April | April | April | 1 - CMSA EVENT: Workshop on Global Categorical Symmetries
9:00 AM-5:00 PM May 1, 2024-May 3, 2024 The CMSA will be hosting a Workshop on Global Categorical Symmetries from April 29–May 3, 2024. Organizers: Dan Freed (Harvard CMSA & Math)
Constantin Teleman (UC Berkeley) Participation in the workshop is by invitation. - NUMBER THEORY SEMINAR: Number Theory Seminar: Modularity of special cycles in orthogonal and unitary Shimura varieties
Speaker: Salim Tayou – Harvard University 3:00 PM-4:00 PM May 1, 2024 1 Oxford Street, Cambridge, MA 02138 USA
Since the work of Jacobi and Siegel, it is well known that Theta series of quadratic lattices produce modular forms. In a vast generalization, Kudla and Millson have proved that the generating series of special cycles in orthogonal and unitary Shimura varieties are modular forms. In this talk, I will explain an extension of these results to toroidal compactifications where we prove that the generating series of divisors is a mixed mock modular form. This recovers and refines earlier results of Bruinier and Zemel. The results of this talk are joint work with Philip Engel and François Greer. ========================================= For more info, see https://ashvin-swaminathan.github.io/home/NTSeminar.html - SEMINARS: Dynamics, Geometry and Moduli Spaces Seminar: Counting minimal surfaces in hyperbolic 3-manifolds
Speaker: Ruojing Jiang – MIT 4:00 PM-5:00 PM May 1, 2024 See webpage for more details: https://people.math.harvard.edu/~ctm/sem/ - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Toric Matroid Bundles
Speaker: Christopher Manon – University of Kentucky 4:15 PM-5:15 PM May 1, 2024
Toric matroid bundles are combinatorial objects which serve as a tropical analogue to vector bundles over toric varieties. I’ll explain how to construct toric matroid bundles, how to check if a toric matroid bundle is globally generated or ample, and how to compute the characteristic classes of a toric matroid bundle in the T-equivariant chow cohomology of the base. Finally, I’ll show that each matroid determines a tautological toric matroid bundle over the permutahedral toric variety. I’ll discuss some properties of these bundles, and I’ll show that the characteristic classes of the tautological toric matroid bundle recover the tautological classes of matroids used by Berget, Eur, Spink, and Tseng to prove log-concavity properties of the Tutte polynomial. =============================== For more info, see https://math.mit.edu/combin/
| 2 - CMSA EVENT: Workshop on Global Categorical Symmetries
9:00 AM-5:00 PM May 2, 2024-May 3, 2024 The CMSA will be hosting a Workshop on Global Categorical Symmetries from April 29–May 3, 2024. Organizers: Dan Freed (Harvard CMSA & Math)
Constantin Teleman (UC Berkeley) Participation in the workshop is by invitation. - CMSA EVENT: CMSA Active Matter Seminar: Control of parametric amplification in space-time modulated mechanical metamaterials
Speaker: Jayson Paulose – University of Oregon 1:30 PM-2:30 PM May 2, 2024
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)
This seminar will be held in person and on Zoom. https://harvard.zoom.us/j/96657833341 Password: cmsa - CMSA EVENT: Symmetry Colloquia – Global Categorical Symmetries: Particle-Soliton Degeneracies from Spontaneously Broken Non-Invertible Symmetry
Speaker: Clay Còrdova – University of Chicago 2:00 PM-2:50 PM May 2, 2024 20 Garden Street, Cambridge, MA 02138 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. https://cmsa.fas.harvard.edu/event/gcs24_cordova/ - CMSA EVENT: Symmetry Colloquia – Global Categorical Symmetries: Symmetries, Invertible Field Theories, and Gauge Theory Phases
Speaker: Thomas Dumitrescu – UCLA 3:00 PM-3:50 PM May 2, 2024 20 Garden Street, Cambridge, MA 02138 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. https://cmsa.fas.harvard.edu/event/gcs24_dumitrescu/ - CMSA EVENT: Symmetry Colloquia – Global Categorical Symmetries: The universal target category
Speaker: Theo Johnson-Freyd – Dalhousie University and Perimeter Institute 4:30 PM-5:20 PM May 2, 2024 20 Garden Street, Cambridge, MA 02138 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. https://cmsa.fas.harvard.edu/event/gcs24_johnson-freyd/
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5 | 6 - CMSA EVENT: CMSA Colloquium: Liouville Theory and Weil-Petersson Geometry
Speaker: Sarah Harrison – Northeastern University 4:30 PM-5:30 PM May 6, 2024 20 Garden Street, Cambridge, MA 02138 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.
| 7 - CMSA EVENT: CMSA Member Seminar: On the landscape of 4d N=2 SCFTs
Speaker: Robert Moscrop – Harvard 12:00 PM-2:00 PM May 7, 2024
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.
Friday, May 10th at 12pm, with lunch, lounge at CMSA (20 Garden Street). Also by Zoom: https://harvard.zoom.us/j/92410768363 - CMSA EVENT: CMSA Member Seminar: On using ML for Economics
Speaker: Sergiy Verstyuk – Harvard 12:00 PM-2:00 PM May 7, 2024
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.
Friday, May 7th at 12pm, with lunch, lounge at CMSA (20 Garden Street). Also by Zoom: https://harvard.zoom.us/j/92410768363 - CMSA EVENT: CMSA General Relativity Seminar: Real-time observables in horizon thermodynamics
Speaker: Albert Law – Stanford University 2:00 PM May 7, 2024
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.
Zoom: https://harvard.zoom.us/j/7855806609 - HARVARD-MIT ALGEBRAIC GEOMETRY SEMINAR: Harvard-MIT Algebraic Geometry Seminar: The Enriques Conjectures
Speaker: Joe Harris – Harvard University 3:00 PM-4:00 PM May 7, 2024 1 Oxford Street, Cambridge, MA 02138 USA
Two fundamental facts about the moduli space M_g of smooth curves of genus g are what are called Harer’s theorems: that the Picard group of M_g is of rank one, generated (over the rational numbers) by the Hodge class; and that the relative Picard group of the universal curve over M_g is also of rank one, generated by the relative dualizing sheaf. We can make analogous statements about the Severi variety of plane curves and the Hurwitz space parametrizing branched covers, which are still open; in fact, the former was conjectured by Enriques more than a century ago and remains open. In this talk I’d like to describe all of these theorems/conjectures, and the implications among them, including Isabel Vogt’s recent work on Severi varieties. I’ll be working entirely with rational coefficients, so torsion classes, which are far more mysterious, will not enter into it. For more information, please see https://researchseminars.org/seminar/harvard-mit-ag-seminar
| 8 - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Fine Mixed Subdivisions of Dilated Simplicies
Speaker: Yuan Yao – MIT 4:15 PM-5:15 PM May 8, 2024 A mixed subdivision is a generalization of zonotope tiling that applies to any Minkowski sums of polytopes. (Fine) mixed subdivisions of dilated simplices have received particular attention in recent years due to their connections to tropical geometry and oriented matroids. In this talk I will introduce some of the backgrounds around these beautiful objects and present some recent results in advancing our understanding of their structures in both the (easier) two-dimensional case and the (much harder) higher-dimensional case. Based on joint works with Derek Liu and Fedir Yudin. =============================== For more info, see https://math.mit.edu/combin/
| 9 - CMSA EVENT: CMSA Algebraic Geometry in String Theory Seminar: Computing periods of hypersurfaces and elliptic surfaces via effective homology
Speaker: Eric Pichon-Pharabod – Universite Paris-Saclay 10:30 AM-11:30 AM May 9, 2024 20 Garden Street, Cambridge, MA 02138
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.
| 10 - CMSA EVENT: CMSA Quantum Matter in Math and Physics Seminar: From quantum Hall to Hubbard physics in twisted bilayer graphene
Speaker: Eslam Khalaf – Harvard 10:00 AM-11:30 AM May 10, 2024 20 Garden Street, Cambridge, MA 02138
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. Zoom: https://harvard.zoom.us/j/977347126 Password: cmsa - HARVARD-MIT COMBINATORICS SEMINAR: Richard P. Stanley Seminar in Combinatorics: Turán numbers of r-graphs on r+1 vertices
Speaker: Alexander Sidorenko – 3:00 PM-3:30 PM May 10, 2024 Let H_k^r be an r-uniform hypergraph with r+1 vertices and k edges where 3 ≤ k ≤ r+1. It is easy to see that such a hypergraph is unique up to isomorphism. The well-known upper bound on its Turán density is 𝝿(H_k^r) ≤ (k-2)/r. In the case k=3, Frankl and Füredi (1984) used a geometric construction to prove 𝝿(H_3^r) ≥ 2^{1-r}. We use classical results from order statistics going back to Rényi (1953) and a geometric construction to prove 𝝿(H_k^r) ≥ r^{-(1 + 1/(k-2))}. =============================== For more info, see https://math.mit.edu/combin/
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12 | 13 - CMSA EVENT: CMSA General Relativity Seminar: An analogue of non-interacting quantum field theory in Riemannian signature
Speaker: Mikhail Molodyk – Stanford University 11:00 AM-12:00 PM May 13, 2024 20 Garden Street, Cambridge, MA 02138
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 Andraěs Vasy.
Zoom: https://harvard.zoom.us/j/7855806609 - CMSA EVENT: CMSA Colloquium: Errors and Correction in Cumulative Knowledge
Speaker: Madhu Sudan – Harvard University 4:30 PM-5:30 PM May 13, 2024 20 Garden Street, Cambridge, MA 02138 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: 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
| 14 | 15 | 16 | 17 - CMSA EVENT: CMSA Quantum Matter in Math and Physics Seminar: Love and Naturalness
Speaker: Mikhail Ivanov – MIT 10:30 AM-12:00 PM May 17, 2024 20 Garden Street, Cambridge, MA 02138
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. Zoom: https://harvard.zoom.us/j/977347126 Password: cmsa
| 18 |
26 | 27 | 28 | 29 - CMSA EVENT: Amplituhedra, Cluster Algebras, and Positive Geometry
9:00 AM-5:00 PM May 29, 2024-May 31, 2024 20 Garden Street, Cambridge, MA 02138  Amplituhedra, Cluster Algebras, and Positive Geometry Dates: May 29-31, 2024 Location: Harvard CMSA, 20 Garden Street, Cambridge MA 02138 & via Zoom In recent years, a remarkable paradigm shift has occurred in understanding quantum observables in particle physics and cosmology, revealing their emergence from underlying novel mathematical objects known as positive geometries. The conference will center on the amplituhedron—the first and major example of a positive geometry. Building on the work of Lusztig and Postnikov on the positive Grassmannian, the physicists Arkani-Hamed and Trnka introduced the amplituhedron in 2013 as a geometric object that “explains” the so-called BCFW recurrence for scattering amplitudes in N = 4 super Yang Mills theory (SYM). Simultaneously, cluster algebras, originally introduced by Fomin and Zelevinsky to study total positivity, have been revealed to have a crucial role in describing singularities of N = 4 SYM scattering amplitudes. Thus, one can use ideas from quantum field theory (QFT) to connect cluster algebras to positive geometries, and in particular to the amplituhedron. Additionally, QFT can also be used to discover new examples of positive geometries. The conference will bring together a wide range of mathematicians and physicists both to draw new connections within algebraic combinatorics and geometry and to advance our physical understanding of scattering amplitudes and QFT. The conference features: Introductory Lectures, an Open Problems Forum, Emerging Scholars Talks, and talks by experts in the fields. Directions to CMSA Register Online for in-person talks Register for Zoom Meeting Confirmed Speakers: - Evgeniya Akhmedova, Weizmann Institute of Science
- Nima Arkani-Hamed, IAS
- Paolo Benincasa, MPI
- Nick Early, Weizmann Institute of Science
- Carolina Figueiredo, Princeton University
- Yu-tin Huang, National Taiwan University
- Dani Kaufman, University of Copenhagen
- Chia-Kai Kuo, National Taiwan University
- Thomas Lam, University of Michigan
- Yelena Mandelshtam, UC Berkeley
- Shruti Paranjape, UC Davis
- Elizabeth Pratt, UC Berkeley
- Lecheng Ren, Brown University
- Sebastian Seemann, KU Leuven
- Khrystyna Serhiyenko, University of Kentucky
- Melissa Sherman-Bennett, MIT & UC Davis
- Marcus Spradlin, Brown University
- Ran Tessler, Weizmann Institute of Science
- Hugh Thomas, Université du Québec à Montréal
- Jaroslav Trnka, UC Davis
- Anastasia Volovich, Brown University
Organizers: This event will be co-funded by the National Science Foundation. Limited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support, please register above and send an email to amplituhedra@cmsa.fas.harvard.edu no later than Friday, April 19, 2024. Please include your name, address, current status, university affiliation, citizenship, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research. If you are a postdoc, please include a copy of your CV. Preliminary Schedule | Wednesday, May 29, 2024 | | 8.45 – 9.00 am | Registration | | 9.00 – 9.45 am | Introductory Lecture #1: The Amplituhedron | | 9.45 – 10.30 am | Introductory Lecture #2: Cluster Algebras | | 10:30 – 10.45 am | Coffee Break | | 10.45 – 11.30 am | Introductory Lecture #3: Positive Geometries | | 11.30 – 12.15 pm | Talk #1 | | 12.30 – 2.00 pm | Lunch Break | | 2.00 – 2.45 pm | Talk #2 | | 2.45 – 3.30 pm | Talk #3 | | 3.30 – 4.00 pm | Coffee Break | | 4.00 – 4.45 pm | Talk #4 | | 5.00 – 6.00 pm | Welcome Reception |
Thursday, May 30, 2024 | | 9.00 – 10.00 am | Talk #5 | | 10.00 – 10.30 am | Coffee Break | | 10.30 – 11.15 am | Talk #6 | | 11.30 – 12.15 om | Talk #7 | | 12.30 – 2.00 pm | Lunch Break | | 2.00 – 2.45 pm | Talk #8 | | 2.45 – 3.30 pm | Talk #9 | | 3.30 – 4.00 pm | Coffee Break | | 4.00 – 5.30 pm | Open Problems Forum | | 6.00 – 8.00 pm | Conference Dinner |
Friday, May 31, 2024 | | 9.00 – 10.00 am | Talk #10 | | 10.00 –10.30 am | Coffee Break | | 10.30 – 12.40 pm | Emerging Scholars Talks | | 10.30 – 10.50 am: Short Talk #1 | | 10.50 – 11.10 am: Short Talk #2 | | 11.10– 11.30 am: Short Talk #3 | | 11.30 – 11.40 am: Short break | | 11.40 – 12.00 pm: Short Talk #4 | | 12.00 – 12.20 pm: Short Talk #5 | | 12.20 – 12.40 pm: Short Talk #6 | | 12.40 – 2.00 pm | Lunch Break | | 2.00 – 2.45 pm | Talk #11 | | 2.45 – 3.30 pm | Talk #12 | | 3.30 – 3.45 pm | Coffee Break | | 3.45 – 4.30 pm | Talk #13 | | 4.30 – 5.00 pm | Farewell Tea |
| 30 - CMSA EVENT: Amplituhedra, Cluster Algebras, and Positive Geometry
9:00 AM-5:00 PM May 30, 2024-May 31, 2024 20 Garden Street, Cambridge, MA 02138 Amplituhedra, Cluster Algebras, and Positive Geometry Dates: May 29-31, 2024 Location: Harvard CMSA, 20 Garden Street, Cambridge MA 02138 & via Zoom In recent years, a remarkable paradigm shift has occurred in understanding quantum observables in particle physics and cosmology, revealing their emergence from underlying novel mathematical objects known as positive geometries. The conference will center on the amplituhedron—the first and major example of a positive geometry. Building on the work of Lusztig and Postnikov on the positive Grassmannian, the physicists Arkani-Hamed and Trnka introduced the amplituhedron in 2013 as a geometric object that “explains” the so-called BCFW recurrence for scattering amplitudes in N = 4 super Yang Mills theory (SYM). Simultaneously, cluster algebras, originally introduced by Fomin and Zelevinsky to study total positivity, have been revealed to have a crucial role in describing singularities of N = 4 SYM scattering amplitudes. Thus, one can use ideas from quantum field theory (QFT) to connect cluster algebras to positive geometries, and in particular to the amplituhedron. Additionally, QFT can also be used to discover new examples of positive geometries. The conference will bring together a wide range of mathematicians and physicists both to draw new connections within algebraic combinatorics and geometry and to advance our physical understanding of scattering amplitudes and QFT. The conference features: Introductory Lectures, an Open Problems Forum, Emerging Scholars Talks, and talks by experts in the fields. Directions to CMSA Register Online for in-person talks Register for Zoom Meeting Confirmed Speakers: - Evgeniya Akhmedova, Weizmann Institute of Science
- Nima Arkani-Hamed, IAS
- Paolo Benincasa, MPI
- Nick Early, Weizmann Institute of Science
- Carolina Figueiredo, Princeton University
- Yu-tin Huang, National Taiwan University
- Dani Kaufman, University of Copenhagen
- Chia-Kai Kuo, National Taiwan University
- Thomas Lam, University of Michigan
- Yelena Mandelshtam, UC Berkeley
- Shruti Paranjape, UC Davis
- Elizabeth Pratt, UC Berkeley
- Lecheng Ren, Brown University
- Sebastian Seemann, KU Leuven
- Khrystyna Serhiyenko, University of Kentucky
- Melissa Sherman-Bennett, MIT & UC Davis
- Marcus Spradlin, Brown University
- Ran Tessler, Weizmann Institute of Science
- Hugh Thomas, Université du Québec à Montréal
- Jaroslav Trnka, UC Davis
- Anastasia Volovich, Brown University
Organizers: This event will be co-funded by the National Science Foundation. Limited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support, please register above and send an email to amplituhedra@cmsa.fas.harvard.edu no later than Friday, April 19, 2024. Please include your name, address, current status, university affiliation, citizenship, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research. If you are a postdoc, please include a copy of your CV. Preliminary Schedule | Wednesday, May 29, 2024 | | 8.45 – 9.00 am | Registration | | 9.00 – 9.45 am | Introductory Lecture #1: The Amplituhedron | | 9.45 – 10.30 am | Introductory Lecture #2: Cluster Algebras | | 10:30 – 10.45 am | Coffee Break | | 10.45 – 11.30 am | Introductory Lecture #3: Positive Geometries | | 11.30 – 12.15 pm | Talk #1 | | 12.30 – 2.00 pm | Lunch Break | | 2.00 – 2.45 pm | Talk #2 | | 2.45 – 3.30 pm | Talk #3 | | 3.30 – 4.00 pm | Coffee Break | | 4.00 – 4.45 pm | Talk #4 | | 5.00 – 6.00 pm | Welcome Reception |
Thursday, May 30, 2024 | | 9.00 – 10.00 am | Talk #5 | | 10.00 – 10.30 am | Coffee Break | | 10.30 – 11.15 am | Talk #6 | | 11.30 – 12.15 om | Talk #7 | | 12.30 – 2.00 pm | Lunch Break | | 2.00 – 2.45 pm | Talk #8 | | 2.45 – 3.30 pm | Talk #9 | | 3.30 – 4.00 pm | Coffee Break | | 4.00 – 5.30 pm | Open Problems Forum | | 6.00 – 8.00 pm | Conference Dinner |
Friday, May 31, 2024 | | 9.00 – 10.00 am | Talk #10 | | 10.00 –10.30 am | Coffee Break | | 10.30 – 12.40 pm | Emerging Scholars Talks | | 10.30 – 10.50 am: Short Talk #1 | | 10.50 – 11.10 am: Short Talk #2 | | 11.10– 11.30 am: Short Talk #3 | | 11.30 – 11.40 am: Short break | | 11.40 – 12.00 pm: Short Talk #4 | | 12.00 – 12.20 pm: Short Talk #5 | | 12.20 – 12.40 pm: Short Talk #6 | | 12.40 – 2.00 pm | Lunch Break | | 2.00 – 2.45 pm | Talk #11 | | 2.45 – 3.30 pm | Talk #12 | | 3.30 – 3.45 pm | Coffee Break | | 3.45 – 4.30 pm | Talk #13 | | 4.30 – 5.00 pm | Farewell Tea |
| 31 - CMSA EVENT: Amplituhedra, Cluster Algebras, and Positive Geometry
9:00 AM-5:00 PM May 31, 2024-May 31, 2024 20 Garden Street, Cambridge, MA 02138 Amplituhedra, Cluster Algebras, and Positive Geometry Dates: May 29-31, 2024 Location: Harvard CMSA, 20 Garden Street, Cambridge MA 02138 & via Zoom In recent years, a remarkable paradigm shift has occurred in understanding quantum observables in particle physics and cosmology, revealing their emergence from underlying novel mathematical objects known as positive geometries. The conference will center on the amplituhedron—the first and major example of a positive geometry. Building on the work of Lusztig and Postnikov on the positive Grassmannian, the physicists Arkani-Hamed and Trnka introduced the amplituhedron in 2013 as a geometric object that “explains” the so-called BCFW recurrence for scattering amplitudes in N = 4 super Yang Mills theory (SYM). Simultaneously, cluster algebras, originally introduced by Fomin and Zelevinsky to study total positivity, have been revealed to have a crucial role in describing singularities of N = 4 SYM scattering amplitudes. Thus, one can use ideas from quantum field theory (QFT) to connect cluster algebras to positive geometries, and in particular to the amplituhedron. Additionally, QFT can also be used to discover new examples of positive geometries. The conference will bring together a wide range of mathematicians and physicists both to draw new connections within algebraic combinatorics and geometry and to advance our physical understanding of scattering amplitudes and QFT. The conference features: Introductory Lectures, an Open Problems Forum, Emerging Scholars Talks, and talks by experts in the fields. Directions to CMSA Register Online for in-person talks Register for Zoom Meeting Confirmed Speakers: - Evgeniya Akhmedova, Weizmann Institute of Science
- Nima Arkani-Hamed, IAS
- Paolo Benincasa, MPI
- Nick Early, Weizmann Institute of Science
- Carolina Figueiredo, Princeton University
- Yu-tin Huang, National Taiwan University
- Dani Kaufman, University of Copenhagen
- Chia-Kai Kuo, National Taiwan University
- Thomas Lam, University of Michigan
- Yelena Mandelshtam, UC Berkeley
- Shruti Paranjape, UC Davis
- Elizabeth Pratt, UC Berkeley
- Lecheng Ren, Brown University
- Sebastian Seemann, KU Leuven
- Khrystyna Serhiyenko, University of Kentucky
- Melissa Sherman-Bennett, MIT & UC Davis
- Marcus Spradlin, Brown University
- Ran Tessler, Weizmann Institute of Science
- Hugh Thomas, Université du Québec à Montréal
- Jaroslav Trnka, UC Davis
- Anastasia Volovich, Brown University
Organizers: This event will be co-funded by the National Science Foundation. Limited funding to help defray travel expenses is available for graduate students and recent PhDs. If you are a graduate student or postdoc and would like to apply for support, please register above and send an email to amplituhedra@cmsa.fas.harvard.edu no later than Friday, April 19, 2024. Please include your name, address, current status, university affiliation, citizenship, and area of study. F1 visa holders are eligible to apply for support. If you are a graduate student, please send a brief letter of recommendation from a faculty member to explain the relevance of the conference to your studies or research. If you are a postdoc, please include a copy of your CV. Preliminary Schedule | Wednesday, May 29, 2024 | | 8.45 – 9.00 am | Registration | | 9.00 – 9.45 am | Introductory Lecture #1: The Amplituhedron | | 9.45 – 10.30 am | Introductory Lecture #2: Cluster Algebras | | 10:30 – 10.45 am | Coffee Break | | 10.45 – 11.30 am | Introductory Lecture #3: Positive Geometries | | 11.30 – 12.15 pm | Talk #1 | | 12.30 – 2.00 pm | Lunch Break | | 2.00 – 2.45 pm | Talk #2 | | 2.45 – 3.30 pm | Talk #3 | | 3.30 – 4.00 pm | Coffee Break | | 4.00 – 4.45 pm | Talk #4 | | 5.00 – 6.00 pm | Welcome Reception |
Thursday, May 30, 2024 | | 9.00 – 10.00 am | Talk #5 | | 10.00 – 10.30 am | Coffee Break | | 10.30 – 11.15 am | Talk #6 | | 11.30 – 12.15 om | Talk #7 | | 12.30 – 2.00 pm | Lunch Break | | 2.00 – 2.45 pm | Talk #8 | | 2.45 – 3.30 pm | Talk #9 | | 3.30 – 4.00 pm | Coffee Break | | 4.00 – 5.30 pm | Open Problems Forum | | 6.00 – 8.00 pm | Conference Dinner |
Friday, May 31, 2024 | | 9.00 – 10.00 am | Talk #10 | | 10.00 –10.30 am | Coffee Break | | 10.30 – 12.40 pm | Emerging Scholars Talks | | 10.30 – 10.50 am: Short Talk #1 | | 10.50 – 11.10 am: Short Talk #2 | | 11.10– 11.30 am: Short Talk #3 | | 11.30 – 11.40 am: Short break | | 11.40 – 12.00 pm: Short Talk #4 | | 12.00 – 12.20 pm: Short Talk #5 | | 12.20 – 12.40 pm: Short Talk #6 | | 12.40 – 2.00 pm | Lunch Break | | 2.00 – 2.45 pm | Talk #11 | | 2.45 – 3.30 pm | Talk #12 | | 3.30 – 3.45 pm | Coffee Break | | 3.45 – 4.30 pm | Talk #13 | | 4.30 – 5.00 pm | Farewell Tea |
| June |