by the subleading Z2 odd operator flows to a gapped phase with two degenerate vacua. This flow enjoys a Fibonacci fusion category symmetry which implies a threefold degeneracy of its particle states, relating the mass of solitons interpolating between vacua and particles supported in a single vacuum.

Symmetry Colloquia - Global Categorical Symmetries
2024-05-02 15:00 - 15:50 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Symmetry Colloquia – Global Categorical Symmetries
May 2, 2024
Location: Room G-10, CMSA, 20 Garden Street, Cambridge MA 02138
Speaker: Thomas Dumitrescu, UCLA
Title: Symmetries, Invertible Field Theories, and Gauge Theory Phases
Abstract: I will start with a brief overview of gauge theory phases in 3+1 dimensions through the lens of higher symmetries — in particular the realization of 1-form symmetries acting on loop order parameters. I will then review recent progress in refining this characterization using invertible field theories, or equivalently symmetry protected topological phases (SPTs). This refinement leads to new results in gauge theories with fundamental matter, such as quantum chromodynamics (QCD), which do not possess 1-form symmetries. I will explain why these theories must sometimes undergo a phase transition between their confining and Higgs regimes, despite the fact that classic results and standard lore say they should be continuously connected.

Symmetry Colloquia - Global Categorical Symmetries
2024-05-02 16:30 - 17:20 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Symmetry Colloquia – Global Categorical Symmetries
May 2, 2024
Location: Room G-10, CMSA, 20 Garden Street, Cambridge MA 02138
Speaker: Theo Johnson-Freyd, Dalhousie University and Perimeter Institute
Title: The Universal Target Category
Abstract: Hilbert’s Nullstellensatz says that the complex numbers C satisfy a universal property among all R-algebras: every not-too-large nonzero commutative R-algebra maps to C. Deligne proved a similar statement in categorical dimension 1: every not-too-large symmetric monoidal category over R maps to the category sVec of super vector spaces. In other words, sVec (and not Vec!) is “algebraically closed”. These statements help explain why quantum field theory requires imaginary numbers and fermions. I will describe the universal symmetric monoidal higher category that extends the sequence C, sVec, …. This is joint work in progress with David Reutter, and builds on closely-related work by GCS collaborators Freed, Scheimbauer, and Teleman and Schlank et al.

Mathematical Aspects of Scattering Amplitudes Lecture
2024-05-03 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Aspects of Scattering Amplitudes Lecture
Speaker: Andrew McLeod, Edinburgh
Title: Genealogical Constraints on Feynman Integrals

Liouville Theory and Weil-Petersson Geometry
2024-05-06 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Sarah Harrison (Northeastern University)
Title: Liouville Theory and Weil-Petersson Geometry
Abstract: Two-dimensional conformal field theory is a powerful tool to understand the geometry of surfaces. Liouville conformal field theory in the classical (large central charge) limit encodes the geometry of the moduli space of Riemann surfaces. I describe an efficient algorithm to compute the Weil–Petersson metric to arbitrary accuracy using Zamolodchikov’s recursion relation for conformal blocks, focusing on examples of a sphere with four punctures and generalizations to other one-complex-dimensional moduli spaces. Comparison with analytic results for volumes and geodesic lengths finds excellent agreement. In the case of M_{0,4}, I discuss numerical results for eigenvalues of the Weil-Petersson Laplacian and connections with random matrix theory.
Based on work with K. Coleville, A. Maloney, K. Namjou, and T. Numasawa.

On using ML for Economics
2024-05-07 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Member Seminar
Speaker: Sergiy Verstyuk
Title: On using ML for Economics
Abstract: I will introduce some tools from the field of machine learning and discuss how they can be leveraged to get a fresh perspective on economics.

Real-time observables in horizon thermodynamics
2024-05-07 14:00 - 15:00 | Virtual
General Relativity Seminar
Speaker: Albert Law, Stanford
Title: Real-time observables in horizon thermodynamics
Abstract: Euclidean black hole 1-loop determinants have recently been shown to compute a renormalized thermal canonical partition function for free fields in Lorentzian signature. A key ingredient is a ‘quasinormal mode (QNM) character’, whose Fourier transform equals the renormalized spectral density of the single-particle Hamiltonian. Using a static patch in de Sitter space as an example, in this talk, I will offer new perspectives on the QNM character, including its connection with the local density of states for the single-particle quantum mechanical problem associated with the Klein-Gordon equation, and its direct relationships with (thermal) correlators of the free fields. I will discuss how these considerations might point toward a generalization to interacting theories.

Mathematical Aspects of Scattering Amplitudes Lecture
2024-05-07 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Aspects of Scattering Amplitudes Lecture
Speaker: Jacob Bourjaily, Penn State
Title: The Algebraic and Transcendental Structure of Perturbative QFT

Mathematical Aspects of Scattering Amplitudes Lecture
2024-05-08 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Aspects of Scattering Amplitudes Lecture
Speaker: Ruth Britto, Trinity
Title: Cuts and Symbols

Computing periods of hypersurfaces and elliptic surfaces via effective homology
2024-05-09 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebraic Geometry in String Theory Seminar
Speaker: Eric Pichon-Pharabod, Universite Paris-Saclay
Title: Computing periods of hypersurfaces and elliptic surfaces via effective homology
Abstract: The period matrix of a smooth complex projective variety X encodes the isomorphism between its singular homology and its algebraic De Rham cohomology. Numerical approximations with sufficient precision of the entries of this matrix, called periods, allow to recover some algebraic invariants of the variety, such as the Néron-Severi group in the case of surfaces. In this talk, we will present a method relying on the computation of an effective description of the homology for obtaining such numerical approximations of the periods of hypersurfaces and elliptic surfaces.

From quantum Hall to Hubbard physics in twisted bilayer graphene
2024-05-10 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Eslam Khalaf (Harvard)
Title: From quantum Hall to Hubbard physics in twisted bilayer graphene

Abstract: Early on it was noticed that twisted bilayer graphene (TBG) has elements in common with two paradigmatic examples of strongly correlated physics: Hubbard physics and quantum Hall physics. On the one hand, TBG hosts flat topological Landau-level-like bands which realize quantum anomalous Hall states and orbital ferromagnetism under the right conditions. On the other hand, these bands are characterized by concentrated charge density and show experimental signs of fluctuating magnetism, and unconventional superconductivty; all characteristics of Hubbard-model-like physics. The emergence of fluctuating moments is particularly surprising, as localized Wannier states do not exist in topological bands. I will discuss a phenomenological model for the flat bands in TBG that centers the concentration of charge density and, relatedly, the concentration of Berry flux. The bands obtained have excellent quantitative agreement with the Bistritzer-Macdonald model for realistic parameters. I will show that, rather remarkably, the model hosts decoupled flavor moments which despite being only power-law delocalized with infinite localization length, have parametrically small overlap with each other. I will show how this unifies many of the observations in TBG and leads to a novel Mott semimetal phase for intermediate temperatures where moments are thermally disordered but charge fluctuations are mostly frozen.

On the landscape of 4d N=2 SCFTs
2024-05-10 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Member Seminar
Speaker: Robert Moscrop, Harvard CMSA
Title: On the landscape of 4d N=2 SCFTs
Abstract: Four-dimensional conformal field theories with sufficient (N = 2) supersymmetry are highly constrained. So much so, there has been an ongoing effort to classify them using only information about their moduli space of vacua. In this talk, I will review recent progress in this classification before detailing a subclass of theories for which the classification problem is particularly tractable.

An analogue of non-interacting quantum field theory in Riemannian signature
2024-05-13 11:00 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
General Relativity Seminar
Speaker: Mikhail Molodyk, Stanford
Title: An analogue of non-interacting quantum field theory in Riemannian signature
Abstract: Recent advances using microlocal tools have led to constructions, for wave operators on various classes of spacetimes, of four distinguished Fredholm inverses which have the singular behavior required of retarded, advanced, Feynman, and anti-Feynman propagators in QFT. Vasy and Wrochna have used these to define a QFT on asymptotically Minkowski spacetimes, for which they construct Hadamard states described by asymptotic data at infinity. I will describe an analogue of this construction on Riemannian manifolds with two asymptotically conic ends, defining quantum fields satisfying the Helmholtz equation and using scattering data to construct states satisfying a wavefront mapping-property version of the Hadamard condition. The absence of a spacetime interpretation lends itself to a sharper focus on the theory’s analytic structure, from whose perspective the Feynman propagators are no less natural than the advanced/retarded ones. I will also highlight some differences between Feynman propagators defined as distinguished inverses and as time-ordered expectations. Based on joint work with András Vasy.

Improving Mean-Field Theory for Quantum Magnets
2024-05-13 13:30 - 14:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Junyi Zhang, Johns Hopkins University
Title: Improving Mean-Field Theory for Quantum Magnets
Abstract: Frustrated magnets have garnered significant attention because of their potential to host exotic spin liquids, while many real material candidates exhibit magnetic orders. Due to their proximity to spin liquid phases, the semiclassical descriptions of these magnetic orders often fall short in capturing their intricate quantum behaviors. In this talk, I will introduce an improved mean-field method, named density-matrix mean-field theory (DMMFT), for these quantum magnets. Using local reduced density matrix, DMMFT can systematically incorporate the quantum fluctuations beyond conventional mean-field theories. Notably, it not only quantitatively evaluates the renormalization of order parameters induced by quantum fluctuations but also has the capability to detect the topological order of quantum phases. DMMFT offers an efficient approach to explore phases displaying unconventional quantum orders, particularly beneficial for investigating frustrated spin systems in high spatial dimensions.
Ref: https://arxiv.org/abs/2401.06236

Errors and Correction in Cumulative Knowledge
2024-05-13 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Madhu Sudan, Harvard University
Title: Errors and Correction in Cumulative Knowledge
Abstract: Societal accumulation of knowledge is a complex, and arguably error-prone, process. The correctness of new units of knowledge depends not only on the correctness of the new reasoning, but also on the correctness of old units that the new one builds on. If left unchecked, errors could completely ruin the validity of most of this knowledge so there must some error-correcting going on. What are the error-corrections processes employed in nature and how effective are they? In this talk, we describe our attempts to model such phenomena using probablistic models – we describe models for growth of cumulative knowledge, emergence of errors and methods to check for errors and eliminate them. We then analyze in this compound model, when effects of errors may survive, and when they are totally eliminated.
The central discovery in our work is the following optimistic statement: If we do checking correctly (most of the time) investing just a constant factor (<1) of our effort in checking (and saving the remaining constant factor towards deriving new units of knowledge), then effects of errors can be kept in check. Notably the amount of effort expended on checking does not scale with the volume of total knowledge or the depth of dependencies in the new units of knowledge, either of which would be overwhelming.
Based on the papers:
Is this correct? Let’s check!
Omri Ben-Eliezer, Dan Mikulincer, Elchanan Mossel, Madhu Sudan
arXiv:2211.12301
Errors are Robustly Tamed in Cumulative Knowledge Processes
Anna Brandenberger, Cassandra Marcussen, Elchanan Mossel, Madhu Sudan
arXiv:2309.05638

Quasilocal mass for general domains in space
2024-05-14 12:30 - 13:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Member Seminar
Speaker: Jue Liu
Title: Quasilocal mass for general domains in space
Abstract: Diffeomorphism-invariant quasilocal mass in classical general relativity has been studied for decades, but it is still an open problem how to define quasi-local mass for general domains with multiple boundaries in space. Using the Hamiltonian formulation, we will provide a new way to define the nonnegative quasi-local mass, and give recent progress in overcoming the difficulties.

Mathematical Aspects of Scattering Amplitudes Lecture
2024-05-14 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Aspects of Scattering Amplitudes Lecture
Speaker: James Drummond, University of Southampton

Title: Multiple light-like Wilson loops in N=4 super Yang-Mills theory

Mathematical Aspects of Scattering Amplitudes Lecture
2024-05-15 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Aspects of Scattering Amplitudes Lecture
Speaker: Matteo Parisi, Harvard CMSA
Title: The amplituhedron and cluster algebras

Mirror symmetry and log del Pezzo surfaces
2024-05-16 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebraic Geometry in String Theory Seminar
Speaker: Franco Rota, University of Glasgow
Title: Mirror symmetry and log del Pezzo surfaces
Abstract: The homological mirror symmetry conjecture predicts a duality, expressed in terms of categorical equivalences, between the complex geometry of a variety X (the B side) and the symplectic geometry of its mirror object Y (the A side). Motivated by this, we study a series of singular surfaces (called log del Pezzo). I will describe the category arising in the B side, using the McKay correspondence and explicit birational geometry. I will discuss early results on the A side, using the language of pseudolattices to focus on the special case of a smooth degree 2 del Pezzo surface. This is joint work with Giulia Gugiatti.

Controlling chaotic advection in 2D active nematics
2024-05-16 13:00 - 14:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Active Matter Seminar
Speaker: Kevin Mitchell, University of California, Merced
Title: Controlling chaotic advection in 2D active nematics
Abstract: Recent years have seen a surge of interest in active materials, in which energy injected at the microscale gives rise to mesoscale coherent motion. One prominent example is an active 2D “liquid crystal” composed of microtubules in the nematic phase. The activity is generated by molecular motors that consume ATP to generate local shearing between the microtubules. The resulting 2D fluid flow exhibits self-generated mesoscale chaotic dynamics with a characteristic folding and stretching pattern. We analyze this dynamics from the perspective of chaotic advection, in which the fluid can be viewed as “stirred” by topological defects in the nematic order parameter. Typically, these defects move in an irregular, chaotic pattern. We explore conditions, both theoretically and in experiments, under which the topological defects can be coaxed to perform regular periodic motion, thus bringing some degree of order to the chaos.

Geometry of Generalized Lienard Equations, Contact Geometry and Metriplectic Structure
2024-05-16 15:00 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Partha Guha, Khalifa University, Abu Dhabi
Title: Geometry of Generalized Lienard Equations, Contact Geometry and Metriplectic Structure
Abstract: We start with a self-contained brief review of the construction of non-standard Lagrangian and Hamiltonian structures using the Jacobi Last Multiplier for the (generalized) reduced Lienard equations satisfying Chiellini integrability condition, we then explore its connection with the contact Hamiltonian mechanics. We also explore Lienard equations, of reaction-diffusion class and conformal (or contact) Hamiltonian Structures. Finally, we present the geometric formulation of the generalized Lienard equations in terms of metriplectic structure.
Joint work with Jose Carinena and Anindya Ghose Choudhury

Love and Naturalness
2024-05-17 10:30 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Mikhail Ivanov (MIT)
Title: Love and Naturalness
Abstract: Recent progress in gravitational wave astronomy has spurred the development of efficient tools to describe gravitational binary dynamics. One such tool is classical worldline effective field theory (EFT). In the first part of my talk, I will show how to use this EFT for systematic studies of tidal heating and deformations (Love numbers) of compact objects. I will present a gauge-invariant definition of Love numbers and show how to extract them in a coordinate-independent way from scattering amplitudes of the gravitational Raman process. I will show that the worldline EFT exhibits strong fine-tuning when applied to black holes. This gives rise to a naturalness paradox associated with the vanishing of black hole static Love numbers. In the second part of my talk, I will present a new symmetry of black holes (Love symmetry) that elegantly resolves this paradox. The Love symmetry is tightly connected to isometries of extremal black holes that appear in many holographic constructions. It also provides a curious example of IR/UV mixing, which may give insights for other hierarchy problems.
