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DTSTART;TZID=America/New_York:20240415T090000
DTEND;TZID=America/New_York:20240524T170000
DTSTAMP:20260427T061656
CREATED:20230904T173915Z
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UID:10000003-1713171600-1716570000@cmsa.fas.harvard.edu
SUMMARY:Program on Mathematical Aspects of Scattering Amplitudes
DESCRIPTION:Mathematical Aspects of Scattering Amplitudes Program \nDates: April 15 – May 24\, 2024 \nLocation: Harvard CMSA\, 20 Garden Street\, Cambridge\, MA 02138 \nThis 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. \nThe program will feature a weekly seminar series. \nTuesday\, April 16\, 2024\n4:15 pm\nSabrina Pasterski\, Perimeter Institute\nTitle: Radiation in Holography \n[Physics Talk]\nWednesday\, April 17\, 2024\n4:30 pm –  Cruft 309\nAna-Maria Raclariu\, King’s College London \nThursday\, April 18\, 2024\n4:15 pm\nLionel Mason\, University of Oxford\nTitle: Hidden symmetries of SD Poincare Einstein metrics in split signature \n[Physics Talk]\nTuesday\, April 23\, 2024\n4:30 pm – Jefferson 256\nJuan Maldacena\, Institute for Advanced Study \nThursday\, April 25\, 2024\n4:15 pm\nTomasz Taylor\, Northeastern University\nTitle: Progress in Yang-Mills-Liouville Theory \n[CMSA Colloquium]\nMonday\, April 29\, 2024\n4:30 – 5:30 pm\nLance Dixon\, Stanford\nTitle: The DNA of Particle Scattering \nTuesday\, April 30\, 2024\n9:00 am- Jefferson 453\nNima Arkani-Hamed\, IAS\nTitle: Surfaceology and the Real World Part 1 \n1:00 pm – Jefferson 453\nNima Arkani-Hamed\, IAS\nTitle: Surfaceology and the Real World Part 2 \n4:00 pm – Jefferson 453\nNima Arkani-Hamed\, IAS\nTitle: Surfaceology and the Real World Part 3 \nWednesday\, May 1\, 2024\n11:00 am – Science Center 507\nJaroslav Trnka\, UC Davis\nTitle: Loops of loops expansion in the Amplituhedron \n3:00 pm\nYu-tin Huang\, National Taiwan University\nTitle: Loop in trees: Chambers in amplitudes and correlation functions \n4:00 pm\nLivia Ferro\, University of Hertfordshire\nTitle: Scattering Amplitudes from Null-cone Geometry \n5:00 pm\nStephan Stieberger\, Max Planck Institute\nTitle: One-loop Double Copy Relation in String Theory and Twisted (Co)homology \nThursday\, May 2\, 2024\n11:00 am – Science Center 310\nDaniil Rudenko\, Chicago\nTitle: Introduction to Cluster Polylogarithms \nFriday\, May 3\, 2024\n11:00 am\nAndrew McLeod\, Edinburgh\nTitle: Genealogical Constraints on Feynman Integrals \nTuesday\, May 7\, 2024\n3:00 pm\nJacob Bourjaily\, Penn State\nTitle: The Algebraic and Transcendental Structure of Perturbative QFT \nWednesday\, May 8\, 2024\n3:00 pm\nRuth Britto\, Trinity\nTitle: Cuts and Symbols \nTuesday\, May 14\, 2024\n3:00 pm\nJames Drummond\, University of Southampton\nTitle: Multiple light-like Wilson loops in N=4 super Yang-Mills theory \nWednesday\, May 15\, 2024\n3:00 pm\nMatteo Parisi\, Harvard CMSA\nTitle: The amplituhedron and cluster algebras \nTuesday\, May 21\, 2024\n11:00 am\nMichael Borinsky\, ETH Zurich\nTitle: On the Euler characteristic of the commutative graph complex and the top-weight cohomology of the moduli space of curves \nWednesday\, May 22\, 2024\n11:00 am\nChaim Even-Zohar\, Technion\nTitle: Amplituhedron tiles and twistor polynomials \n  \nOrganizers: \n\nNima Arkani-Hamed (Institute for Advanced Study)\nMarcus Spradlin (Brown University)\nAndrew Strominger (Harvard University)\nAnastasia Volovich (Brown University)\nLauren Williams (Harvard University)\n\nParticipants: \n\n\nMichael Borinsky\, ETH Zurich\nJacob Bourjaily\, Pennsylvania State University\nRuth Britto\, Trinity College\nLance Dixon\, Stanford Linear Accelerator Center\nJames Drummond\, University of Southampton\nChaim Even-Zohar\, Technion\nLivia Ferro\, University of Hertfordshire\nCarolina Figueiredo\, Princeton University\nHadleigh Frost\, Oxford University\nBruno Gimenez\, University of Southampton\nOmer Gurdogan\, University of Southampton\nXuhua He\, Chinese University of Hong Kong\nPaul Heslop\, Durham University\nYu-Tin Huang\, National Taiwan University\nDani Kaufman\, University of Copenhagen\nJianrong Li\, University of Vienna\nTomasz Lukowski\, University of Hertfordshire\nYelena Mandelshtam\, University of California\, Berkeley\nLionel Mason\, University of Oxford\nAndrew McLeod\, University of Edinburgh\nNatalie Paquette\, University of Washington\nMatteo Parisi\, Harvard University\nSabrina Pasterski\, Perimeter Institute\nDmitri Pavlov\, Max Planck Institute for Mathematics in the Sciences\, Leipzig\nLizzie Pratt\, University of California\, Berkeley\nClaudia Rella\, University of Geneva\nDaniil Rudenko\, University of Chicago\nGiulio Salvatori\, Max Planck Institute for Physics\nMelissa Sherman-Bennett\, Massachusetts Institute of Technology\nJonah Stalknecht\, University of Hertfordshire\nStephan Stieberger\, Max Planck Institute\nTomasz Taylor\, Northeastern University\nRan Tessler\, Weizmann Institute of Science\nHugh Thomas\, Université du Québec à Montréal\nJaroslav Trnka\, University of California\, Davis\nCristian Vergu\, Pennsylvania State University
URL:https://cmsa.fas.harvard.edu/event/scattering-amplitudes/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Programs
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Page-88-from-2310.17727_crop.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240429T090000
DTEND;TZID=America/New_York:20240503T170000
DTSTAMP:20260427T061656
CREATED:20240105T071054Z
LAST-MODIFIED:20240624T182013Z
UID:10001119-1714381200-1714755600@cmsa.fas.harvard.edu
SUMMARY:Workshop on Global Categorical Symmetries
DESCRIPTION:The CMSA will be hosting a Workshop on Global Categorical Symmetries from April 29–May 3\, 2024. \nParticipation in the workshop is by invitation. \nThe workshop will hold three Symmetry Colloquia open to the community on Thursday\, May 2\, 2024. \nLocation:  Room G-10\, CMSA\, 20 Garden Street\, Cambridge MA 02138 \nTime: 2:00 – 2:50 pm \nSpeaker: Clay Còrdova\, University of Chicago \nTitle: Particle-Soliton Degeneracies from Spontaneously Broken Non-Invertible Symmetry \nAbstract: 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. \n  \nLocation:  Room G-10\, CMSA\, 20 Garden Street\, Cambridge MA 02138 \nTime: 3:00 – 3:50 pm \nSpeaker: Thomas Dumitrescu\, UCLA \nTitle: Symmetries\, Invertible Field Theories\, and Gauge Theory Phases \nAbstract: 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. \n  \nLocation:  Room G-10\, CMSA\, 20 Garden Street\, Cambridge MA 02138 \nTime: 4:30 – 5:20 pm \nSpeaker: Theo Johnson-Freyd\, Dalhousie University and Perimeter Institute \nTitle: The Universal Target Category \nAbstract: 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. \n  \nOrganizers:\nDan Freed (Harvard CMSA & Math)\nConstantin Teleman  (UC Berkeley) \nThis event is co-sponsored by the Simons Foundation. 
URL:https://cmsa.fas.harvard.edu/event/globalcomputing24/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Workshop
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Symmetry-Lectures-poster-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240502T140000
DTEND;TZID=America/New_York:20240502T145000
DTSTAMP:20260427T061656
CREATED:20240415T162849Z
LAST-MODIFIED:20240417T181513Z
UID:10003356-1714658400-1714661400@cmsa.fas.harvard.edu
SUMMARY:Symmetry Colloquia - Global Categorical Symmetries
DESCRIPTION:Symmetry Colloquia – Global Categorical Symmetries \nMay 2\, 2024 \nLocation: Room G-10\, CMSA\, 20 Garden Street\, Cambridge MA 02138 \nSpeaker: Clay Còrdova\, University of Chicago \nTitle:  Particle-Soliton Degeneracies from Spontaneously Broken Non-Invertible Symmetry \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/gcs24_cordova/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Symmetry Colloquia
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Pages-from-2403.08883_2.47.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240502T150000
DTEND;TZID=America/New_York:20240502T155000
DTSTAMP:20260427T061656
CREATED:20240415T163531Z
LAST-MODIFIED:20240417T181737Z
UID:10003357-1714662000-1714665000@cmsa.fas.harvard.edu
SUMMARY:Symmetry Colloquia  - Global Categorical Symmetries
DESCRIPTION:Symmetry Colloquia – Global Categorical Symmetries \nMay 2\, 2024 \nLocation: Room G-10\, CMSA\, 20 Garden Street\, Cambridge MA 02138 \nSpeaker: Thomas Dumitrescu\, UCLA \nTitle: Symmetries\, Invertible Field Theories\, and Gauge Theory Phases \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/gcs24_dumitrescu/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Symmetry Colloquia
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Pages-from-2312.16898_phase-transition.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240502T163000
DTEND;TZID=America/New_York:20240502T172000
DTSTAMP:20260427T061656
CREATED:20240415T163546Z
LAST-MODIFIED:20240422T153733Z
UID:10003358-1714667400-1714670400@cmsa.fas.harvard.edu
SUMMARY:Symmetry Colloquia  - Global Categorical Symmetries
DESCRIPTION:Symmetry Colloquia – Global Categorical Symmetries \nMay 2\, 2024 \nLocation: Room G-10\, CMSA\, 20 Garden Street\, Cambridge MA 02138 \nSpeaker: Theo Johnson-Freyd\, Dalhousie University and Perimeter Institute \nTitle: The Universal Target Category \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/gcs24_johnson-freyd/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Symmetry Colloquia
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Pages-from-2105.15167_Johnson-Freyd.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240529T090000
DTEND;TZID=America/New_York:20240531T170000
DTSTAMP:20260427T061656
CREATED:20240105T071351Z
LAST-MODIFIED:20240624T164905Z
UID:10001120-1716973200-1717174800@cmsa.fas.harvard.edu
SUMMARY:Amplituhedra\, Cluster Algebras\, and Positive Geometry
DESCRIPTION:Amplituhedra\, Cluster Algebras\, and Positive Geometry \nDates: May 29-31\, 2024 \nLocation: Harvard CMSA\, 20 Garden Street\, Cambridge MA 02138 & via Zoom \nIn 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. \nThe conference features: Introductory Lectures\, an Open Problems Forum\, Emerging Scholars Talks\, and talks by experts in the fields. \n  \nConference Videos (Youtube Playlist) \n  \nConfirmed Speakers: \n\nEvgeniya Akhmedova\, Weizmann Institute of Science\nNima Arkani-Hamed\, IAS\nPaolo Benincasa\, MPI\nNick Early\, Weizmann Institute of Science\nCarolina Figueiredo\, Princeton University\nYu-tin Huang\, National Taiwan University\nDani Kaufman\, University of Copenhagen\nChia-Kai Kuo\, National Taiwan University\nThomas Lam\, University of Michigan\nYelena Mandelshtam\, UC Berkeley\nShruti Paranjape\, UC Davis\nLizzie Pratt\, UC Berkeley\nLecheng Ren\, Brown University\nSebastian Seemann\, KU Leuven\nKhrystyna Serhiyenko\, University of Kentucky\nMelissa Sherman-Bennett\, MIT & UC Davis\nMarcus Spradlin\, Brown University\nRan Tessler\, Weizmann Institute of Science\nHugh Thomas\, Université du Québec à Montréal\nJaroslav Trnka\, UC Davis\nAnastasia Volovich\, Brown University\n\nOrganizers: \n\nMatteo Parisi\, Harvard CMSA\nLauren Williams\, Harvard Mathematics\n\nParticipants (PDF) \nThis event is co-funded by the National Science Foundation. \nLimited 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. \nPlease 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. \n\nSCHEDULE (pdf download) \nWednesday\, May 29\, 2024\n8:30 – 9:00 am\nRegistration and Breakfast \n9:00 – 10:00 am\nJaroslav Trnka\, UC Davis\nTitle: Amplituhedron\nAbstract: I will review basics of the Amplituhedron\, connection to the positive Grassmannian on the mathematical side\, and the scattering amplitudes on the physics side. \n10:00 – 10:15 am\nCoffee Break \n10:15 – 11:15 am\nvia Zoom\nKhrystyna Serhiyenko\, University of Kentucky\nTitle: Introduction to Cluster Algebras\nAbstract: Cluster algebras is a class of commutative rings with an intricate combinatorial structure. They were introduced by Fomin and Zelevinsky in 2002 to study total positivity and canonical basis in Lie Theory\, but quickly evolved into a highly active research area with surprising connections to numerous other areas of mathematics and physics.\nIn this course we will introduce cluster algebras and discuss their basic properties including positivity and Laurent phenomenon. We will also review cluster structures coming from coordinate rings of Grassmannians and the combinatorics of plabic graphs. \n11:15 – 11:30 am\nCoffee Break \n11:30 – 12:30 pm\nThomas Lam\, University of Michigan\nTitle: Introductory Lecture on Positive Geometries\nAbstract: Positive geometries are semialgebraic spaces that appear in the study of scattering amplitudes. Examples include polytopes\, totally nonnegative parts of flag varieties\, and conjecturally\, the amplituhedron. We will give a broad introduction to positive geometries\, and to their canonical forms. \n12:30 – 2:00 pm\nLunch Break \n2:00 – 2:50 pm\nAnastasia Volovich\, Brown University\nTitle: Scattering Amplitudes and Cluster Algebras\nAbstract: I will review some of the deep connections between cluster algebras and the (loop level) scattering amplitudes in N=4 super Yang-Mills theory\, focusing on the cases of n=6 and 7 particles where the corresponding Grassmannian cluster algebras Gr(4\,n) are finite and certain features of the amplitudes are known or believed to be true to all loop order. \n2:50 – 3:00 pm\nCoffee Break \n3:00 – 3:50 pm\nMarcus Spradlin\, Brown University\nTitle: Scattering Amplitudes\, Positive Geometry and the Amplituhedron\nAbstract: I will review the status of (loop level) scattering amplitudes in N=4 super Yang-Mills theory for n>7\, where the corresponding Grassmannian cluster algebras Gr(4\,n) are infinite and novel features emerge\, notably the appearance of certain “marginally positive” algebraic functions of cluster variables. \n3:50 – 4:00 pm\nCoffee Break \n4:00 – 4:30 pm\nCarolina Figueiredo\, Princeton University\nTitle: All-order splits and multi-soft limits for particle and string amplitude\nAbstract: The most important aspects of scattering amplitudes have long been thought to be associated with their poles. Recently a very different sort of “split” factorizations for a wide range of particle and string tree amplitudes have been discovered away from poles. In this talk\, I will explain how natural properties of the binary geometry of the curve integral formulation for scattering amplitudes for Tr$(\Phi^3)$ theory give a simple\, conceptual origin for these splits\, that generalizes them to all orders in the topological expansion. I will also explain how the splits allow us to access and compute loop-integrated multi-soft limits for particle and string amplitudes in Tr$(\Phi^3)$ theory\, the non-linear sigma model and Yang-Mills theory. \n4:30 – 5:15 pm\nYelena Mandelshtam\, UC Berkeley\nTitle: Combinatorics of m=1 Grasstopes\nAbstract: A Grasstope is a linear projection of the totally nonnegative Grassmannian to a smaller Grassmannian. This is a generalization of the amplituhedron\, a geometric object of great importance to calculating scattering amplitudes in physics. The amplituhedron is a Grasstope arising from a totally positive linear map. While amplituhedra are relatively well-studied\, much less is known about general Grasstopes. In this talk\, I will discuss combinatorics and geometry of Grasstopes in the m=1 case. In particular\, I will show that they can be characterized as unions of cells of a hyperplane arrangement satisfying a certain sign variation condition and argue that amplituhedra are (in a certain sense) minimal Grasstopes. This is based on joint work with Dmitrii Pavlov and Lizzie Pratt. \n5:30 – 6:30 pm\nWelcome Reception \n  \nThursday\, May 30\, 2024 \n8:30 – 9:00 am\nBreakfast \n9:00 – 10:00 am\nNima Arkani-Hamed\, IAS\nTitle: Surface Kinematics and THE all-loop integrand for gluon amplitudes \n10:00 – 10:30 am\nCoffee Break \n10:30 – 11:20 am\nHugh Thomas\, Université du Québec à Montréal\nTitle: u-equations from finite dimensional algebras\nAbstract: In this talk\, I will explain how to write down and solve a system of u-equations associated to any finite dimensional algebra with finitely many indecomposable representations. These vastly generalize the system of equations written down by Koba and Nielsen in 1969\, which from our point of view are associated to the representation theory of a Dynkin type A quiver. I will discuss features of the resulting solution spaces\, including connections to tau-tilting theory\, and the relationships that exist among different spaces of solutions. I will also say something about how different choices of finite-dimensional algebra put us in (i) the setting of cluster algebras\, (ii) the Grassmannian combinatorics of non-kissing complexes\, or (iii) the curves-on-surfaces model directly relevant to amplitudes. This talk reports on joint work with Nima Arkani-Hamed\, Hadleigh Frost\, Pierre-Guy Plamondon\, and Giulio Salvatori. \n11:20 – 11:30 am\nCoffee Break \n11:30 – 12:20 pm\nDani Kaufman\, University of Copenhagen\nTitle: Affine Cluster Algebras\nAbstract: Affine cluster algebras form the simplest examples of non-finite type cluster algebras. While they have infinitely many clusters\, they are still mutation finite and have essentially one mutation sequence which produces infinitely many clusters. I will give an introduction to these cluster algebras by comparing them with finite cluster algebras. I will also show how some structures similar to finite type cluster algebras appear “in the limit” along this infinite mutation sequence. If time I will also mention how the “infinite cluster variables” which live in the limit are related to the algebraic letters appearing in the symbol alphabet for 8 particle N=4 SYM amplitudes. \n12:30-12:45 pm\nGroup Photo\, 20 Garden Street\, front entrance stairs outside building \n12:45 – 2:00 pm\nLunch Break \n2:00 – 2:50 pm\nvia Zoom\nRan Tessler\, Weizmann Institute of Science\nTitle: The magic number for the m=2 amplituhedron\nAbstract: We will start by reviewing the amplituhedron and its tilings.\nWe will then show that all tilings of the m=2 amplituhedron have the same cardinality (“the magic number”)\, proving the m=2 case of a conjecture that the same holds for all even-m amplituhedra. If time permits we will discuss related results and consequences.\nBased on a joint work with Parisi\, Sherman-Bennett and Williams. \n2:50 – 3:00 pm\nCoffee Break \n3:00 – 3:50 pm\nMelissa Sherman-Bennett\, MIT & UC Davis\nTitle: Cluster algebras and tilings of amplituhedra\nAbstract: Physicists Arkani-Hamed and Trnka introduced the amplituhedron to better understand scattering amplitudes in N=4 super Yang-Mills theory. The amplituhedron is the image of the totally nonnegative Grassmannian under the “amplituhedron map”. Examples of amplituhedra include cyclic polytopes\, the totally nonnegative Grassmannian itself\, and cyclic hyperplane arrangements. Of primary interest to physics are tilings of amplituhedra\, which are roughly analogous to subdivisions of polytopes. I will discuss joint work with Even-Zohar\, Lakrec\, Parisi\, Tessler and Williams on BCFW tilings of m=4 amplituhedra and the surprising connection between these tilings and the cluster algebra structure of the Grassmannian. \n3:50 – 4:00 pm\nCoffee Break \n4:00 – 5:30 pm\nOpen Problems Forum \n6:00 – 8:00 pm\nConference Dinner (by invitation) \n  \nFriday\, May 31\, 2024 \n8:30 – 9:00 am\nBreakfast \n9:00 – 10:00 am\nYu-tin Huang\, National Taiwan University\nTitle: Chambers and all loop geometry for four-point correlators\nAbstract: The all loop amplituhedron for N=4 SYM (and ABJM theory) can be recast into the notion of loop fibration over tree geometry. This leads to a further dissection of the tree geometry into “chambers”\, whose boundaries represents when the associated loop-form changes. In this talk I will present a new geometry associated with the all loop four-point correlator of N=4 SYM\, where similar description is present. Interestingly\, at four-loops\, this gives a first example where the chamber form is rational even though it’s loop form contains elliptic integrals. \n10:00 – 10:15 am\nCoffee Break \n10:15 – 12:30 am\nEmerging Scholar Talks \n10:15 – 10:40 am\nEvgeniya Akhmedova\, Weizmann Institute of Science\nTitle: The tropical amplituhedron\nAbstract: The Amplituhedron is a geometric object discovered recently by Arkani-Hamed and Trnka\, that provides a completely new direction for calculating scattering amplitudes in quantum field theory. We define a tropical analogue of this object\, the tropicial amplituhedron and study its structure and boundaries. It can be considered as both the tropical limit of the amplituhedron and a generalization of the tropical positive Grassmannian. \n10:40 – 11:10 am\nLizzie Pratt\, UC Berkeley\nTitle: The Chow-Lam Form\nAbstract: The classical Chow form encodes any projective variety by one equation. We introduce the Chow-Lam form for subvarieties of a Grassmannian. By evaluating the Chow-Lam form at twistor coordinates\, we obtain universal projection formulas\, which were pioneered by Thomas Lam for positroid varieties in the study of amplituhedra. This is joint work with Bernd Sturmfels. \n11:10– 11:30 am\nSebastian Seemann\, KU Leuven\nTitle: Vandermonde cells as positive geometries\nAbstract: Vandermonde cells represent semialgebraic subsets of R^n\, characterized as the image of a simplex under the Vandermonde map. However\, within the realm of positive geometry\, several challenges arise in establishing canonical forms for these cells. These include issues such as non-normal boundaries\, non-transversal intersections\, and singularities of boundary curves. Even more difficulties appear when considing the limiting Vandermonde cell\, which is not semi-algebraic and thus doesn’t fit within the standard framework of positive geometries. In this presentation\, I will first review the notion of Polypols and their canonical forms\, examining the complexities encountered when dealing with Vandermonde cells. In particular\, I will explain what goes wrong in the case of Vandermonde cells and which obstructions we can deal with. \n11:30 – 11:40 am\nCoffee break \n11:40 – 12:10 pm\nChia-Kai Kuo\, National Taiwan University\nTitle: Geometric transition from maximal SYM to ABJM\nAbstract: Recently\, the ABJM amplituhedron has been proposed\, encoding all-loop and all-multiplicity ABJM amplitudes. It is constructed by slightly modifying the original definition. In this talk\, I will explore the significance of these modifications in transitioning theoretical models from super Yang-Mills theory to ABJM theory. A key focus will be on how symplectic reduction and the overall sign change in the positivity conditions ensure the consistency of ABJM amplitudes. Additionally\, I will discuss some distinct features of this geometry. \n12:10– 12:30 pm\nLecheng Ren\, Brown University\nTitle: Symbol alphabets from tensor diagrams\nAbstract: We propose to use tensor diagrams and the Fomin-Pylyavskyy conjectures to explore the connection between symbol alphabets of n-particle amplitudes in planar N= 4 Yang-Mills theory and certain polytopes associated to the Grassmannian Gr(4\, n). We show how to assign a web (a planar tensor diagram) to each facet of these polytopes. Webs with no inner loops are associated to cluster variables (rational symbol letters). For webs with a single inner loop we propose and explicitly evaluate an associated web series that contains information about algebraic symbol letters. In this manner we reproduce the results of previous analyses of n ≤ 8\, and find that the polytope C(4\,9) encodes all rational letters\, and all square roots of the algebraic letters\, of known nine-particle amplitudes. \n12:30 – 2:00 pm\nLunch Break \n2:00 – 2:50 pm\nvia Zoom\nPaolo Benincasa\,  MPI\nTitle: Cosmological Polytopes & Beyond\nAbstract: Together with being the source of the most profound questions in fundamental physics\, cosmology turns out to be an arena from where novel combinatorial structures emerge. In this talk\, I will give a gentle introduction to the cosmological polytopes\, describing the so-called Bunch-Davies wavefunction for a large class of scalar theories\, and how it can be used to define and characterize less conventional objects\, named optical polytopes and weighted cosmological polytopes\, which provide examples of non-convex and weighted geometries respectively. \n2:50 – 3:00 pm\nCoffee Break \n3:00 – 3:45 pm\nShruti Paranjape\, UC Davis\nTitle: Loops in a loop expansion\nAbstract: In a paper by Arkani-Hamed\, Henn and Trnka\, it was shown that the amplituhedron construction of N=4 SYM can be recast in terms of negative geometries with a certain hierarchy of loops (closed cycles) in the space of loop momentum twistors. Furthermore\, using differential equation methods\, it was possible to calculate and resum integrated expressions and obtain strong coupling results. In this talk\, we provide a more general framework for the loops of loops expansion and outline a powerful method for the determination of differential forms for higher-order geometries. In particular\, we will focus on the case of 1 closed cycle in loop space and select integrated results. \n3:45 – 4:30 pm\nNick Early\, Weizmann Institute of Science\nTitle: Minimal Kinematics on $\mathcal{M}_{0\,n}$\, and beyond\nAbstract: Minimal Kinematics (MK) identifies kinematic degenerations of the CHY scattering potential where the critical points are given by rational formulas. These rest on the Horn uniformization of Kapranov-Huh; they are specified combinatorially by 2-trees. On the other hand\, Planar Kinematics (PK) identifies the locus in $M_{0\,n}$ which is fixed by cyclic permutation.  Combining MK and PK realizes a maximally thin relative of the associahedron known as the PK polytope; it is a reflexive polytope\, and its polar dual\, the root polytope\, has volume a Catalan number. In this talk\, we start by exploring MK and PK on the moduli space $M_{0\,n}$.  We explain how this story generalizes to moduli spaces $X(k\,n)$ of points in projective space $\mathbb{P}^{k-1}$\, to CEGM amplitudes and beyond. \n4:30 – 5:00 pm\nCoffee and Farewell \n  \n \n  \nAbout the image: \n\nLeft: the 3-dimensional associahedron\, Fomin and Zelevinsky\n\nCenter: artistic depiction of the amplituhedron\, Gilmore\nRight: Schlegel diagram of a hypersimplex\, Ziegler
URL:https://cmsa.fas.harvard.edu/event/amplituhedra2024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Conference
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/amplituhedron_cluster-algebras_posgeometry.png
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