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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240415T090000
DTEND;TZID=America/New_York:20240524T170000
DTSTAMP:20260417T033213
CREATED:20230904T173915Z
LAST-MODIFIED:20240624T181936Z
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:20240508T150000
DTEND;TZID=America/New_York:20240508T160000
DTSTAMP:20260417T033213
CREATED:20240415T180235Z
LAST-MODIFIED:20240429T182143Z
UID:10003368-1715180400-1715184000@cmsa.fas.harvard.edu
SUMMARY:Mathematical Aspects of Scattering Amplitudes Lecture
DESCRIPTION:Mathematical Aspects of Scattering Amplitudes Lecture \nSpeaker: Ruth Britto\, Trinity \nTitle: Cuts and Symbols
URL:https://cmsa.fas.harvard.edu/event/scatteringamplitudes_5824/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Scattering Amplitudes Lectures
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240509T103000
DTEND;TZID=America/New_York:20240509T113000
DTSTAMP:20260417T033213
CREATED:20240416T133629Z
LAST-MODIFIED:20240507T152049Z
UID:10000890-1715250600-1715254200@cmsa.fas.harvard.edu
SUMMARY:Computing periods of hypersurfaces and elliptic surfaces via effective homology
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Eric Pichon-Pharabod\, Universite Paris-Saclay \nTitle: Computing periods of hypersurfaces and elliptic surfaces via effective homology \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/agst-5924/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Algebraic-Geometry-in-String-Theory-05.09.2024.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240510T100000
DTEND;TZID=America/New_York:20240510T113000
DTSTAMP:20260417T033213
CREATED:20240507T190917Z
LAST-MODIFIED:20240508T195139Z
UID:10001518-1715335200-1715340600@cmsa.fas.harvard.edu
SUMMARY:From quantum Hall to Hubbard physics in twisted bilayer graphene
DESCRIPTION:Quantum Matter in Mathematics and Physics Seminar \nSpeaker: Eslam Khalaf (Harvard) \nTitle: From quantum Hall to Hubbard physics in twisted bilayer graphene \n\nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/qm_51024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-05.10.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240510T120000
DTEND;TZID=America/New_York:20240510T130000
DTSTAMP:20260417T033213
CREATED:20240416T185907Z
LAST-MODIFIED:20240507T190133Z
UID:10000695-1715342400-1715346000@cmsa.fas.harvard.edu
SUMMARY:On the landscape of 4d N=2 SCFTs
DESCRIPTION:CMSA Member Seminar \nSpeaker: Robert Moscrop\, Harvard CMSA \nTitle: On the landscape of 4d N=2 SCFTs \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-51024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-05.10.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240513T110000
DTEND;TZID=America/New_York:20240513T120000
DTSTAMP:20260417T033213
CREATED:20240411T181646Z
LAST-MODIFIED:20240514T142424Z
UID:10003354-1715598000-1715601600@cmsa.fas.harvard.edu
SUMMARY:An analogue of non-interacting quantum field theory in Riemannian signature
DESCRIPTION:General Relativity Seminar \nSpeaker: Mikhail Molodyk\, Stanford \nTitle: An analogue of non-interacting quantum field theory in Riemannian signature \nAbstract: Recent advances using microlocal tools have led to constructions\, for wave operators on various classes of spacetimes\, of four distinguished Fredholm inverses which have the singular behavior required of retarded\, advanced\, Feynman\, and anti-Feynman propagators in QFT. Vasy and Wrochna have used these to define a QFT on asymptotically Minkowski spacetimes\, for which they construct Hadamard states described by asymptotic data at infinity. I will describe an analogue of this construction on Riemannian manifolds with two asymptotically conic ends\, defining quantum fields satisfying the Helmholtz equation and using scattering data to construct states satisfying a wavefront mapping-property version of the Hadamard condition. The absence of a spacetime interpretation lends itself to a sharper focus on the theory’s analytic structure\, from whose perspective the Feynman propagators are no less natural than the advanced/retarded ones. I will also highlight some differences between Feynman propagators defined as distinguished inverses and as time-ordered expectations. Based on joint work with András Vasy.
URL:https://cmsa.fas.harvard.edu/event/general-relativity-51324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-05.13.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240513T133000
DTEND;TZID=America/New_York:20240513T143000
DTSTAMP:20260417T033213
CREATED:20240509T150634Z
LAST-MODIFIED:20240509T162010Z
UID:10003386-1715607000-1715610600@cmsa.fas.harvard.edu
SUMMARY:Improving Mean-Field Theory for Quantum Magnets
DESCRIPTION:Quantum Matter in Mathematics and Physics Seminar \nSpeaker: Junyi Zhang\, Johns Hopkins University \nTitle: Improving Mean-Field Theory for Quantum Magnets \nAbstract: Frustrated magnets have garnered significant attention because of their potential to host exotic spin liquids\, while many real material candidates exhibit magnetic orders.  Due to their proximity to spin liquid phases\, the semiclassical descriptions of these magnetic orders often fall short in capturing their intricate quantum behaviors. In this talk\, I will introduce an improved mean-field method\, named density-matrix mean-field theory (DMMFT)\, for these quantum magnets. Using local reduced density matrix\, DMMFT can systematically incorporate the quantum fluctuations beyond conventional mean-field theories. Notably\, it not only quantitatively evaluates the renormalization of order parameters induced by quantum fluctuations but also has the capability to detect the topological order of quantum phases. DMMFT offers an efficient approach to explore phases displaying unconventional quantum orders\, particularly beneficial for investigating frustrated spin systems in high spatial dimensions. \nRef: https://arxiv.org/abs/2401.06236
URL:https://cmsa.fas.harvard.edu/event/qm_51324/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-05.13.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240513T163000
DTEND;TZID=America/New_York:20240513T173000
DTSTAMP:20260417T033213
CREATED:20240130T151206Z
LAST-MODIFIED:20240508T203329Z
UID:10000814-1715617800-1715621400@cmsa.fas.harvard.edu
SUMMARY:Errors and Correction in Cumulative Knowledge
DESCRIPTION:Colloquium \nSpeaker: Madhu Sudan\, Harvard University \nTitle: Errors and Correction in Cumulative Knowledge \nAbstract: 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. \nThe 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. \nBased on the papers: \nIs this correct? Let’s check!\nOmri Ben-Eliezer\, Dan Mikulincer\, Elchanan Mossel\, Madhu Sudan\narXiv:2211.12301 \nErrors are Robustly Tamed in Cumulative Knowledge Processes\nAnna Brandenberger\, Cassandra Marcussen\, Elchanan Mossel\, Madhu Sudan\narXiv:2309.05638
URL:https://cmsa.fas.harvard.edu/event/colloquium-4124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Colloquium
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Colloquium-05.13.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240514T123000
DTEND;TZID=America/New_York:20240514T133000
DTSTAMP:20260417T033213
CREATED:20240424T200426Z
LAST-MODIFIED:20240510T202406Z
UID:10003382-1715689800-1715693400@cmsa.fas.harvard.edu
SUMMARY:Quasilocal mass for general domains in space
DESCRIPTION:CMSA Member Seminar \nSpeaker: Jue Liu \nTitle: Quasilocal mass for general domains in space \nAbstract: Diffeomorphism-invariant quasilocal mass in classical general relativity has been studied for decades\, but it is still an open problem how to define quasi-local mass for general domains with multiple boundaries in space. Using the Hamiltonian formulation\, we will provide a new way to define the nonnegative quasi-local mass\, and give recent progress in overcoming the difficulties.
URL:https://cmsa.fas.harvard.edu/event/member-seminar-51424/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Member Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Member-Seminar-05.14.24.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240514T150000
DTEND;TZID=America/New_York:20240514T160000
DTSTAMP:20260417T033213
CREATED:20240415T180344Z
LAST-MODIFIED:20240510T144105Z
UID:10003369-1715698800-1715702400@cmsa.fas.harvard.edu
SUMMARY:Mathematical Aspects of Scattering Amplitudes Lecture
DESCRIPTION:Mathematical Aspects of Scattering Amplitudes Lecture \nSpeaker: James Drummond\, University of Southampton\n \nTitle: Multiple light-like Wilson loops in N=4 super Yang-Mills theory
URL:https://cmsa.fas.harvard.edu/event/scatteringamplitudes_51424/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Scattering Amplitudes Lectures
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240515T150000
DTEND;TZID=America/New_York:20240515T160000
DTSTAMP:20260417T033213
CREATED:20240415T182551Z
LAST-MODIFIED:20240517T135756Z
UID:10003371-1715785200-1715788800@cmsa.fas.harvard.edu
SUMMARY:Mathematical Aspects of Scattering Amplitudes Lecture
DESCRIPTION:Mathematical Aspects of Scattering Amplitudes Lecture \nSpeaker: Matteo Parisi\, Harvard CMSA \nTitle: The amplituhedron and cluster algebras
URL:https://cmsa.fas.harvard.edu/event/scatteringamplitudes_51524/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Scattering Amplitudes Lectures
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240516T103000
DTEND;TZID=America/New_York:20240516T113000
DTSTAMP:20260417T033213
CREATED:20240416T133753Z
LAST-MODIFIED:20240514T183407Z
UID:10003374-1715855400-1715859000@cmsa.fas.harvard.edu
SUMMARY:Mirror symmetry and log del Pezzo surfaces
DESCRIPTION:Algebraic Geometry in String Theory Seminar \nSpeaker: Franco Rota\, University of Glasgow \nTitle: Mirror symmetry and log del Pezzo surfaces \nAbstract: The homological mirror symmetry conjecture predicts a duality\, expressed in terms of categorical equivalences\, between the complex geometry of a variety X (the B side) and the symplectic geometry of its mirror object Y (the A side). Motivated by this\, we study a series of singular surfaces (called log del Pezzo). I will describe the category arising in the B side\, using the McKay correspondence and explicit birational geometry. I will discuss early results on the A side\, using the language of pseudolattices to focus on the special case of a smooth degree 2 del Pezzo surface. This is joint work with Giulia Gugiatti.
URL:https://cmsa.fas.harvard.edu/event/agist_51624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Algebraic Geometry in String Theory Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/Algebraic-Geometry-in-String-Theory-05.16.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240516T130000
DTEND;TZID=America/New_York:20240516T140000
DTSTAMP:20260417T033213
CREATED:20240416T181859Z
LAST-MODIFIED:20240510T175438Z
UID:10003377-1715864400-1715868000@cmsa.fas.harvard.edu
SUMMARY:Controlling chaotic advection in 2D active nematics
DESCRIPTION:Active Matter Seminar \nSpeaker: Kevin Mitchell\, University of California\, Merced \nTitle: Controlling chaotic advection in 2D active nematics \nAbstract: Recent years have seen a surge of interest in active materials\, in which energy injected at the microscale gives rise to mesoscale coherent motion. One prominent example is an active 2D “liquid crystal” composed of microtubules in the nematic phase. The activity is generated by molecular motors that consume ATP to generate local shearing between the microtubules. The resulting 2D fluid flow exhibits self-generated mesoscale chaotic dynamics with a characteristic folding and stretching pattern. We analyze this dynamics from the perspective of chaotic advection\, in which the fluid can be viewed as “stirred” by topological defects in the nematic order parameter. Typically\, these defects move in an irregular\, chaotic pattern. We explore conditions\, both theoretically and in experiments\, under which the topological defects can be coaxed to perform regular periodic motion\, thus bringing some degree of order to the chaos.
URL:https://cmsa.fas.harvard.edu/event/active-matter-51624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Active Matter Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Active-Matter-Seminar-05.16.2024.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240516T150000
DTEND;TZID=America/New_York:20240516T160000
DTSTAMP:20260417T033213
CREATED:20240510T170616Z
LAST-MODIFIED:20240510T175234Z
UID:10003387-1715871600-1715875200@cmsa.fas.harvard.edu
SUMMARY:Geometry of Generalized Lienard Equations\, Contact Geometry and Metriplectic Structure
DESCRIPTION:Speaker: Partha Guha\, Khalifa University\, Abu Dhabi \nTitle: Geometry of Generalized Lienard Equations\, Contact Geometry and Metriplectic Structure \nAbstract: We start with a self-contained brief review of the construction of non-standard Lagrangian and Hamiltonian structures using the Jacobi Last Multiplier for the (generalized) reduced Lienard equations satisfying Chiellini integrability condition\, we then explore its connection with the contact Hamiltonian mechanics. We also explore Lienard equations\, of reaction-diffusion class and conformal (or contact) Hamiltonian Structures. Finally\, we present the geometric formulation of the generalized Lienard equations in terms of metriplectic structure. \nJoint work with Jose Carinena and Anindya Ghose Choudhury
URL:https://cmsa.fas.harvard.edu/event/geometry_51624/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Special Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-Geometry-and-Physics-Seminar-05.16.2024.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240517T103000
DTEND;TZID=America/New_York:20240517T120000
DTSTAMP:20260417T033213
CREATED:20240411T151408Z
LAST-MODIFIED:20240425T140248Z
UID:10001514-1715941800-1715947200@cmsa.fas.harvard.edu
SUMMARY:Love and Naturalness
DESCRIPTION:Quantum Matter in Mathematics and Physics Seminar \nSpeaker: Mikhail Ivanov (MIT) \nTitle: Love and Naturalness \nAbstract: 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.
URL:https://cmsa.fas.harvard.edu/event/qm_51724/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-04.26.2024.docx-1.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240521T110000
DTEND;TZID=America/New_York:20240521T120000
DTSTAMP:20260417T033213
CREATED:20240415T182747Z
LAST-MODIFIED:20240520T144708Z
UID:10003372-1716289200-1716292800@cmsa.fas.harvard.edu
SUMMARY:Mathematical Aspects of Scattering Amplitudes Lecture
DESCRIPTION:Mathematical Aspects of Scattering Amplitudes Lecture \nSpeaker: Michael Borinsky\, ETH Zurich \nTitle: On the Euler characteristic of the commutative graph complex and the top-weight cohomology of the moduli space of curves
URL:https://cmsa.fas.harvard.edu/event/scatteringamplitudes_52124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Scattering Amplitudes Lectures
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240522T110000
DTEND;TZID=America/New_York:20240522T120000
DTSTAMP:20260417T033213
CREATED:20240415T182841Z
LAST-MODIFIED:20240510T202735Z
UID:10003373-1716375600-1716379200@cmsa.fas.harvard.edu
SUMMARY:Mathematical Aspects of Scattering Amplitudes Lecture
DESCRIPTION:Mathematical Aspects of Scattering Amplitudes Lecture \nSpeaker: Chaim Even-Zohar\, Technion \nTitle: Amplituhedron tiles and twistor polynomials
URL:https://cmsa.fas.harvard.edu/event/scatteringamplitudes_52224/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Scattering Amplitudes Lectures
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240529T090000
DTEND;TZID=America/New_York:20240531T170000
DTSTAMP:20260417T033213
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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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240604T140000
DTEND;TZID=America/New_York:20240604T150000
DTSTAMP:20260417T033213
CREATED:20240523T135748Z
LAST-MODIFIED:20240813T164205Z
UID:10003391-1717509600-1717513200@cmsa.fas.harvard.edu
SUMMARY:Corks for exotic diffeomorphisms
DESCRIPTION:Speaker: Slava Krushkal\, University of Virginia \nTitle: Corks for exotic diffeomorphisms \nAbstract: Exotic smooth structures on simply-connected 4-manifolds are known to be related by cork twists: cutting out and re-gluing certain smooth contractible submanifolds. Work in progress\, joint with A. Mukherjee\, M. Powell\, and T. Warren\, provides a localization result for exotic diffeomorphisms of 4-manifolds. I will also discuss applications to known examples of exotic diffeomorphisms. \n 
URL:https://cmsa.fas.harvard.edu/event/corks-for-exotic-diffeomorphisms/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Special Seminar
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END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240604T160000
DTEND;TZID=America/New_York:20240604T170000
DTSTAMP:20260417T033213
CREATED:20240523T135549Z
LAST-MODIFIED:20240813T164318Z
UID:10003390-1717516800-1717520400@cmsa.fas.harvard.edu
SUMMARY:Can embedding problems be used to distinguish S^4 from other (possible) homotopy 4-spheres?
DESCRIPTION:Speaker: Michael Freedman\, Harvard CMSA \nTitle: Can embedding problems be used to distinguish S^4 from other (possible) homotopy 4-spheres? \nAbstract: There are approaches in the literature (using Khovanov homology) to detecting a homotopy 4-sphere\, via the 4-ball genus of knots. I’d like to suggest moving from surfaces to 3-manifolds\, that is approaching the problem by considering the which closed 3-manifolds embed.  Embedding in the actual S^4 implies a curious condition on the possible Heegaard diagrams for the 3-manifold. I’ll explain this condition and speculate on how it might be exploited.
URL:https://cmsa.fas.harvard.edu/event/can-embedding-problems-be-used-to-distinguish-s4-from-other-possible-homotopy-4-spheres/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Special Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/LowDimTop.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240607T143000
DTEND;TZID=America/New_York:20240607T160000
DTSTAMP:20260417T033213
CREATED:20240529T212219Z
LAST-MODIFIED:20240603T150758Z
UID:10003392-1717770600-1717776000@cmsa.fas.harvard.edu
SUMMARY:Phases and Phase Transitions of Spin Chains with Non-invertible Symmetries
DESCRIPTION:Quantum Matter in Mathematics and Physics Seminar \nSpeaker: Arkya Chatterjee (MIT) \nTitle: Phases and Phase Transitions of Spin Chains with Non-invertible Symmetries \nAbstract: Non-invertible symmetries are often emergent at low-energies in gapless states of quantum matter. It is useful to construct lattice models that have these as exact symmetries in order to provide a UV-complete setting in which they are well-controlled. To that end\, we propose to study one-dimensional Hamiltonians defined on tensor product Hilbert spaces with finite on-site dimension — referred to as “spin chains” in short — with exact non-invertible symmetries. We focus on two concrete examples: a spin chain with (invertible) S_3 symmetry and one with (non-invertible) Rep(S_3) symmetry. These models are largely analytically tractable and demonstrate all spontaneous symmetry breaking (SSB) phases of these symmetries. With the aid of tensor network algorithms\, we systematically study the phase transitions between these SSB phases. Both models possess (intrinsically) non-invertible self-duality symmetries\, for which we provide sequential circuit implementations. On the self-dual manifold in parameter space\, we discover an incommensurate gapless phase with an anomalous U(1) symmetry which emanates from lattice translation. \n 
URL:https://cmsa.fas.harvard.edu/event/qmmp_6724/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-06.07.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240621T140000
DTEND;TZID=America/New_York:20240621T153000
DTSTAMP:20260417T033213
CREATED:20240620T133636Z
LAST-MODIFIED:20240620T133710Z
UID:10003393-1718978400-1718983800@cmsa.fas.harvard.edu
SUMMARY:Landscape of Tensor Network States Preparable from Measurement
DESCRIPTION:Quantum Matter in Mathematics and Physics Seminar \nSpeaker: Rahul Sahay (Harvard)\n\nTitle: Landscape of Tensor Network States Preparable from Measurement\n\nAbstract: Measurements and feedback have emerged as powerful resources for creating many-body quantum states. However\, a detailed understanding of what is possible is restricted to fixed-point representatives of phases of matter. In this talk\, we go beyond this\, characterizing more general patterns of many-body entanglement that can be deterministically created from measurement. In 1D\, a complete framework is developed for the case where a single round of measurements is the only entangling operation. Specifically\, we completely classify the space of 1D preparable quantum states (forming a strict subset of all matrix product states)\, and characterize their physical constraints. In doing so\, we find an intriguing physical trade-off between the richness of the preparable entanglement spectrum and correlation functions\, naturally implying a powerful no-go theorem for preparing certain quantum states. Moreover\, our classification enables one to search for and engineer preparable quantum states with a range of desired correlation lengths and entanglement properties. We conclude by charting out generalizations\, such as higher dimensional examples\, considering multiple rounds of measurements\, and implementing matrix product operators. At a high level\, our work offers a resource-theoretic perspective on preparable quantum entanglement and shows how to systematically create states of matter\, away from their fixed points\, in quantum devices. This is based on two recent works with Ruben Verresen [arXiv:2404.17087; arXiv:2404.16753].\n 
URL:https://cmsa.fas.harvard.edu/event/qm_62124/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-06.21.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240624T080000
DTEND;TZID=America/New_York:20240626T170000
DTSTAMP:20260417T033213
CREATED:20240415T161428Z
LAST-MODIFIED:20241212T160959Z
UID:10003355-1719216000-1719421200@cmsa.fas.harvard.edu
SUMMARY:Workshop on Fibration and Degeneration in Calabi-Yau Geometry
DESCRIPTION:Workshop on Fibration and Degeneration in Calabi-Yau Geometry \nDates: June 24-26\, 2024 \nLocation: Harvard CMSA\, 20 Garden Street\, Cambridge\, MA 02138 \nOrganizer: Chuck Doran\, Harvard CMSA \n\nCalabi-Yau manifolds occupy a central place in geometry. Their critical role as the cut-case between basic Fano building blocks and the zoo of General Type manifolds is key to the wide variety of important applications of Calabi-Yau geometry to theoretical physics. In turn\, ideas from theoretical physics\, such as Mirror Symmetry\, help shape investigations in Calabi-Yau geometry \nThis workshop focuses on a structural feature of Calabi-Yau geometry identified a decade ago by Doran\, Harder\, and Thompson. It is an organizing principle that conjecturally underlies any and all constructions of mirror pairs of Calabi-Yau manifolds. Put simply\, the DHT Mirror Symmetry slogan is: “Degeneration is mirror to fibration.” \n\n\nConfirmed Speakers: \n\nDavid Favero (University of Minnesota)\nAndrew Harder (Lehigh University)\nJesse Huang (University of Alberta)\nMohsen Karkheiran* (University of Alberta)\nMatt Kerr* (Washington University in St. Louis)\nThorsten Schimannek* (Utrecht University)\nMichael Schultz (Virginia Tech)\nAlan Thompson (Loughborough University)\nFenglong You (University of Nottingham & ETH Zurich)\n\n*= via Zoom \n  \nSchedule \nMonday\, June 24\, 2024 \n9:30 – 10:00 am: Breakfast \n10:00 – 11:00 am\nSpeaker: Alan Thompson\, Loughborough University\nTitle: Mirror symmetry for fibrations and degenerations of K3 surfaces\nAbstract: I will describe recent progress\, joint with Luca Giovenzana\, on the DHT problem for K3 surfaces. I will give an lattice-theoretic definition for when a Tyurin degeneration of K3 surfaces and an elliptically-fibred K3 surface\, with an appropriate splitting of the base\, form a mirror pair. I will then explain how this definition is compatible with lattice polarised mirror symmetry for K3 surfaces and with Fano-LG mirror symmetry for (quasi) del Pezzo surfaces. The upshot will be a concrete statement of the DHT conjecture for K3 surfaces. \n12:00 – 1:00: Lunch \n1:00 – 2:00 pm\nSpeaker: David Favero\, University of Minnesota\nTitle: Homotopy Path Algebras and Resolutions\nAbstract: A homotopy path algebra is like a directed version of the group ring on a fundamental group.  One can imagine a directed graph (quiver) embedded in a topological space and considering the path algebra up to homotopy.  Alternatively\, one can think of homotopy classes of directed paths in a stratified topological space.  I will introduce homotopy path algebras and describe their connections to mirror symmetry and resolutions of coherent sheaves on toric varieties. \n3:00 – 4:00 pm\nSpeaker: Andrew Harder\, Lehigh University\nTitle: Tropical Hodge theory for hypersurfaces and Clarke duality\nAbstract: Results of Itenberg\, Katzarkov\, Mikhalkin\, and Zharkov (IKMZ) show that if a projective variety admits a smooth tropicalization\, then there is a collection of sheaves on its tropicalization that can be used to compute its Hodge numbers. However\, smooth tropicalizations fail to exist even in the case of toric hypersurfaces. In work with Sukjoo Lee\, we show that for any toric hypersurface\, an analogue of IKMZ’s result holds. I’ll discuss this sheaf\, and how this allows us to prove that Clarke dual pairs of Landau-Ginzburg models satisfy a particular Hodge number duality. This is a vast generalization of work of Batyrev and Borisov from the 90s. \n4:00 – 4:30 pm: Coffee/Tea \n  \nTuesday\, June 25\, 2024 \n9:30 – 10:00 am: Breakfast \n10:00 – 11:00 am\nSpeaker: Matt Kerr\, Washington University in St. Louis\nTitle: Hypergeometric families and Beilinson’s conjectures\nAbstract: I will describe the construction of motivic cohomology classes on hypergeometric families of Calabi-Yau 3-folds using Hadamard convolutions. These are analogous to elements of the Mordell-Weil group for families of elliptic curves\, and produce solutions to certain inhomogeneous Picard-Fuchs equations. This is part of a joint project with Vasily Golyshev in which we numerically verify Beilinson’s conjectures in some new cases. \n12:00 – 1:00: Lunch \n1:00 – 2:00 pm\nSpeaker: Fenglong You\, University of Nottingham & ETH Zurich\nTitle: Theta functions in mirror symmetry\nAbstract: To obtain a mirror of a Calabi—Yau manifold using Gross—Siebert’s intrinsic mirror symmetry\, one considers a maximally unipotent monodromy degeneration of the Calabi—Yau and take proj of the degree zero part of a relative quantum cohomology ring associated with the degeneration. Theta functions form a canonical basis of the degree zero part of the relative quantum cohomology ring. Theta functions can also be defined in terms of punctured invariants of the broken line type. I will explain a variant of intrinsic mirror symmetry using orbifold invariants\, theta functions for general snc pairs and a relation with the DHT conjecture. \n3:00 – 4:00 pm\nSpeaker: Mohsen Karkheiran\, University of Alberta\nTitle: Emergence of Heterotic-Type II duality from DHT conjecture\nAbstract: The duality between Heterotic and Type IIA strings was conjectured in mid-90’s based on the properties of 4D N=2 field theories and solitonic strings in 6D. Here\, we show that this duality can also emerge from the DHT conjecture. We assume both IIA and IIB strings are compactified over toric Calabi-Yau threefolds which admit K3-fibrations with arbitrary polarizations. Then by applying the Hori-Vafa mirror symmetry to the “pieces” of these Calabi-Yau manifolds\, we will be able to derive the defining data for Heterotic strings. This approach works for any gauge group on the Heterotic side\, and we will show how it can be practically useful to derive the Heterotic dual for any toric Calabi-Yau threefolds in Type IIA or F-theory. \n4:00 – 4:30 pm: Coffee/Tea \n  \nWednesday\, June 26\, 2024 \n9:30 – 10:00 am: Breakfast \n10:00 – 11:00 am\nSpeaker: Thorsten Schimannek\, Utrecht University\nTitle: Enumerative geometry and modularity in two-modulus K3-fibered Calabi-Yau threefolds\nAbstract: Smooth M_m-polarized K3-fibered Calabi-Yau (CY) 3-folds have been classified in [DHNT] and [KT] in terms of the choice of a generalized functional invariant (GFI) and\, in the case m=1\, a generalized homological invariant (GHI). The resulting geometries generally exhibit a small number of complex structure moduli greater or equal to two. I will start my talk by discussing a concrete choice of these invariants that realizes (almost all of) the geometries with exactly two moduli and describe the structure of the corresponding moduli spaces. The corresponding variations of Hodge structure are entirely determined by the regular periods\, for which we obtain a generic expression in terms of m and three integers i\,j\,s. Using the form of this period and Batyrev-Borisov mirror symmetry I will then explicitly construct the corresponding mirror CY 3-folds with two Kaehler moduli and show consistency with the DHT conjecture. In the cases with s=0\, the mirror CY 3-folds are again K3-fibered but with a 2m-polarization. The generic form of the periods allows us to derive generic modular expressions for the A-model topological string free energies and we argue that those are a consequence of a Tyurin degeneration of the GFI with the central fiber being an M_m-polarized K3.\nThe talk is based on work in progress with Charles Doran and Boris Pioline. \n12:00 – 1:00: Lunch \n1:00 – 2:00 pm\nSpeaker: Michael Schultz\, Virginia Tech\nTitle: Mirror Symmetry from Irrationality Proofs and a Proposal for Local Invariants\nAbstract: While Apéry’s original proof of the irrationality of ζ(3) stunned the mathematics community in 1978\, subsequent generations of mathematicians (including a number of those at this workshop) have discovered geometric and modular structures underlying these irrationality proofs that are arguably even more striking. One such well known example are connections to modular pencils of elliptic curves and K3 surfaces and their Picard-Fuchs operators\, which exhibit maximally unipotent monodromy. These objects are respectively mirror dual to anticanonical divisors in certain del Pezzo surfaces and Fano threefolds\, and their Picard-Fuchs operators to the A-side connection on small quantum cohomology for these varieties. Although the Yukawa couplings calculated in classical mirror symmetry for elliptic curves and K3 surfaces are trivial\, I will show in this talk how a blend of the perspectives above allows one to define “virtual” Yukawa couplings for these families that are not trivial. It will be proposed that the utility of this perspective is in computing local invariants related to the mirror\, which recovers some known results in the literature and utilizes connections to work on the DHT conjecture and the twist construction of Doran & Malmendier. \n3:00 – 4:00 pm\nSpeaker: Jesse Huang\, University of Alberta\nTitle: An invitation to global toric mirror symmetry \n4:00 – 4:30 pm: Coffee/Tea \n  \n \n\n 
URL:https://cmsa.fas.harvard.edu/event/fibration/
LOCATION:20 Garden Street\, Cambridge\, MA 02138\, MA\, MA\, 02138\, United States
CATEGORIES:Workshop
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/calabi-yau-manifold-1.png
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240815T110000
DTEND;TZID=America/New_York:20240815T120000
DTSTAMP:20260417T033213
CREATED:20240801T143800Z
LAST-MODIFIED:20240808T164904Z
UID:10003404-1723719600-1723723200@cmsa.fas.harvard.edu
SUMMARY:Compactified Hyperboloidal Evolution in Numerical Relativity
DESCRIPTION:Speaker: Shalabh Gautam\, International Center for Theoretical Sciences\, Tata Institute of Fundamental Research \nTitle: Compactified Hyperboloidal Evolution in Numerical Relativity \nAbstract: In the field of numerical relativity\, a major challenge is to incorporate future null infinity into the computational domain using a well-posed formulation. Achieving this goal would not only allow us to accurately simulate any astrophysical system\, such as binary black holes\, and extract the resulting signal\, like gravitational waves\, at future null infinity\, but it would also facilitate the study of various fundamental phenomena. One proposed solution is to use hyperboloidal slices. In this presentation\, I will introduce an alternative approach to numerical relativity that leverages these slices in spherical symmetry. I will also discuss our ongoing efforts to establish a well-posed formulation of the Einstein Field Equations on these slices\, and propose numerical schemes to ensure stability and convergence for linear hyperbolic systems over long durations. Additionally\, I will present our method for constructing initial data corresponding to an asymptotically flat spacetime. A natural extension of our work will be to generalize these methods to the Einstein Field Equations with appropriate initial data in the full 3d.
URL:https://cmsa.fas.harvard.edu/event/compactified-hyperboloidal-evolution-in-numerical-relativity/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:General Relativity Seminar
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-GR-Seminar-08.15.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240826T090000
DTEND;TZID=America/New_York:20240828T170000
DTSTAMP:20260417T033213
CREATED:20240209T180835Z
LAST-MODIFIED:20241212T152847Z
UID:10001874-1724662800-1724864400@cmsa.fas.harvard.edu
SUMMARY:Advances in Probability Theory and Interacting Particle Systems
DESCRIPTION:Advances in Probability Theory and Interacting Particle Systems\n\nA conference in honor of S. R. Srinivasa Varadhan.\n\nAugust 26 – August 28\, 2024\n\nHarvard Geological Lecture Hall\n\n\nConference Website: www.math.harvard.edu/event/math-conference-honoring-srinivasa-varadhan\n\nSpeakers\n\n\nInes Armendariz\, Universidad de Buenos Aires\nYuri Bakhtin\, Courant Institute\nGérard Ben Arous\, Courant Institute\nSourav Chatterjee\, Stanford University\nAmir Dembo\, Stanford University\nPeter K. Friz\, TU-Berlin\nNina Holden\, Courant Institute\nJiaoyang Huang\, University of Pennsylvania\nElena Kosygina\, City University of New York\nClaudio Landim\, IMPA\nEyal Lubetzky\, Courant Institute\nChiranjib Mukherjee\, Uni Münster\nStefano Olla\, Université Paris Dauphine\nJeremy Quastel\, University of Toronto\nKavita Ramanan\, Brown University\nAlejandro Ramirez\, NYU Shanghai\nFraydoun Rezakhanlou\, Berkeley\nSunder Sethuraman\, University of Arizona\nScott Sheffield\, MIT\nOfer Zeitouni\, Weizmann Institute\n\nOrganizers: Paul Bourgade (New York University\, Courant Institute) and Horng-Tzer Yau (Harvard University).\n\n\nSponsored by Harvard University Department of Mathematics and the Center of Mathematical Studies and Applications (CMSA).\n\nHarvard 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.
URL:https://cmsa.fas.harvard.edu/event/advances-in-probability-theory-and-interacting-particle-systems/
LOCATION:Harvard Geological Lecture Hall\, 24 Oxford St\, Cambridge\, 02138\, United States
CATEGORIES:Conference,Event
ATTACH;FMTTYPE=application/pdf:https://cmsa.fas.harvard.edu/media/Varadhan-Poster.pdf
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240828T140000
DTEND;TZID=America/New_York:20240828T153000
DTSTAMP:20260417T033213
CREATED:20240822T161627Z
LAST-MODIFIED:20240826T155342Z
UID:10003416-1724853600-1724859000@cmsa.fas.harvard.edu
SUMMARY:Instanton in Lattice QCD from Higher Categories and Higher Anafunctors
DESCRIPTION:Speaker: Jing-Yuan Chen\, Tsinghua University \nTitle: Instanton in Lattice QCD from Higher Categories and Higher Anafunctors\n\n\nAbstract:  Putting continuum QFT (not just TQFT) on the lattice is important for both fundamental understandings and practical numerics. The traditional way of doing so\, based on simple intuitions\, however\, does not admit natural definitions for general topological operators of continuous-valued fields—one such example is the long standing problem in lattice QCD of lacking a natural definition for Yang-Mills instantons.\nIn this talk\, I will explain a more systematic way to relate continuum and lattice QFT\, based on higher categories and higher anafunctors\, so that the topological operators in the continuum can be naturally defined on the lattice. The idea\, though formulated formally\, is physically very intuitive—we want to effectively capture the different possibilities of how a lattice field may interpolate into the continuum\, so the higher categories that are employed to study higher homotopy theory should be naturally involved. Via this formalism\, we resolve the long-standing problem of defining instanton (as well as Chern-Simons term) in lattice Yang-Mills theory\, in terms of multiplicative bundle gerbes. Moreover\, when the fields become discrete\, our formalism can recover the Dijkgraaf-Witten and Turaev-Viro theory\, so we hope this formalism to be a good starting point towards (in the very long term) a comprehensive categorical understanding of QFT that encompass both continuous and discrete degrees of freedom\, applicable both to IR and to UV.
URL:https://cmsa.fas.harvard.edu/event/qm_82824/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Quantum Matter
ATTACH;FMTTYPE=image/png:https://cmsa.fas.harvard.edu/media/CMSA-QMMP-08.28.2024.png
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240903T090000
DTEND;TZID=America/New_York:20241101T170000
DTSTAMP:20260417T033213
CREATED:20240105T033600Z
LAST-MODIFIED:20250305T175957Z
UID:10001112-1725354000-1730480400@cmsa.fas.harvard.edu
SUMMARY:Mathematics and Machine Learning Program
DESCRIPTION:Mathematics and Machine Learning Program \nDates: September 3 – November 1\, 2024 \nLocation: Harvard CMSA\, 20 Garden Street\, Cambridge\, MA 0213 \nMachine learning and AI are increasingly important tools in all fields of research. Recent milestones in machine learning for mathematics include data-driven discovery of theorems in knot theory and representation theory\, the discovery and proof of new singular solutions of the Euler equations\, new counterexamples and lower bounds in graph theory\, and more. Rigorous numerical methods and interactive theorem proving are playing an important part in obtaining these results. Conversely\, much of the spectacular progress in AI has a surprising simplicity at its core. Surely there are remarkable mathematical structures behind this\, yet to be elucidated. \nThe program will begin and end with two week-long workshops\, and will feature focus weeks on number theory\, knot theory\, graph theory\, rigorous numerics in PDE\, and interactive theorem proving\, as well as a course on geometric aspects of deep learning.\n\n  \nSeptember 3–5\, 2024: Opening Workshop: AI for Mathematicians\, with Leon Bottou\, François Charton\, David McAllester\, Adam Wagner and Geordie Williamson.   A series of six lectures covering logic and theorem proving\, AI methods\, theory of machine learning\, two lectures on case studies in math-AI\, and a lecture and discussion on open problems and the ethics of AI in science.\nOpening Workshop Youtube Playlist \n\nSeptember 6–7\, 2024: Big Data Conference \n  \nSeptember 9–13\, 2024: Applying Machine Learning to Math\, with François Charton and Geordie Williamson\nPublic Lecture September 12\, 2024: Geordie Williamson\, University of Sydney: Can AI help with hard mathematics? (Youtube link)\nThe focus of this week will be on practical examples and techniques for the mathematics researcher keen to explore or deepen their use of AI techniques. We will have talks showcasing easily stated problems\, on which machine learning techniques can be employed profitably. These provide excellent toy examples for generating intuition. We will also have expert talks on some of the technical subtleties which arise. There are several instances where the accepted heuristics emerging from the study of large language models (LLM) and image recognition don’t appear to apply on mathematics problems\, and we will try to highlight these subtleties.\nApplying Machine Learning to Math Youtube Playlist \n  \nSeptember 16–20\, 2024: Number theory\, with Drew Sutherland\nThe focus of this week will be on the use of ML as a tool for finding and understanding statistical patterns in number-theoretic datasets\, using the recently discovered (and still largely unexplained) “murmurations” in the distribution of Frobenius traces in families of elliptic curves and other arithmetic L-functions as a motivating example.\nNumber Theory Youtube Playlist \n  \nSeptember 23–27\, 2024: Knot theory\, with Sergei Gukov\nKnot theory is a great source of labeled data that can be synthetically generated. Moreover\, many outstanding problems in knot theory and low-dimensional topology can be formulated as decision and classification tasks\, e.g. “Is the knot 123_45 slice?” or “Can two given Kirby diagrams be related by a sequence of Kirby moves?” During this focus week we will explore various ways in which AI can be applied to problems in knot theory and how\, based on these applications\, mathematical reasoning can advance development of AI algorithms. Another goal will be to develop formal knot theory libraries (e.g. contributions to mathlib) and to apply AI models to formal proof systems\, in particular in the context of knot theory.\nKnot Theory Youtube Playlist \n  \nSeptember 30: Teaching and Machine Learning Panel Discussion\, 3:30-5:30 pm ET \n  \nSeptember 30–October 4\, 2024: Graph theory and combinatorics\, with Adam Wagner\nThis week\, we will consider how machine learning can help us solve problems in combinatorics and graph theory\, broadly interpreted\, in practice. The advantage of these fields is that they deal with finite objects that are simple to set up using computers\, and programs that work for one problem can often be adapted to work for several other related problems as well. Many times\, the best constructions for a problem are easy to interpret\, making it simpler to judge how well a particular algorithm is performing. On the other hand\, there are lots of open conjectures that are simple to state\, for which the best-known constructions are counterintuitive\, making it perhaps more likely that machine learning methods can spot patterns that are difficult to understand otherwise.\nGraph Theory and Combinatorics Youtube Playlist \n  \nOctober 7–11\, 2024: More number theory\, with Drew Sutherland\nThe focus of this week will be on the use of AI as a tool to search for and/or construct interesting or extremal examples in number theory and arithmetic geometry\, using LLM-based genetic algorithms\, generative adversarial networks\, game-theoretic methods\, and heuristic tree pruning as alternatives to conventional local search strategies.\nMore Number Theory Youtube Playlist \n  \nOctober 14 –18\, 2024: Interactive theorem proving\nThis week we will discuss the use of interactive theorem proving systems such as Lean\, Coq and Isabelle in mathematical research\, and AI systems which prove theorems and translate between informal and formal mathematics.\nInteractive Theorem Proving Youtube Playlist \n  \nOctober 21–25\, 2024: Numerical Partial Differential Equations (PDE)\, with Tristan Buckmaster and Javier Gomez-Serrano\nThe focus of this week will be on constructing solutions to partial differential equations and dynamical systems (finite and infinite dimensional) more broadly defined. We will discuss several toy problems and comment on issues like sampling strategies\, optimization algorithms\, ill-posedness\, or convergence. We will also outline strategies about further developing machine-learning findings and turn them into mathematical theorems via computer-assisted approaches.\nNumerical PDEs Youtube Playlist \n  \nOctober 28–Nov. 1\, 2024: Closing Workshop: The closing workshop will provide a forum for discussing the most current research in these areas\, including work in progress and recent results from program participants.\nMath and Machine Learning Closing Workshop Youtube Playlist \n  \nSeptember 3–Nov. 1: Graduate topics in deep learning theory (Boston College) taught by Eli Grigsby\, held at the CMSA Tuesdays and Thursdays 2:30–3:45 pm Eastern Time. Course website (link).\nGraduate Topics in Deep Learning Youtube Playlist \nCourse description: This is a course on geometric aspects of deep learning theory. Broadly speaking\, we’ll investigate the question: How might human-interpretable concepts be expressed in the geometry of their data encodings\, and how does this geometry interact with the computational units and higher-level algebraic structures in various parameterized function classes\, especially neural network classes? During the portion of the course Sep. 3-Nov. 1\, the course will be presented as part of the Math and Machine Learning program at the CMSA in Cambridge. During that portion\, we will focus on the current state of research on mechanistic interpretability of transformers\, the architecture underlying large language models like Chat-GPT. \n\n\n\n\nPrerequisites: This course is targeted to graduate students and advanced undergraduates in mathematics and theoretical computer science. No prior background in machine learning or learning theory will be assumed\, but I will assume a degree of mathematical maturity (at the level of–say—the standard undergraduate math curriculum+ first-year graduate geometry/topology sequence)\n\n\n\n\n\nProgram Organizers \n\nFrancois Charton (Meta AI)\nMichael R. Douglas (Harvard CMSA)\nMichael Freedman (Harvard CMSA)\nFabian Ruehle (Northeastern)\nGeordie Williamson (Univ. of Sydney)\n\n\nProgram Schedule  \nMonday\n10:30–noon\nOpen Discussion\nRoom G10 \n12:00–1:30 pm\nGroup lunch\nCMSA Common Room \nTuesday\n2:30–3:45 pm\nTopics in deep learning theory\nRoom G10 \n4:00–5:00 pm\nOpen Discussion/Tea\nCMSA Common Room \nWednesday\n10:30 am–12:00 pm\nOpen Discussion\nRoom G10 \n2:00–3:00 pm\nNew Technologies in Mathematics Seminar\nRoom G10 \nThursday\n2:30–3:45 pm\nTopics in deep learning theory\nRoom G10 \nFriday\n10:30 am–12:00 pm\nOpen Discussion\nRoom G10 \n\nHarvard CMSA thanks Mistral AI for a generous donation of computing credit.
URL:https://cmsa.fas.harvard.edu/event/mml2024/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Event,Programs
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/Machine-Learning-Program-poster-1.jpg
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BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240903T100000
DTEND;TZID=America/New_York:20240905T160000
DTSTAMP:20260417T033213
CREATED:20240105T031946Z
LAST-MODIFIED:20240918T190637Z
UID:10001110-1725357600-1725552000@cmsa.fas.harvard.edu
SUMMARY:Mathematics and Machine Learning Program Opening Workshop
DESCRIPTION:Mathematics and Machine Learning Program Opening Workshop \nDates: September 3 – 5\, 2024 \nLocation: Room G10\, CMSA\, 20 Garden Street\, Cambridge MA & via Zoom Webinar \nAI for Mathematicians\, with Leon Bottou\, François Charton\, David McAllester\, Adam Wagner\, Boris Hanin\, and Geordie Williamson.  A series of 6 tutorial lectures introducing concepts of AI and of theorem proving\, with many case studies of AI applied to mathematics\, and including lectures and discussion sessions on open questions\, future prospects\, and ethical questions.\n  \nSpeakers \n\nLeon Bottou (Meta AI)\nFrançois Charton (Meta AI)\nMichael R. Douglas (Harvard CMSA)\nBoris Hanin (Princeton)\nDavid McAllester (TTIC)\nAdam Wagner (WPI)\nGeordie Williamson (University of Sydney)\n\nSchedule (link to downloadable pdf) \nVideos from the Opening Workshop (Youtube Link) \n\n\n\nTuesday Sep. 3\, 2024\n\n\n9:30–10:00 am\nMorning refreshments\n\n\n10:00–11:30 am\nMike Douglas: Overview of AI for mathematics\nSlides (pdf)\n\n\n11:30 am–12:00 pm\nDiscussion\n\n\n12:00–1:30 pm\nBreak\n\n\n1:30–2:30 pm\nDavid McAllester: Logic and formal methods\nSlides (pdf)\n\n\n2:30–3:00 pm\nCoffee break\n\n\n3:00–4:00 pm\nPanel Discussion: Automated mathematical discovery\n\n\n\n  \n\n\n\nWednesday Sep. 4\, 2024\n\n\n9:30–10:00 am\nMorning refreshments\n\n\n10:00–11:30 am\nBoris Hanin: Theory of Machine Learning\nSlides (pdf)\n\n\n11:30 am–12:00 pm\nDiscussion\n\n\n12:00–1:30 pm\nBreak\n\n\n1:30–2:30 pm\nAdam Wagner: Case studies I: Reinforcement learning and pattern finding\nSlides (pdf)\n\n\n2:30–3:00 pm\nCoffee break\n\n\n\n  \n\n\n\nThursday Sep. 5\, 2024\n\n\n9:30–10:00 am\nMorning refreshments\n\n\n10:00–11:30 am\nFrançois Charton (slides-pdf)\nand Geordie Williamson: Case studies II\n\n\n11:30 am–12:00 pm\nDiscussion\n\n\n12:00–1:30 pm\nBreak\n\n\n1:30–2:30 pm\nLeon Bottou: Open questions in AI\nSlides (pdf)\n\n\n2:30–3:00 pm\nCoffee break\n\n\n3:00–4:00 pm\nPanel Discussion: How might AI change mathematics?\n\n\n\n  \n  \n 
URL:https://cmsa.fas.harvard.edu/event/mmlworkshop_924/
LOCATION:CMSA Room G10\, CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Workshop
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/ML_Opening-workshop-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240905T160000
DTEND;TZID=America/New_York:20240905T170000
DTSTAMP:20260417T033213
CREATED:20240710T192944Z
LAST-MODIFIED:20241212T195515Z
UID:10003398-1725552000-1725555600@cmsa.fas.harvard.edu
SUMMARY:CMSA/Math Fall Gathering
DESCRIPTION:September 5\, 2024 \n4:00 pm \nCMSA Common Room\, 20 Garden Street\, Cambridge MA \nAll CMSA and Math affiliates are invited.
URL:https://cmsa.fas.harvard.edu/event/fallgathering2024/
LOCATION:CMSA 20 Garden Street Cambridge\, Massachusetts 02138 United States
CATEGORIES:Event
ATTACH;FMTTYPE=image/jpeg:https://cmsa.fas.harvard.edu/media/CMSA-2-600x338-1-1.jpg
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20240906T090000
DTEND;TZID=America/New_York:20240907T170000
DTSTAMP:20260417T033213
CREATED:20240325T141950Z
LAST-MODIFIED:20250415T154033Z
UID:10003287-1725613200-1725728400@cmsa.fas.harvard.edu
SUMMARY:Big Data Conference 2024
DESCRIPTION:  \n \nYoutube Playlist \nOn September 6-7\, 2024\, the CMSA hosted the tenth annual Conference on Big Data. The Big Data Conference features speakers from the Harvard community as well as scholars from across the globe\, with talks focusing on computer science\, statistics\, math and physics\, and economics. \nLocation: Harvard University CMSA\, 20 Garden Street\, Cambridge & via Zoom \n  \nSpeakers: \n\nTianxi Cai\, Harvard Chan School\nRaj Chetty\, Harvard\nBianca Dumitrascu\, Columbia\nBoris Hanin\, Princeton\nPeter Hull\, Brown\nJamie Morgenstern\, U Washington\nKavita Ramanan\, Brown\nNeil Thompson\, MIT\nMelanie Weber\, Harvard\nKun-Hsing Yu\, Harvard Medical School\n\nOrganizers: \n\nRediet Abebe\, Harvard Society of Fellows\nMorgane Austern\, Harvard University Statistics\nMichael R. Douglas\, Harvard CMSA\nYannai Gonczarowski\, Harvard University Economics and Computer Science\nSam Kou\, Harvard University Statistics\n\nSCHEDULE (downloadable pdf) \nFriday\, Sep. 6\, 2024 \n9:00 am: Breakfast \n9:30 am: Introductions \n9:45–10:45 am\nSpeaker: Peter Hull\, Brown University\nTitle: Measuring Discrimination in Multi-Phase Systems\, with an Application to Child Protection\nAbstract: Large racial disparities have been documented in many high-stakes settings—such as employment\, health care\, housing\, and criminal justice—raising concerns of discrimination by individual decision-makers. At the same time\, there is growing understanding that a focus on individual decisions can yield an incomplete view of discrimination; an extensive theoretical literature shows how discrimination can arise and compound across multiple decision-makers in interconnected systems. We develop new empirical tools for studying discrimination in such multi-phase systems and apply them to the setting of foster care placement by child protective services. Leveraging the quasi-random assignment of two sets of decision-makers—initial hotline call screeners and subsequent investigators—we study how unwarranted racial disparities arise and propagate through this system. Using a sample of over 200\,000 maltreatment allegations\, we find that calls involving Black children are 55% more likely to result in foster care placement than calls involving white children with the same potential for future maltreatment in the home. Call screeners account for up to 19% of this unwarranted disparity\, with the remainder due to investigators. Unwarranted disparity is concentrated in cases with potential for future maltreatment\, suggesting that white children may be harmed by “underplacement” in high-risk situations. \n10:45–11:00 am: Break \n11:00 am –12:00 pm\nSpeaker: Jamie Morgenstern\, U Washington\nTitle: What governs predictive disparity in modern machine learning applications?\nAbstract: The deployment of statistical models in impactful environments is far from new—simple correlations have been used to guide decisions throughout the sciences\, health care\, political campaigns\, and in pricing financial instruments and other products for decades. Many such models\, and the decisions they supported\, were known to have different degrees of predictive power for different demographic groups. These differences had numerous sources\, including: limited expressiveness of the statistical models; limited availability of data from marginalized populations; noisier measurements of both features and targets from certain populations; and features with less mutual information about the prediction target for some populations than others.\nModern decision systems which use machine learning are more ubiquitous than ever\, as are their differences in performance for different populations of people. In this talk\, I will discuss some similarities and differences in the sources of differing performance in contemporary ML systems including facial recognition systems and those incorporating generative AI. \n12:00–1:30 pm: Lunch Break \n1:30–2:30 pm\nSpeaker: Kavita Ramanan\, Brown University\nTitle: Understanding High-dimensional Stochastic Dynamics on Realistic Networks\nAbstract: Large collections of randomly evolving particles that interact locally with respect to an underlying network model a variety of phenomena ranging from magnetism\, the spread of diseases\, neural and neuronal networks\, opinion dynamics and load balancing on computer networks. Due to their high-dimensional nature\, these systems are typically intractable to analyze exactly. Classical work\, falling under the rubric of mean-field approximations\, has mostly focused on the case when this interaction graph is dense.  However\, most real-world networks are sparse and often random. We describe a new approach to develop principled approximations for dynamics on realistic networks that beats the curse of dimensionality\, and illustrate its efficacy on a class of epidemiological models. This is based on joint works with Michel Davydov\, Ankan Ganguly and Juniper Cocomello. \n2:30–2:45 pm: Break \n2:45–3:45 pm\nSpeaker: Raj Chetty\, Harvard University\nTitle: The Science of Economic Opportunity: New Insights from Big Data\nAbstract: How can we improve economic opportunities for children growing up in low-income families? This talk will present findings from a recent set of studies that use various sources of big data — ranging from anonymized tax records to social network data — to understand the science of economic opportunity. Among other topics\, the talk will discuss how and why children’s chances of climbing the income ladder vary across neighborhoods\, the drivers of racial disparities in economic mobility\, how highly selective colleges may amplify the persistence of privilege\, and the role of social capital as a driver of upward mobility. The talk will conclude by giving examples of how academic research using big data is informing policy decisions from the local to federal level to expand opportunities for all. \n3:45–4:00 pm: Break \n4:00–5:00 pm\nSpeaker: Neil Thompson\nTitle: How Algorithmic Progress is driving progress in Big Data and AI\nAbstract: Algorithm improvement is one of the purest forms of innovation: it allows the same computational task to be achieved with far fewer resources by proposing clever new ways to do that computation. In this talk\, I will discuss the work that my lab has done tracking and quantifying progress across decades of algorithm research and practice. As I will show\, this algorithmic progress has often outpaced hardware improvement as the most important driver of progress in Big Data and AI. \n  \nSaturday\, Sep. 7\, 2024 \n9:00 am: Breakfast \n9:30 am: Introductions \n9:45–10:45 am\nSpeaker: Tianxi Cai\, Harvard Chan School\nTitle: Crowdsourcing with Multi-institutional EHR to Improve Reliability of Real World Evidence – Opportunities and Challenges\nAbstract: The wide adoption of electronic health records (EHR) systems has led to the availability of large clinical datasets available for discovery research. EHR data\, linked with bio- repository\, is a valuable new source for deriving real-word\, data-driven prediction models of disease risk and progression. Yet\, they also bring analytical difficulties especially when aiming to leverage multi-institutional EHR data. Synthesizing information across healthcare systems is challenging due to heterogeneity and privacy. Statistical challenges also arise due to high dimensionality in the feature space. In this talk\, I’ll discuss analytical approaches for mining EHR data to improve the reliability and generalizability of real world evidence generated from the analyses. These methods will be illustrated using EHR data from Mass General Brigham and Veteran Health Administration. \n10:45–11:00 am: Break \n11:00 am–12:00 pm\nSpeaker: Bianca Dumitrascu\, Columbia Data Science Institute\nTitle: Statistical machine learning for learning representations of embryonic development\nAbstract: During embryonic development\, single cells read in local information from their environments and use this information to move\, divide and specialize. As a result\, the environments themselves change.  However\, it remains unclear how gene expression programs interact with cell morphology and mechanical forces to orchestrate organogenesis in early embryos. Recent advances in single cell techniques and in toto imaging enable unique venues in exploring this link between genomics and biophysics\, which dynamically maps cells to organisms.\nIn this talk\, I will describe statistical machine learning frameworks aimed at understanding how tissue level mechanical and morphometric information impact gene expression patterns in spatio-temporal contexts. We use these tools to understand boundary formation in the early development of mouse embryos and to align data from light sheet recordings of pre-gastrulation development. \n12:00–1:30 pm: Lunch Break \n1:30–2:30 pm\nSpeaker: Melanie Weber\, Harvard Mathematics\nTitle: Data and Model Geometry in Deep Learning\nAbstract: Data with geometric structure is ubiquitous in machine learning. Often such structure arises from fundamental symmetries in the domain\, such as permutation-invariance in graphs and sets\, and translation-invariance in images. In this talk we discuss implications of this structure on the design and complexity of neural networks. Equivariant architectures\, which encode symmetries as inductive bias\, have shown great success in applications with geometric data\, but can suffer from instabilities as their depths increases. We propose a new architecture based on unitary group convolutions\, which allows for deeper networks with less instability. In the second part of the talk we discuss the impact of data and model geometry on the learnability of neural networks. We discuss learnability in several geometric settings\, including equivariant neural networks\, as well as learnability with respect to the geometry of the input data manifold. \n2:30–2:45 pm: Break \n2:45–3:45 pm\nSpeaker: Boris Hanin\, Princeton University\nTitle: Scaling Limits of Neural Networks\nAbstract: Neural networks are often studied analytically through scaling limits: regimes in which taking some structural network parameters (e.g. depth\, width\, number of training datapoints\, and so on) to infinity results in simplified models of learning. I will motivative and discuss recent results using several such approaches. I will emphasize both new theoretical insights into how model\, training data\, and optimizer impact learning and their practical implications for hyperparameter transfer. \n3:45–4:00 pm: Break \n4:00–5:00 pm\nSpeaker: Kun-Hsing Yu\, Harvard Medical School\nTitle: Foundation Models for Real-Time Cancer Diagnosis\nAbstract: Artificial intelligence (AI) is transforming the landscape of medical research and practice. Recent advances in microscopic image digitization\, foundation models\, and scalable computing infrastructure have opened new avenues for AI-enhanced cancer diagnosis. In this talk\, I will highlight recent breakthroughs in multi-modal AI systems for cancer pathology evaluation\, discuss integrative biomedical informatics methods that link cell morphology with molecular profiles\, and outline critical challenges in developing robust medical AI systems. \n  \n\nInformation about the 2023 Big Data Conference can be found here.
URL:https://cmsa.fas.harvard.edu/event/bigdata_2024/
LOCATION:20 Garden Street\, Cambridge\, MA 02138\, MA\, MA\, 02138\, United States
CATEGORIES:Big Data Conference,Conference,Event
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