CMSA

Mathematical Aspects of Scattering Amplitudes Lecture
2024-05-08 15:00 - 16:00 (America/New_York) | 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

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

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.

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.

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.

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

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.

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 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.

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)

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

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
2024-05-01 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 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 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
2024-04-30 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
2024-04-30 13:00 - 14:00 | 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 2
(Note change of venue to Jefferson 453)

CMSA Q&A Seminar 4/30/2024
2024-04-30 12:30 - 13:30 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Speaker: Lakshminarayanan Mahadevan

Question: What is morphogenesis? (Morphogenesis: geometry and biology)

Mathematical Aspects of Scattering Amplitudes Lecture
2024-04-30 09:00 - 10:00 | 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 1
(Note change of venue to Jefferson 453)

The DNA of Particle Scattering
2024-04-29 16:30 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Colloquium
Speaker: Lance Dixon (SLAC, Stanford University)
Title: The DNA of Particle Scattering
Abstract: At the Large Hadron Collider, the copious scattering of quarks and gluons in quantum chromodynamics (QCD) produces Higgs bosons and many backgrounds to searches for new physics. At short distances, scattering in QCD can be evaluated in perturbation theory and leads to highly intricate, multivariate mathematical functions such as generalized polylogarithms. To gain further insight, one can study a cousin of QCD called planar N=4 super-Yang-Mills theory. Some processes in this theory can be computed to eighth order in perturbation theory, versus second or third order in QCD. The computation and analysis of these results rely on a Hopf algebra coaction on polylogarithms. Its maximal iteration is called the ‘symbol’, which serves as a ‘genetic code’ for amplitudes. The symbol is a linear combination of words, sequences of letters analogous to sequences of DNA base pairs. Understanding the alphabet, and then reading the code, exposes the physics and mathematics of quantum scattering, including bizarre new symmetries. For example, the two scattering amplitudes that are known to the highest orders in perturbation theory (8 loops) are related to each other by an ‘antipodal duality’, which involves reading the code backwards as well as forwards. A third scattering amplitude, which contains the other two as limits, has an antipodal self-duality which ‘explains’ the other duality. However, we still don’t know ‘who ordered’ this property, or what it really means.

Workshop on Global Categorical Symmetries
2024-04-29 09:00 - 2024-05-03 17:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
The CMSA will be hosting a Workshop on Global Categorical Symmetries from April 29–May 3, 2024.
Participation in the workshop is by invitation.
The workshop will hold three Symmetry Colloquia open to the community on Thursday, May 2, 2024.
Location: Room G-10, CMSA, 20 Garden Street, Cambridge MA 02138
Time: 2:00 – 2:50 pm
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.

Location: Room G-10, CMSA, 20 Garden Street, Cambridge MA 02138
Time: 3:00 – 3:50 pm
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.

Location: Room G-10, CMSA, 20 Garden Street, Cambridge MA 02138
Time: 4:30 – 5:20 pm
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.

Organizers:
Dan Freed (Harvard CMSA & Math)
Constantin Teleman (UC Berkeley)
This event is co-sponsored by the Simons Foundation.

Member Seminar
2024-04-26 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Member Seminar
Speaker: Matteo Parisi, Harvard CMSA

What Observables are Safe to Calculate?
2024-04-26 10:30 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Jesse Thaler, MIT
Title: What Observables are Safe to Calculate?
Abstract: In collider physics, perturbative quantum field theory is the workhorse framework for computing theoretical predictions to compare to experimental measurements. An observable is called “safe” if its cross section can be predicted order-by-order in perturbation theory with controlled non-perturbative corrections. In this talk, I show that naive definitions of “safety” are inadequate to determine which observable are perturbatively calculable. I then argue for a more refined definition of safety based on principles from optimal transport theory.

Mathematical Aspects of Scattering Amplitudes Lecture
2024-04-25 16:15 - 17:15 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Aspects of Scattering Amplitudes Lecture
Speaker: Tomasz Taylor, Northeastern University
Title: Progress in Yang-Mills-Liouville Theory

The logarithmic double ramification locus
2024-04-25 10:30 - 11:30 | Virtual
Algebraic Geometry in String Theory Seminar
Speaker: Alessandro Chiodo, IMJ-Paris Rive Gauche (Jussieu)
Title: The logarithmic double ramification locus
Abstract: Given a family of smooth curves C -> S with a line bundle L on C, it is natural to study the locus of points x in S where L_x is trivial on C_x. When the family is stable, the definition can be extended, not directly on the base scheme S, but more naturally on a (logarithmic) blow-up S’ of S. The problem is in many ways analogue to the problem of defining a Néron model on the moduli space of stable curves (instead of a DVR). Over the past years, David Holmes and his collaborators pioneered a new approach on a logarithmic modification of the entire moduli space of curves. In this talk, we determine this logarithmic double ramification cycle and several variants and alternative presentations of it (work in collaboration with David Holmes).

CMSA Q&A Seminar 4/23/2024
2024-04-23 12:30 - 13:30 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q and A Seminar

Speaker: Melanie Weber, Harvard

Question: What is the Ricci curvature of a graph?

Quantum Energy Inequalities
2024-04-23 10:00 - 11:00 | Virtual
General Relativity Seminar
Speaker: Chris Fewster, York University
Title: Quantum Energy Inequalities
Abstract: Many theorems of mathematical relativity, including singularity and positive mass theorems, include the classical energy conditions among their hypotheses. However, matter described by quantum field theory can violate the classical energy conditions and indeed there is no lower bound to the energy density at a given point as the quantum state is varied. Do the classical theorems apply to quantised matter?
In this talk I discuss Quantum Energy Inequalities, lower bounds on averages of the energy density along timelike curves or over spacetime regions, that have been proved in QFT and are the remnants of the classical energy conditions after quantisation. I will also discuss some of their consequences.

Member Seminar
2024-04-19 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Member Seminar
Speaker: Sunghyuk Park, Harvard CMSA
Title: 3D quantum trace map
Abstract: I will speak about my recent work (joint with Sam Panitch) constructing the 3d quantum trace map, a homomorphism from the Kauffman bracket skein module of an ideally triangulated 3-manifold to its (square root) quantum gluing module, thereby giving a precise relationship between the two quantizations of the character variety of ideally triangulated 3-manifolds. Our construction is based on the study of stated skein modules and their behavior under splitting, especially into face suspensions.

Fusion Rule Measurement in a Topological Qubit
2024-04-19 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Chetan Nayak, Microsoft and UCSB
Title: Fusion Rule Measurement in a Topological Qubit

Geometric local systems on very general curves
2024-04-18 10:15 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebraic Geometry in String Theory Seminar
Speaker: Aaron Landesman, MIT
Title: Geometric local systems on very general curves
Abstract: What is the smallest genus h of a non-isotrivial curve over the generic genus g curve? In joint work with Daniel Litt, we show h is more than $sqrt{g}$ by proving amore general result about variations of Hodge structure on sufficiently general curves. As a consequence, we show that local systems on a sufficiently general curve of geometric origin are not Zariski dense in the character variety parameterizing such local systems. This gives counterexamples to conjectures of Esnault-Kerz and Budur-Wang.
