Phase diagram and confining strings in a minimal model of nematopolar matter
2024-04-05 12:00 - 13:00 (America/New_York) | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Member Seminar
Speaker: Farzan Vafa
Title: Phase diagram and confining strings in a minimal model of nematopolar matter
Abstract: We investigate a minimal model of a nematopolar system. We analytically uncover a phase diagram consisting of a locked phase where the polar order and nematic order are locked, and unlocked phases which could be ordered or disordered. In particular, we develop two complementary perspectives on the locked phase: (i) the nematic order induces polar order, (ii) in the locked phase, all 1/2 integral nematic topological charges are confined. In particular, a polar +1 defect fattens from a point along a string with constant tension and confines a pair of nematic +1/2 defects at its ends.

Current Developments in Mathematics Conference 2024
2024-04-05 14:00 - 2024-04-06 17:00 | Harvard Science Center, 1 Oxford Street, Cambridge, MA, 02138
CURRENT DEVELOPMENTS IN MATHEMATICS 2024
APRIL 5-6, 2024
HARVARD UNIVERSITY SCIENCE CENTER
LECTURE HALL C
https://www.math.harvard.edu/event/current-developments-in-mathematics-2024/

Speakers:
Daniel Cristofaro-Gardiner – University of Maryland
Samit Dasgupta – Duke University
Jiaoyang Huang – University of Pennsylvania
Daniel Litt – University of Toronto
Lisa Piccirillo – MIT/University of Texas

Download PDF for a detailed schedule of lectures and events.

Friday, April 5

Saturday, April 6

1:30 p.m. – 2:20 p.m. Part 1
2:20 p.m. – 2:30 p.m. Break
2:30 p.m. – 3:20 p.m. Part 2

Jiaoyang Huang
Random Matrix Statistics and Airy Line Ensembles

9:05 a.m. – 9:55 a.m. Part 1
9:55 a.m. – 10:05 a.m. Break
10:05 a.m. – 10:55 a.m. Part 2

Daniel Litt
Motives, mapping class groups, and monodromy

3:20 p.m. – 3:35 p.m.
Break

10:55 a.m. – 11:10 a.m.
Break

3:35 p.m. – 4:25 p.m. Part 1
4:25 p.m. – 4:35 p.m. Break
4:35 p.m. – 5:25 p.m. Part 2

Lisa Piccirillo
Exotic phenomena in dimension 4

11:10 a.m. – 12 p.m. Part 1
12 p.m. – 1:30 p.m. Lunch
1:30 p.m. – 2:20 p.m. Part 2

Samit Dasgupta
Stark’s conjectures and explicit class field theory

2:20 p.m. – 2:35 p.m.
Break

2:35 p.m. – 3:25 p.m. Part 1
3:25 p.m. – 3:35 p.m. Break
3:35 p.m. – 4:25 p.m. Part 2

Dan Cristofaro-Gardiner
Low-dimensional topology and dynamics

Organizers: David Jerison, Paul Seidel, Nike Sun (MIT); Denis Auroux, Mark Kisin, Lauren Williams, Horng-Tzer Yau, Shing-Tung Yau (Harvard).
Sponsored by the National Science Foundation, Harvard University Mathematics, and the Massachusetts Institute of Technology.
Harvard University is committed to maintaining a safe and healthy educational and work environment in which no member of the University community is, on the basis of sex, sexual orientation, or gender identity, excluded from participation in, denied the benefits of, or subjected to discrimination in any University program or activity. More information can be found here.

Mirror symmetry for fibrations and degenerations of K3 surfaces
2024-04-11 10:30 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Algebraic Geometry in String Theory Seminar
Speaker: Alan Thompson (Loughborough University)
Title: Mirror symmetry for fibrations and degenerations of K3 surfaces
Abstract: In 2016, Doran, Harder, and I conjectured a mirror symmetric relationship between Tyurin degenerations and splittings of codimension 1 fibrations on Calabi-Yau manifolds. In this talk I will discuss recent work to make this conjecture rigorous in the case of K3 surfaces. I will give a precise definition of what it means for a Tyurin degeneration of K3’s to be mirror to a splitting of an elliptically fibred K3, and show that this definition enjoys the following compatibilities with existing mirror symmetric theories: 1) The general fibre of the Tyurin degeneration is mirror to the elliptically fibred K3, in the sense of Dolgachev-Nikulin. 2) Components of the Tyurin degeneration and pieces of the splitting satisfy a homological version of the (quasi-) Fano-LG correspondence. 3) Components of the Tyurin degeneration which are weak del Pezzo are mirror to pieces of the splitting that arise as restrictions of the corresponding lattice polarised LG models to discs. This is joint work with Luca Giovenzana.

Global weak solutions of 3+1 dimensional vacuum Einstein equations
2024-04-12 12:00 - 13:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Member Seminar
Speaker: Puskar Mondal
Title: Global weak solutions of 3+1 dimensional vacuum Einstein equations
Abstract: It is important to understand if the `solutions’ of non-linear evolutionary PDEs persist for all time or become extinct in finite time through the blow-up of invariant entities. Now the question of this global existence or finite time blow up in the PDE settings is well defined if the regularity of the solution is specified. Most physically interesting scenarios demand control of the point-wise behavior of the solution. Unfortunately, most times this level of regularity is notoriously difficult to obtain for non-linear equations. In this talk, I will discuss very low regularity solutions namely distributional (or weak) solutions of vacuum Einsten’s equations in 3+1 dimensions. I prove that on a globally hyperbolic spacetime foliated by closed connected oriented negative Yamabe slices, weak solutions of the Einstein equations exist for all time. The monotonicity of a Coercive Entity called reduced Hamiltonian that controls the minimum regularity required for the weak solution is employed. This is in the same spirit as Leray’s global weak solutions of Navier-Stokes in 3+1 dimensions and the first result in the context of Einstein equations.

Program on Mathematical Aspects of Scattering Amplitudes
2024-04-15 09:00 - 2024-05-24 17:00 | CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Aspects of Scattering Amplitudes Program
Dates: April 15 – May 24, 2024
Location: Harvard CMSA, 20 Garden Street, Cambridge, MA 02138
This program will bring together and foster interaction between theoretical physicists and mathematicians working on various topics connected to recent developments in our understanding of scattering amplitudes in quantum field theory. The field has advanced considerably since 2019 when the CMSA hosted the program “Spacetime and Quantum Mechanics, Total Positivity and Motives.” Recent developments have primed this area for further significant advances, which will be facilitated by bringing together many of the relevant experts for intensive discussion and collaboration.
The program will feature a weekly seminar series.
Tuesday, April 16, 2024
4:15 pm
Sabrina Pasterski, Perimeter Institute
Title: Radiation in Holography
[Physics Talk]
Wednesday, April 17, 2024
4:30 pm – Cruft 309
Ana-Maria Raclariu, King’s College London
Thursday, April 18, 2024
4:15 pm
Lionel Mason, University of Oxford
Title: Hidden symmetries of SD Poincare Einstein metrics in split signature
[Physics Talk]
Tuesday, April 23, 2024
4:30 pm – Jefferson 256
Juan Maldacena, Institute for Advanced Study
Thursday, April 25, 2024
4:15 pm
Tomasz Taylor, Northeastern University
Title: Progress in Yang-Mills-Liouville Theory
[CMSA Colloquium]
Monday, April 29, 2024
4:30 – 5:30 pm
Lance Dixon, Stanford
Title: The DNA of Particle Scattering
Tuesday, April 30, 2024
9:00 am- Jefferson 453
Nima Arkani-Hamed, IAS
Title: Surfaceology and the Real World Part 1
1:00 pm – Jefferson 453
Nima Arkani-Hamed, IAS
Title: Surfaceology and the Real World Part 2
4:00 pm – Jefferson 453
Nima Arkani-Hamed, IAS
Title: Surfaceology and the Real World Part 3
Wednesday, May 1, 2024
11:00 am – Science Center 507
Jaroslav Trnka, UC Davis
Title: Loops of loops expansion in the Amplituhedron
3:00 pm
Yu-tin Huang, National Taiwan University
Title: Loop in trees: Chambers in amplitudes and correlation functions
4:00 pm
Livia Ferro, University of Hertfordshire
Title: Scattering Amplitudes from Null-cone Geometry
5:00 pm
Stephan Stieberger, Max Planck Institute
Title: One-loop Double Copy Relation in String Theory and Twisted (Co)homology
Thursday, May 2, 2024
11:00 am – Science Center 310
Daniil Rudenko, Chicago
Title: Introduction to Cluster Polylogarithms
Friday, May 3, 2024
11:00 am
Andrew McLeod, Edinburgh
Title: Genealogical Constraints on Feynman Integrals
Tuesday, May 7, 2024
3:00 pm
Jacob Bourjaily, Penn State
Title: The Algebraic and Transcendental Structure of Perturbative QFT
Wednesday, May 8, 2024
3:00 pm
Ruth Britto, Trinity
Title: Cuts and Symbols
Tuesday, May 14, 2024
3:00 pm
James Drummond, University of Southampton
Title: Multiple light-like Wilson loops in N=4 super Yang-Mills theory
Wednesday, May 15, 2024
3:00 pm
Matteo Parisi, Harvard CMSA
Title: The amplituhedron and cluster algebras
Tuesday, May 21, 2024
11:00 am
Michael Borinsky, ETH Zurich
Title: On the Euler characteristic of the commutative graph complex and the top-weight cohomology of the moduli space of curves
Wednesday, May 22, 2024
11:00 am
Chaim Even-Zohar, Technion
Title: Amplituhedron tiles and twistor polynomials

Organizers:

Nima Arkani-Hamed (Institute for Advanced Study)
Marcus Spradlin (Brown University)
Andrew Strominger (Harvard University)
Anastasia Volovich (Brown University)
Lauren Williams (Harvard University)

Participants:

Michael Borinsky, ETH Zurich
Jacob Bourjaily, Pennsylvania State University
Ruth Britto, Trinity College
Lance Dixon, Stanford Linear Accelerator Center
James Drummond, University of Southampton
Chaim Even-Zohar, Technion
Livia Ferro, University of Hertfordshire
Carolina Figueiredo, Princeton University
Hadleigh Frost, Oxford University
Bruno Gimenez, University of Southampton
Omer Gurdogan, University of Southampton
Xuhua He, Chinese University of Hong Kong
Paul Heslop, Durham University
Yu-Tin Huang, National Taiwan University
Dani Kaufman, University of Copenhagen
Jianrong Li, University of Vienna
Tomasz Lukowski, University of Hertfordshire
Yelena Mandelshtam, University of California, Berkeley
Lionel Mason, University of Oxford
Andrew McLeod, University of Edinburgh
Natalie Paquette, University of Washington
Matteo Parisi, Harvard University
Sabrina Pasterski, Perimeter Institute
Dmitri Pavlov, Max Planck Institute for Mathematics in the Sciences, Leipzig
Lizzie Pratt, University of California, Berkeley
Claudia Rella, University of Geneva
Daniil Rudenko, University of Chicago
Giulio Salvatori, Max Planck Institute for Physics
Melissa Sherman-Bennett, Massachusetts Institute of Technology
Jonah Stalknecht, University of Hertfordshire
Stephan Stieberger, Max Planck Institute
Tomasz Taylor, Northeastern University
Ran Tessler, Weizmann Institute of Science
Hugh Thomas, Université du Québec à Montréal
Jaroslav Trnka, University of California, Davis
Cristian Vergu, Pennsylvania State University

New Well-Posed Boundary Conditions for Semi-Classical Euclidean Gravity
2024-04-16 11:00 - 12:00 | Virtual
General Relativity Seminar
Speaker: Xiaoyi Liu, UCSB
Title: New Well-Posed Boundary Conditions for Semi-Classical Euclidean Gravity
Abstract: We consider four-dimensional Euclidean gravity in a finite cavity. We point out that there exists a one-parameter family of boundary conditions, parameterized by a real constant, where a suitably Weyl-rescaled boundary metric is fixed, and all give a well-posed elliptic system, as opposed to the Dirichlet boundary condition. Focussing on static Euclidean solutions, we derive a thermodynamic first law. Restricting to a spherical spatial boundary, the infillings are flat space or the Schwarzschild solution and have similar thermodynamics to the Dirichlet case. We study the stability behavior of several geometries under these boundary conditions in both Euclidean and Lorentzian signatures and find two puzzles.

CMSA Q&A Seminar 4/16/2024
2024-04-16 12:30 - 13:30 | Common Room, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
CMSA Q and A Seminar

Speaker: Cengiz Pehlevan, Harvard

Question: What is feature learning?

Mathematical Aspects of Scattering Amplitudes Lecture
2024-04-16 16:15 - 17:15 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Mathematical Aspects of Scattering Amplitudes Lecture
Speaker: Sabrina Pasterski, Perimeter Institute
Title: Radiation in Holography

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.

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

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.

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.

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?

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).

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

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.

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

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.

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.

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)

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 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)

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.
