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DTSTART;TZID=America/New_York:20180924T175600
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UID:10002417-1537811760-1537811760@cmsa.fas.harvard.edu
SUMMARY:9/24/2018 Topological Aspects of Condensed Matter Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/9-24-2018-topological-aspects-of-condensed-matter-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180910T103000
DTEND;TZID=America/New_York:20180910T120000
DTSTAMP:20260517T155126
CREATED:20240213T103024Z
LAST-MODIFIED:20240213T103024Z
UID:10002433-1536575400-1536580800@cmsa.fas.harvard.edu
SUMMARY:9/10/18 Topology Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/9-10-18-topology-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180829T173600
DTEND;TZID=America/New_York:20180829T173600
DTSTAMP:20260517T155126
CREATED:20240213T102633Z
LAST-MODIFIED:20240213T102633Z
UID:10002424-1535564160-1535564160@cmsa.fas.harvard.edu
SUMMARY:Topological Aspects of Condensed Matter Seminar
DESCRIPTION:As part of the Program on Topological Aspects of Condensed Matter\, a weekly seminar will be held on Mondays from 10:00-11:30pm in CMSA room G10. \n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\n8/29/2018\nZeng-Cheng Gu\nTitle: Towards a complete classification of symmetry protected topological phases for interacting fermions in three dimensions and a general group supercohomology theory \nAbstract: Classification and construction of symmetry protected topological (SPT) phases in interacting boson and fermion systems have become a fascinating theoretical direction in recent years. It has been shown that the (generalized) group cohomology theory or cobordism theory can give rise to a complete classification of SPT phases in interacting boson/spin systems. Nevertheless\, the construction and classification of SPT phases in interacting fermion systems are much more complicated\, especially in 3D. In this talk\, I will revisit this problem based on the equivalent class of fermionic symmetric local unitary (FSLU) transformations. I will show how to construct very general fixed point SPT wavefunctions for interacting fermion systems. I will also discuss the procedure of deriving a general group super-cohomology theory in arbitrary dimensions.\n\n\n9/10/2018\nDominic Else\, MIT \nVideo\nTitle: Phases and topology in periodically driven (Floquet) systems \nAbstract: I will give a pedagogical overview of new topological phenomena that occur in systems that are driven periodically in time (Floquet systems). As a warm-up\, I will review new topological invariants in free-fermion Floquet systems. Then\, I will discuss the richer physics that occurs in interacting Floquet phases\, stabilized in systems with strong quenched disorder by many-body-localization (MBL). Finally\, time permitting\, I will explain how to realize interacting topological phenomena in a metastable (“pre-thermal”) regime of a clean system.\n\n\n9/17/2018\nAdrian Po\, MIT \nVideo\nTitle: A modern solution to the old problem of symmetries in band theory \nAbstract: There are 230 space groups and 1\,651 magnetic space groups in three dimensions. Thankfully\, these are finite numbers\, and one might go about solving all the possible ways free electrons represent them. This is a central question in the nine-decade-old band theory\, which is long-thought to be solvable if only one had the time and patience to crank through all the cases. In this talk\, I would describe how this problem can be solved efficiently from the modern perspective of band topology. As a by-product\, we will describe a simple method to detect topologically nontrivial band insulators using only symmetry eigenvalues\, which offers great computational advantage compared to the traditional\, wave-function-based definitions of topological band invariants.\n\n\n9/24/2018\nMaxim Metlitski\nTitle: Surface Topological Order and a new ‘t Hooft Anomaly of Interaction Enabled 3+1D Fermion SPTs \nAbstract: Symmetry protected topological (SPT) phases have attracted a lot of attention in recent years. A key property of SPTs is the presence of non-trivial surface states. While for 1+1D and 2+1D SPTs the boundary must be either symmetry broken or gapless\, some 3+1D SPTs admit symmetric gapped surface states that support anyon excitation (intrinsic topological order). In all cases\, the boundary of an SPT is anomalous – it cannot be recreated without the bulk; furthermore\, the anomaly must “match” the bulk. I will review this bulk-boundary correspondence for 3d SPT phases of bosons with topologically ordered boundaries where it is fairly well understood. I will then proceed to describe recent advances in the understanding of strongly interacting 3+1D SPT phases of fermions and their topologically ordered surface states.\n\n\n10/1/2018\nCancelled\n\n\n\n10/9/2018 \nTuesday \n3:00-4:30pm\nSagar Vijay\nTitle: Fracton Phases of Matter \nAbstract:  Fracton phases are new kinds of highly-entangled quantum matter in three spatial dimensions that are characterized by gapped\, point-like excitations (“fractons”) that are strictly immobile at zero temperature\, and by degenerate ground-states that are locally indistinguishable.  Fracton excitations provide an alternative to Fermi or Bose statistics in three spatial dimensions\, and these states of matter are a gateway for exploring mechanisms for quantum information storage\, and for studying “slow” dynamical behavior in the absence of disorder. I will review exactly solvable models for these phases\, constructions of these states using well-studied two-dimensional topological phases\, and a model in which the fracton excitations carry a protected internal degeneracy\, which provides a natural generalization of non-Abelian anyons to three spatial dimensions.  I will then describe recent advances in categorizing these states of matter using finite-depth unitary transformations.\n\n\n10/15/2018\nEthan Lake\nTitle: A primer on higher symmetries \nAbstract: The notion of a higher symmetry\, namely a symmetry whose charged objects have a dimension greater than zero\, is proving to be very useful for organizing our understanding of gauge theories and topological phases of matter. Just like regular symmetries\, higher symmetries can be gauged\, spontaneously broken\, and can have anomalies. I will review these aspects of higher symmetries and motivate why beyond their conceptual utility\, they are often an indispensable tool for making statements about dualities and phase diagrams of theories with gauge fields.\n\n\n10/22/2018 \nRoom G02\nYin-Chen He\, Perimeter\nTitle: Emergent QED3 and QCD3 in condensed matter system \nAbstract: QED3-Chern-Simons and QCD3-Chern-Simons theories are interesting critical theories in the 2+1 dimension. These theories are described by gapless Dirac fermions interacting with dynamical gauge fields (U(1)\, SU(N)\, U(N)\, etc.) with a possible Chern-Simon term. These theories have fundamental importance as it will flow to the 3D conformal field theories and have interesting dualities in the infrared. Various of condensed matter system are described by these critical theories. I will introduce several examples including the Dirac spin liquid in the frustrated magnets (kagome\, triangular lattice)\, quantum phase transitions in the fractional quantum Hall systems and Kitaev materials.\n\n\n10/29/2018\nDominic Williamson\, Yale \nVideo\nTitle: Symmetry and topological order in tensor networks \nAbstract: I will present an overview of how topological states of matter with global symmetries can be described using tensor networks. First reviewing the classification of 1D symmetry-protected topological phases with matrix product states\, before moving on to the description of 2D symmetry-enriched topological phases with projected-entangled pair states.\n\n\n11/13/2018 \nTuesday \n3:00-4:30pm\nJason Alicea\, Caltech\nTitle: Time-crystalline topological superconductors\n\n\n11/19/2018\nX. G. Wen\, MIT \nVideo\nTitle: A classification of 3+1D topological orders \nAbstract: I will discuss a classification of 3+1D topological orders in terms of fusion 2 category. The 3+1D topological orders can be divided into two classes: the ones without emergent fermions and the ones with emergent fermions. The 3+1D topological orders with emergent fermions can be further divided into two classes: the ones without emergent Majorana zero mode and the ones with emergent Majorana zero mode. I will present pictures to understand those 3+1D topological orders.\n\n\n12/3/2018 \n*Room G02*\nClaudio Chamon\, Boston University\nTitle: Many-body scar states with topological properties in 1D\, 2D\, and 3D. \nAbstract: We construct (some) exact excited states of a class of non-integrable quantum many-body Hamiltonians in 1D\, 2D and 3D. These high energy many-body “scar” states have area law entanglement entropy\, and display properties usually associated to gapped ground states of symmetry protected topological phases or topologically ordered phases of matter\, including topological degeneracies.\n\n\n12/10/2018 \nRoom G02\nAnders Sandvik\, Boston University and Institute of Physics\, CAS\, Beijing\nTitle: Quantum Monte Carlo simulations of exotic states in 2D quantum magnets \nAbstract: Some exotic ground states of 2D quantum magnets can be accessed through sign-free quantum Monte Carlo simulations of certain “designer Hamiltonians”. I will discuss recent examples within the J-Q family of models\, where the standard Heisenberg exchange J on the square lattice is supplemented by multi-spin terms Q projecting correlated singlets\, such that dimer (columnar valence-bond) order is favored. In addition to a possible deconfined quantum critical point separating the Neel and dimer phases\, I will discuss recent work on a modified model where a rather strongly first-order transition between the Neel state and a plaquette-singlet-solid is associated with emergent O(4) symmetry up to length scales of at least 100 lattice spacings. This type of transition may be realized in SrCu2(BO3)2 under pressure. I will also discuss a random-singlet state obtained when randomness is introduced in a system with dimerized ground state. This type of state may be realized in some frustrated disordered quantum magnets.\n\n\n1/8/2019\nLukasz Fidkowski\, Univ. of Washington \nVideo\nTitle: Non-trivial quantum cellular automata in 3 dimensions \nAbstract: Motivated by studying the entanglement structure of certain symmetry protected topological phases\, we construct a non-trivial quantum cellular automaton in a Hilbert space for a 3d lattice of spin 1/2 degrees of freedom.  This is an operator which takes local operators to nearby local operators\, but is not locally generated. We discuss implications for the classification of SPT phases in equilibrium and Floquet settings.\n\n\n3/18/2019\nAri Turner\, Technion \nVideo\nTitle:  Trapping Excitations at Phantasmagoric Wave Vectors \nAbstract:  This talk will explain some properties of the fracton state devised by Jeongwan Haah. A fracton state has excitations that are extremely localized–it is impossible for them to move (unlike Anderson localization\, e.g.–Anderson localized excitations can move if there is an external field to provide energy). One can understand why in a simple way using “mod 2” Fourier analysis. I will explain this\, and also introduce “finite fields”\, which are the number systems one needs to define exponentials mod. 2.\n\n\n4/1/2019\nYi-Zhuang You (UCSD)\nTitle: Emergent Symmetry and Conserved Currents at Deconfined Quantum Critical Points \nAbstract: Noether’s theorem is one of the fundamental laws of physics\, relating continuous symmetries and conserved currents. Here we explore the role of Noether’s  theorem at the deconfined quantum critical point (DQCP)\, which is an exotic quantum phase transition beyond the Landau-Ginzburg-Wilson paradigm. It was expected that a larger continuous symmetry could emerge at the DQCP\, which\, if true\, should lead to conserved current at low energy. By identifying the emergent current fluctuation in the spin excitation spectrum\, we can quantitatively study the current-current correlation in large-scale quantum Monte Carlo simulations. Our results reveal the conservation of the emergent current\, as signified by the vanishing anomalous dimension of the current operator\, and hence provide supporting evidence for the emergent symmetry at the DQCP. We also extend our discussion of emergent conserved current to the recently proposed one-dimensional analog of DQCP and confirm the emergent O(2)xO(2) symmetry in that case. Finally\, I will briefly discuss the significance of our findings in a potential realization of DQCP in the Shastry-Sutherland lattice material SrCu2(BO3)2.\n\n\n4/8/2019\nAdam Nahum (Oxford)\nTitle: Emergent statistical mechanics of entanglement in random unitary circuits \nAbstract: I will talk about quantum-classical mappings for real-time observables in some simple many-body systems (random unitary circuits). Specifically I will discuss how (1) entanglement entropy growth and (2) two-point correlation functions in these systems can be related to partition functions for interacting random walks. If time permits I will mention a phase transition in the entanglement structure of a repeatedly measured quantum state.\n\n\n4/16/2019 \nLyman 425 \n1:30pm\nXie Chen (Calthech)\nTitle: Foliated Fracton Order \nAbstract: The quantum information study of quantum codes and quantum memory has led to the discovery of a new class of exactly solvable lattice models called the fracton models. The fracton models are similar to the better understood topological models in that they also support fractional excitations and have stable ground state degeneracy. But it is also clear that the fracton models exist beyond the realm of conventional topological order due to their extensive ground state degeneracy and the restricted motion of their fractional excitations. In this talk\, I will present a new framework\, which we call the “foliated fracton order”\, to capture the nontrivial nature of the order in a large class of fracton models. Such a framework not only clarifies the connection between various different models\, but also points to the direction of search for interesting new features.\n\n\n4/24/2019 \n10:30am\nMichael Freedman (Microsoft Station Q) \nVideo\nTitle: Quantum cellular automata in higher dimensions \nAbstract: I’ll discuss Joint work with Matt Hastings on local endomorphisms of the operator algebra. We found these have a cohomological invariant similar to that of an incompressible flow.\n\n\n4/26/2019 \n10:30am\nMaissam Barkeshli (University of Maryland) \nVideo\nTitle: Relative anomalies in (2+1)D symmetry enriched topological states \nAbstract: It has recently been understood that some patterns of symmetry fractionalization in topologically ordered phases of matter are anomalous\, in the sense that they can only occur at the surface of a higher dimensional symmetry-protected topological (SPT) state. In this talk I will explain some recent advances in our understanding of how to compute relative anomalies between different symmetry fractionalization classes in (2+1)D topological states. The theory applies to general types of symmetries\, including symmetries that permute anyon types and space-time reflection symmetries. This allows us to compute anomalies for more general types of space-time reflection symmetries than previously known methods.\n\n\n5/3/2019\nYuan-Ming Lu (Ohio State)\nTitle: Spontaneous symmetry breaking from anyon condensation \nAbstract: In the context of quantum spin liquids\, it is long known that the condensation of fractionalized excitations can inevitably break certain physical symmetries. For example\, condensing spinons will usually break spin rotation and time reversal symmetries. We generalize these phenomena to the context of a generic continuous quantum phase transition between symmetry enriched topological orders\, driven by anyon condensation. We provide two rules to determine whether a symmetry is enforced to break across an anyon condensation transition or not. Using a dimensional reduction scheme\, we establish a mapping between these symmetry-breaking anyon-condensation transitions in two spatial dimensions\, and deconfined quantum criticality in one spatial dimension.\n\n\n5/9/2019 \n10:30am\nMichael Zaletel (UC Berkeley)\nTitle: Three-partite entanglement in CFTs and chiral topological orders \nAbstract: While the entanglement entropy provides an essentially complete description of two-partite entanglement\, multi-partite entanglement is far richer\, with a concomitant zoo of possible measures. This talk will focus on applications of one such measure\, the “entanglement of purification\,” in many-body systems. I will first present a holographic prescription for calculating it which we can compare with numerical calculations. Interestingly\, we find that a 1+1D CFT on a ring contains a universal number of GHZ states for any tri-partition of the ring. Using this result I’ll conjecture a bulk entanglement diagnostic for 2+1D chiral orders\, and solicit the audience’s help in proving or disproving it.\n\n\n5/28/2019 \n10:30am\nMasaki Oshikawa (U Tokyo)\nTitle: Gauge invariance\, polarization\, and conductivity \n  \nAbstract: The large gauge transformation on a quantum many-body system under a periodic boundary condition has had numerous applications including generalizations of Lieb-Schultz-Mattis theorem. It is also deeply related to the electric polarization in insulators. I will discuss an application to a scaling of the fluctuation of the polarization in conductors\, and also to general constraints on the electric conductivity.\n\n\n7/18/2019\nEslam Khalaf (Harvard)\n\n\nTitle: Dynamical correlations in anomalous disordered wires \n\nAbstract: In a (multichannel) disordered wire\, classical diffusion at short times (large frequencies) gives way to Anderson localization at long times (small frequencies). I study what happens in a disordered wire with topologically protected channels\, e.g. a wire with unequal number of left and right movers which is realizable at the edge of a Quantum Hall system. In this case\, the classical dynamics are described by diffusion + drift\, but it is unclear what the effect of quantum corrections in the long time (small frequency) limit is.\n\nThe problem is described by a 0+1-dimensional supersymmetric (graded) non-linear sigma model with a topological WZW term and a scalar potential. The computation of the local dynamical correlations of this model is equivalent to finding the ground state (zero mode) of the Laplace-Beltrami operator on a symmetric superspace with specific scalar and vector potentials. Surprisingly\, I find that this zero mode has a relatively simple explicit integral representation in the Wigner-Dyson symmetry classes which has no counterpart in the absence of supersymmetry. This leads to an exact mapping between the local correlation functions in this 0+1D theory and observables in a 0+0D chiral random matrix problem.\n\nThe mapping is used to explicitly compute two simple dynamical observables: the diffusion probability of return and the correlation of local density of states. In the former\, we find that the interference effects change the exponential decay expected from drift-diffusion to a power law decay. In the latter\, we find that the local density of states exhibits statistical level attraction in contrast to the level repulsion expected in a a standard Anderson insulator. At the end\, I discuss possible relationship to the recently developed framework of non-Hermitian topological systems.
URL:https://cmsa.fas.harvard.edu/event/topological-aspects-of-condensed-matter-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180420T171800
DTEND;TZID=America/New_York:20180420T171800
DTSTAMP:20260517T155126
CREATED:20240213T101921Z
LAST-MODIFIED:20240213T101921Z
UID:10002412-1524244680-1524244680@cmsa.fas.harvard.edu
SUMMARY:4-20-2018 Social Science Applications Forum
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/4-20-2018-social-science-applications-forum/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180417T120000
DTEND;TZID=America/New_York:20180417T133000
DTSTAMP:20260517T155126
CREATED:20240213T100552Z
LAST-MODIFIED:20240213T100938Z
UID:10002389-1523966400-1523971800@cmsa.fas.harvard.edu
SUMMARY:4-17-2018 Special Algebraic Geometry Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/4-17-2018-special-algebraic-geometry-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180416T171600
DTEND;TZID=America/New_York:20180416T171600
DTSTAMP:20260517T155126
CREATED:20240213T101737Z
LAST-MODIFIED:20240213T101737Z
UID:10002409-1523898960-1523898960@cmsa.fas.harvard.edu
SUMMARY:4-16-2018 Social Science Applications Forum
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/4-16-2018-social-science-applications-forum/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180413T110000
DTEND;TZID=America/New_York:20180413T120000
DTSTAMP:20260517T155126
CREATED:20240213T101255Z
LAST-MODIFIED:20240213T101255Z
UID:10002403-1523617200-1523620800@cmsa.fas.harvard.edu
SUMMARY:4-13-2018 Mirror Symmetry Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/4-13-2018-mirror-symmetry-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180315T150000
DTEND;TZID=America/New_York:20180315T160000
DTSTAMP:20260517T155126
CREATED:20240213T100139Z
LAST-MODIFIED:20240213T100209Z
UID:10002381-1521126000-1521129600@cmsa.fas.harvard.edu
SUMMARY:Dmytro Shklyrov HMS Focused Lecture Series
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/dmytro-shklyrov-hms-focused-lecture-series/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180302T110000
DTEND;TZID=America/New_York:20180302T120000
DTSTAMP:20260517T155126
CREATED:20240213T095700Z
LAST-MODIFIED:20240213T095700Z
UID:10002372-1519988400-1519992000@cmsa.fas.harvard.edu
SUMMARY:3-2-2018 Mirror Symmetry Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/3-2-2018-mirror-symmetry-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180227T150000
DTEND;TZID=America/New_York:20180227T160000
DTSTAMP:20260517T155126
CREATED:20240213T100343Z
LAST-MODIFIED:20240213T100343Z
UID:10002386-1519743600-1519747200@cmsa.fas.harvard.edu
SUMMARY:2-27-2018 HMS Lecture
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/2-27-2018-hms-lecture/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180223T100000
DTEND;TZID=America/New_York:20180223T110000
DTSTAMP:20260517T155126
CREATED:20240213T100016Z
LAST-MODIFIED:20240213T100016Z
UID:10002377-1519380000-1519383600@cmsa.fas.harvard.edu
SUMMARY:2-23-2018 Mirror Symmetry Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/2-23-2018-mirror-symmetry-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180216T110000
DTEND;TZID=America/New_York:20180216T110000
DTSTAMP:20260517T155126
CREATED:20240213T101018Z
LAST-MODIFIED:20240213T101018Z
UID:10002397-1518778800-1518778800@cmsa.fas.harvard.edu
SUMMARY:2-16-2018 Mirror Symmetry Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/2-16-2018-mirror-symmetry-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180209T110000
DTEND;TZID=America/New_York:20180209T110000
DTSTAMP:20260517T155126
CREATED:20240213T102158Z
LAST-MODIFIED:20240213T102158Z
UID:10002416-1518174000-1518174000@cmsa.fas.harvard.edu
SUMMARY:02-09-2018 Mirror Symmetry Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/02-09-2018-mirror-symmetry-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180202T144400
DTEND;TZID=America/New_York:20180202T144400
DTSTAMP:20260517T155126
CREATED:20240213T102555Z
LAST-MODIFIED:20240213T102555Z
UID:10002423-1517582640-1517582640@cmsa.fas.harvard.edu
SUMMARY:2-2-2018 Mirror Symmetry Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/2-2-2018-mirror-symmetry-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180126T143700
DTEND;TZID=America/New_York:20180126T143700
DTSTAMP:20260517T155126
CREATED:20240213T102934Z
LAST-MODIFIED:20240213T102934Z
UID:10002431-1516977420-1516977420@cmsa.fas.harvard.edu
SUMMARY:01-26-2018 Mirror Symmetry Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/01-26-2018-mirror-symmetry-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180125T142100
DTEND;TZID=America/New_York:20180125T142100
DTSTAMP:20260517T155126
CREATED:20240213T103415Z
LAST-MODIFIED:20240213T103415Z
UID:10002441-1516890060-1516890060@cmsa.fas.harvard.edu
SUMMARY:Quantum Cohomology\, Nakajima Varieties and Quantum groups
DESCRIPTION:During the Spring 2018 Semester Artan Sheshmani (QGM/CMSA) will be teaching a CMSA special lecture series on Quantum Cohomology\, Nakajima Vareties and Quantum groups. The lectures will be held Tuesdays and Thursdays beginning January 25th\, from 1:00 to 3:00pm in room G10\, CMSA Building. \nYou can watch Prof. Sheshmani describe the series here. \nThe Syllabus is as follows: \n\n\n\nDate………..\nTopic\nVideo/Audio\n\n\n1-25-2018\nGromov-Witten invariants  \nDefinition\, examples via algebraic geometry I\nVideo / Audio / Combined  \n\n*due to technical difficulties the audio and video are split for this lecture.\n\n\n 2-01-2018\nGromov-Witten invariants  \nVirtual Fundamental Class I (definition)\nVideo / Audio / Combined  \n\n*due to technical difficulties the audio and video are split for this lecture\n\n\n2-13-2018\nGromov-Witten invariants  \nVirtual Fundamental Class II (computation in some cases)\n\n\n\n 2-15-2018\nComputing GW invariants  \nThree level GW classes \nGenus zero invariants of the projective plane\n\n\n\n 2-20-2018\nQuantum Cohomology  \nSmall Quantum Cohomology (Definition and Properties) I\n\n\n\n2-22-2018\nQuantum Cohomology  \nSmall Quantum Cohomology (Definition and Properties) II\n\n\n\n2-27-2018\nQuantum Cohomology  \nBig Quantum Cohomology I\n\n\n\n 3-1-2018\nQuantum Cohomology  \nBig Quantum Cohomology II \nGW potential \nWDVV equation\n\n\n\n3-6-2018\nGW invariants via Quantum Cohomology  \nThe Quintic threefold case \nThe P^2 case\n\n\n\n\nGW invariants via Quantum Cohomology  \nDubrovin (quantum) connection\n\n\n\n\nNakajima varieties  \n-Algebraic and symplectic reduction\n\n\n\n\nNakajima varieties  \nQuasi maps to Nakajima varieties\n\n\n\n\nQuantum cohomology of Nakajima varieties  \nSmall Quantum Cohomology of Hilb^n (C2) I\n\n\n\n\nQuantum cohomology of Nakajima varieties  \nSmall Quantum Cohomology of Hilb^n (C2) II\n\n\n\n\nQuantum cohomology of Nakajima varieties  \nSmall Quantum Cohomology of Hilb^n (C2) III\n\n\n\n\nQuantum cohomology of Nakajima varieties  \nBig Quantum Cohomology of Hilb^n (C2) I\n \n\n\n\nQuantum cohomology of Nakajima varieties  \nBig Quantum Cohomology of Hilb^n (C2) II\n\n\n\n\nQuantum cohomology of Nakajima varieties  \nBig Quantum Cohomology of Hilb^n (C2) III\n\n\n\n\nQuantum cohomology of Nakajima varieties  \nBig Quantum Cohomology of Hilb^n (C2) IV\n 
URL:https://cmsa.fas.harvard.edu/event/quantum-cohomology-nakajima-varieties-and-quantum-groups/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20180123T170000
DTEND;TZID=America/New_York:20180123T170000
DTSTAMP:20260517T155126
CREATED:20240213T103131Z
LAST-MODIFIED:20240213T103131Z
UID:10002436-1516726800-1516726800@cmsa.fas.harvard.edu
SUMMARY:2018 HMS Focused Lecture Series
DESCRIPTION:As part of their CMSA visitation\, HMS focused visitors will be giving lectures on various topics related to Homological Mirror Symmetry throughout the Spring 2018 Semester. The lectures will take place  on Tuesdays and Thursdays in the CMSA Building\, 20 Garden Street\, Room G10. \nThe schedule will be updated below. \n\n\n\nDate\nSpeaker\nTitle/Abstract\n\n\nJanuary 23\, 25\, 30 and February 1  \n3-5pm \n*Room G10*\nIvan Losev  \n(Northeastern)\nTitle: BGG category O: towards symplectic duality  \nAbstract: We will discuss a very classical topic in the representation theory of semisimple Lie algebras: the Bernstein-Gelfand-Gelfand (BGG) category O. Our aim will be to motivate and state a celebrated result of Beilinson\, Ginzburg and Soergel on the Koszul duality for such categories\, explaining how to compute characters of simple modules (the Kazhdan-Lusztig theory) along the way. The Koszul duality admits a conjectural generalization (Symplectic duality) that is a Mathematical manifestation of 3D Mirror symmetry. We will discuss that time permitting. \nApproximate (optimistic) plan of the lectures: \n1) Preliminaries and BGG category O. \n2) Kazhdan-Lusztig bases. Beilinson-Bernstein localization theorem. \n3) Localization theorem continued. Soergel modules. \n4) Koszul algebras and Koszul duality for categories O. \nTime permitting: other instances of Symplectic duality. \nPrerequisites: \nSemi-simple Lie algebras and their finite dimensional representation theory. \nSome  Algebraic geometry. No prior knowledge of category O/ Geometric \nRepresentation theory is assumed. \nScanned from a Xerox Multifunction Device\n\n\nFebruary 27\,  \nand March 1 \n3-5pm\nColin Diemer  \n(IHES)\nTitle: Moduli spaces of Landau-Ginzburg models and (mostly Fano) HMS.  \nAbstract: Mirror symmetry as a general phenomenon is understood to take place near the large complex structure limit resp. large radius limit\, and so implicitly involves degenerations of the spaces under consideration. Underlying most mirror theorems is thus a mirror map which gives a local identification of respective A-model and B-model moduli spaces. When dealing with mirror symmetry for Calabi-Yau’s the role of the mirror map is well-appreciated. In these talks I’ll discuss the role of moduli in mirror symmetry of Fano varieties (where the mirror is a Landau-Ginzburg (LG) model). Some topics I expect to cover are a general structure theory of moduli of LG models (follows Katzarkov\, Kontsevich\, Pantev)\, the interplay of the topology  of LG models with autoequivalence relations in the Calabi-Yau setting\, and the relationship between Mori theory in the B-model and degenerations of the LG A-model. For the latter topic we’ll focus on the case of del Pezzo surfaces (due to unpublished work of Pantev) and the toric case (due to the speaker with Katzarkov and G. Kerr). Time permitting\, we may make some speculations on the role of LG moduli in the work of Gross-Hacking-Keel (in progress work of the speaker with T. Foster).\n\n\nMarch 6 and 8  \n4-5pm\nAdam Jacob  \n(UC Davis)\nTitle: The deformed Hermitian-Yang-Mills equation  \nAbstract: In this series I will discuss the deformed Hermitian-Yang-Mills equation\, which is a complex analogue of the special Lagrangian graph equation of Harvey-Lawson. I will describe its derivation in relation to the semi-flat setup of SYZ mirror symmetry\, followed by some basic properties of solutions. Later I will discuss methods for constructing solutions\, and relate the solvability to certain geometric obstructions. Both talks will be widely accessible\, and cover joint work with T.C. Collins and S.-T. Yau.\n\n\nMarch 6\, 8\, 13\, 15  \n3-4pm\nDmytro Shklyarov  \n(TU Chemnitz)\nTitle: On categories of matrix factorizations and their homological invariants  \nAbstract: The talks will cover the following topics: \n1. Matrix factorizations as D-branes. According to physicists\, the matrix factorizations of an isolated hypersurface singularity describe D-branes in the Landau-Ginzburg (LG) B-model associated with the singularity. The talk is devoted to some mathematical implications of this observation. I will start with a review of open-closed topological field theories underlying the LG B-models and then talk about their refinements. \n2. Semi-infinite Hodge theory of dg categories. Homological mirror symmetry asserts that the “classical” mirror correspondence relating the number of rational curves in a CY threefold to period integrals of its mirror should follow from the equivalence of the derived Fukaya category of the first manifold and the derived category of coherent sheaves on the second one. The classical mirror correspondence can be upgraded to an isomorphism of certain Hodge-like data attached to both manifolds\, and a natural first step towards proving the assertion would be to try to attach similar Hodge-like data to abstract derived categories. I will talk about some recent results in this direction and illustrate the approach in the context of the LG B-models. \n3. Hochschild cohomology of LG orbifolds. The scope of applications of the LG mod- els in mirror symmetry is significantly expanded once we include one extra piece of data\, namely\, finite symmetry groups of singularities. The resulting models are called orbifold LG models or LG orbifolds. LG orbifolds with abelian symmetry groups appear in mir- ror symmetry as mirror partners of varieties of general type\, open varieties\, or other LG orbifolds. Associated with singularities with symmetries there are equivariant versions of the matrix factorization categories which\, just as their non-equivariant cousins\, describe D-branes in the corresponding orbifold LG B-models. The Hochschild cohomology of these categories should then be isomorphic to the closed string algebra of the models. I will talk about an explicit description of the Hochschild cohomology of abelian LG orbifolds.\n\n\nApril 10 & 12  \n3-4pm\nMauricio Romo  \n(IAS)\nTitle: Gauged Linear Sigma Models\, Supersymmetric Localization and Applications  \nAbstract: In this series of lectures I will review various results on connections between gauged linear sigma models (GLSM) and mathematics. I will start with a brief introduction on the basic concepts about GLSMs\, and their connections to quantum geometry of Calabi-Yaus (CY). In the first lecture I will focus on nonperturbative results on GLSMs on closed 2-manifolds\, which provide a way to extract enumerative invariants and the elliptic genus of some classes of CYs. In the second lecture I will move to nonperturbative results in the case where the worldsheet is a disk\, in this case nonperturbative results provide interesting connections with derived categories and stability conditions. We will review those and provide applications to derived functors and local systems associated with  CYs. If time allows we will also review some applications to non-CY cases (in physics terms\, anomalous GLSMs). \nLecture notes\n\n\nApril 17\, 19\, 26  \n3-5pm\nAndrew  Harder  \n(University of Miami)\nTitle: Perverse sheaves of categories on surfaces  \nAbstract: Perverse sheaves of categories on a Riemann surface S are systems of categories and functors which are encoded by a graphs on S\, and which satisfy conditions that resemble the classical characterization of perverse sheaves on a disc. \nI’ll review the basic ideas behind Kapranov and Schechtman’s notion of a perverse schober and generalize this to perverse sheaves of categories on a punctured Riemann surface. Then I will give several examples of perverse sheaves of categories in both algebraic geometry\, symplectic geometry\, and category theory. Finally\, I will describe how one should be able to use related ideas to prove homological mirror symmetry for certain noncommutative deformations of projective 3-space. \n \n \n \n\n\nMay 15\, 17  \n1-3pm\nCharles Doran  \n(University of Alberta)\n\n\n\n\n\n\nLecture One:\nTitle: Picard-Fuchs uniformization and Calabi-Yau geometry\nAbstract:\n\n\n\n\n\n\nPart 1:  We introduce the notion of the Picard-Fuchs equations annihilating periods in families of varieties\, with emphasis on Calabi-Yau manifolds.  Specializing to the case of K3 surfaces\, we explore general results on “Picard-Fuchs uniformization” of the moduli spaces of lattice-polarized K3 surfaces and the interplay with various algebro-geometric normal forms for these surfaces.  As an application\, we obtain a universal differential-algebraic characterization of Picard rank jump loci in these moduli spaces.\n\nPart 2:  We next consider families with one natural complex structure modulus\, (e.g.\, elliptic curves\, rank 19 K3 surfaces\, b_1=4 Calabi-Yau threefolds\, …)\, where the Picard-Fuchs equations are ODEs.  What do the Picard-Fuchs ODEs for such families tell us about the geometry of their total spaces?  Using Hodge theory and parabolic cohomology\, we relate the monodromy of the Picard-Fuchs ODE to the Hodge numbers of the total space.  In particular\, we produce criteria for when the total space of a family of rank 19 polarized K3 surfaces can be Calabi-Yau.\n\n\n  \n\nLecture Two:\nTitle: Calabi-Yau fibrations: construction and classification\nAbstract: \nPart 1:  Codimension one Calabi-Yau submanifolds induce fibrations\, with the periods of the total space relating to those of the fibers and the structure of the fibration.  We describe a method of iteratively constructing Calabi-Yau manifolds in tandem with their Picard-Fuchs equations. Applications include the tower of mirrors to degree n+1 hypersurfaces in P^n and a tower of Calabi-Yau hypersurfaces encoding the n-sunset Feynman integrals. \nPart 2:  We develop the necessary theory to both construct and classify threefolds fibered by lattice polarized K3 surfaces.  The resulting theory is a complete generalization to threefolds of that of Kodaira for elliptic surfaces.  When the total space of the fibration is a Calabi-Yau threefold\, we conjecture a unification of CY/CY mirror symmetry and LG/Fano mirror symmetry by mirroring fibrations as Tyurin degenerations.  The detailed classification of Calabi-Yau threefolds with certain rank 19 polarized fibrations provides strong evidence for this conjecture by matching geometric characteristics of the fibrations with features of smooth Fano threefolds of Picard rank 1.
URL:https://cmsa.fas.harvard.edu/event/2018-hms-focused-lecture-series/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170914T150000
DTEND;TZID=America/New_York:20170914T160000
DTSTAMP:20260517T155126
CREATED:20240212T072955Z
LAST-MODIFIED:20240212T072955Z
UID:10001875-1505401200-1505404800@cmsa.fas.harvard.edu
SUMMARY:Algebraic Geometry Seminar\, Thursdays
DESCRIPTION:This seminar will not be held in the Spring 2018 Semester. \nThe Algebraic Geometry Seminar will be every Thursday from 3pm-4pm in CMSA Building\, 20 Garden Street\, Room G10. \nThe schedule will be updated as details are confirmed. \n  \n  \n\n\n\nDate\nName\nTitle/Abstract\n\n\n09-14-17\n Yu-Wei Fan (Harvard Math)\n\nEntropy of an autoequivalence on Calami-Yau manifolds \nAbstract:  We will recall the notion of entropy of an autoequivalence on triangulated categories\, and provide counterexamples of a conjecture by Kikuta-Takahashi. \n\n\n\n11-1-17 \n*5:00pm\, G10*\n Shamil Shakirov\, Harvard Math\n\nUndulation invariants of plane curves \nAbstract: “One of the general problems in algebraic geometry is to determine algorithmically whether or not a given geometric object\, defined by explicit polynomial equations (e.g. a curve or a surface)\, satisfies a given property (e.g. has singularities or other distinctive features of interest). A classical example of such a problem\, described by Cayley and Salmon in 1852\, is to determine whether or not a given plane curve of degree r > 3 has undulation points — the points where the tangent line meets the curve with multiplicity four. Cayley proved that there exists an invariant of degree (r – 3)(3 r – 2) that vanishes if and only if the curve has undulation points. We construct this invariant explicitly for quartics (r=4) as the determinant of a 21 times 21 matrix with polynomial entries\, and we conjecture a generalization for r = 5 \n\n\n\n11-2-17 \n \nAlexander Moll\, IHES\n\nHilbert Schemes from Geometric Quantization of Dispersive Periodic Benjamin-Ono Waves \nABSTRACT: By Grojnowski and Nakajima\, Fock spaces are cohomology rings of Hilbert scheme of points in the plane.  On the other hand\, by Pressley-Segal\, Fock spaces are spaces of J-holomorphic functions on the loop space of the real line that appear in geometric quantization with respect to the Kähler structure determined by the Sobolev regularity s= -1/2 and the Hilbert transform J.  First\, we show that the classical periodic Benjamin-Ono equation is a Liouville integrable Hamiltonian system with respect to this Kähler structure.  Second\, we construct an integrable geometric quantization of this system in Fock space following Nazarov-Sklyanin and describe the spectrum explicitly after a non-trivial rewriting of our coefficients of dispersion \ebar = e_1 + e_2 and quantization \hbar = – e_1 e_2 that is invariant under e_2 <-> e_1.  As a corollary of Lehn’s theorem\, our construction gives explicit creation and annihilation operator formulas for multiplication by new explicit universal polynomials in the Chern classes of the tautological bundle in the equivariant cohomology of our Hilbert schemes\, in particular identifying \ebar with the deformation parameter of the Maulik-Okounkov Yangian and \hbar with the handle-gluing element.  Our key ingredient is a simple formula for the Lax operators as elliptic generalized Toeplitz operators on the circle together with the spectral theory of Boutet de Monvel and Guillemin.  As time permits\, we discuss the relation of dispersionless \ebar -> 0 and semi-classical \hbar \rightarrow 0 limits to Nekrasov’s BPS/CFT Correspondence. \n\n\n\n11-9-17\n  TBD\n  TBD\n\n\n11-16-17\n TBD\n TBD\n\n\n11-23-17\n  TBD\n  TBD\n\n\n11-30-17\n  TBD\n  TBD\n\n\n12-7-17\n  TBD\n  TBD\n\n\n12-15-17\n  TBD\n  TBD
URL:https://cmsa.fas.harvard.edu/event/algebraic-geometry-seminar-thursdays/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170908T130000
DTEND;TZID=America/New_York:20170908T160000
DTSTAMP:20260517T155126
CREATED:20240209T112503Z
LAST-MODIFIED:20240209T112503Z
UID:10001855-1504875600-1504886400@cmsa.fas.harvard.edu
SUMMARY:Combinatorics & Complexity Seminar\, Fridays
DESCRIPTION:The seminar on Combinatorics and Complexity will be held every Friday from 1:00-4:00pm in CMSA Building\, 20 Garden Street\, Room G10. \nThe list of speakers for the upcoming academic year will be posted below and updated as details are confirmed. Titles and abstracts for the talks will be added as they are received. \nAdditional information on CMSA’s Combinatorics and Complexity program can be found here. \n  \n\n\n\nDate\nName\nTitle/Abstract\n\n\n09-08-17\n\nTBA\n\n\n09-15-2017\n\nTBA\n\n\n09-22-17\n\nTBA\n\n\n09-29-17\n\nTBA\n\n\n10-06-17\n\n TBA\n\n\n10-13-2017\n\nTBA\n\n\n10-20-2017\n\nTBA\n\n\n10-27-2017\n\nTBA\n\n\n11-03-2017\n\nTBA\n\n\n11-10-2017\n\nTBA\n\n\n11-17-2017\n\nTBA\n\n\n11-24-2017\n\nTBA\n\n\n12-01-2017\n\nTBA\n\n\n12-08-2017\n\n TBA
URL:https://cmsa.fas.harvard.edu/event/combinatorics-complexity-seminar-fridays/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170502T133000
DTEND;TZID=America/New_York:20170502T133000
DTSTAMP:20260517T155126
CREATED:20240213T102711Z
LAST-MODIFIED:20240213T102711Z
UID:10002427-1493731800-1493731800@cmsa.fas.harvard.edu
SUMMARY:5-2-2017 Social Sciences Application Forum
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/5-2-2017-social-sciences-application-forum/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170418T110000
DTEND;TZID=America/New_York:20170418T120000
DTSTAMP:20260517T155126
CREATED:20240213T093734Z
LAST-MODIFIED:20240220T144719Z
UID:10002348-1492513200-1492516800@cmsa.fas.harvard.edu
SUMMARY:4-18-2017 Social Science Applications Forum
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/4-18-2017-social-science-applications-forum/
LOCATION:CMSA\, 20 Garden Street\, Cambridge\, MA\, 02138\, United States
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170414T124600
DTEND;TZID=America/New_York:20170414T124600
DTSTAMP:20260517T155126
CREATED:20240213T100101Z
LAST-MODIFIED:20240213T100101Z
UID:10002378-1492173960-1492173960@cmsa.fas.harvard.edu
SUMMARY:4-14-2017 Special Lecture Series
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/4-14-2017-special-lecture-series/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170412T125300
DTEND;TZID=America/New_York:20170412T125300
DTSTAMP:20260517T155126
CREATED:20240213T095445Z
LAST-MODIFIED:20240213T095445Z
UID:10002368-1492001580-1492001580@cmsa.fas.harvard.edu
SUMMARY:4-12-2017 Social Science Applications Forum
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/4-12-2017-social-science-applications-forum/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170412T124400
DTEND;TZID=America/New_York:20170412T124400
DTSTAMP:20260517T155126
CREATED:20240213T100333Z
LAST-MODIFIED:20240213T100333Z
UID:10002385-1492001040-1492001040@cmsa.fas.harvard.edu
SUMMARY:4-12-2017 Special Lecture Series
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/4-12-2017-special-lecture-series/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170411T130000
DTEND;TZID=America/New_York:20170411T130000
DTSTAMP:20260517T155126
CREATED:20240213T094754Z
LAST-MODIFIED:20240213T094754Z
UID:10002365-1491915600-1491915600@cmsa.fas.harvard.edu
SUMMARY:4-11-2017 Social Science Applications Forum
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/4-11-2017-social-science-applications-forum/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170407T124300
DTEND;TZID=America/New_York:20170407T124300
DTSTAMP:20260517T155126
CREATED:20240213T100607Z
LAST-MODIFIED:20240213T100607Z
UID:10002391-1491568980-1491568980@cmsa.fas.harvard.edu
SUMMARY:4-7-2017 Special Lecture Series
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/4-7-2017-special-lecture-series/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170405T124200
DTEND;TZID=America/New_York:20170405T124200
DTSTAMP:20260517T155126
CREATED:20240213T101247Z
LAST-MODIFIED:20240213T101247Z
UID:10002402-1491396120-1491396120@cmsa.fas.harvard.edu
SUMMARY:4-5-2017 Special Lecture Series
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/4-5-2017-special-lecture-series/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170330T123800
DTEND;TZID=America/New_York:20170330T123800
DTSTAMP:20260517T155126
CREATED:20240213T102411Z
LAST-MODIFIED:20240213T102411Z
UID:10002418-1490877480-1490877480@cmsa.fas.harvard.edu
SUMMARY:3-30-2017 CMSA Special Seminar
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/3-30-2017-cmsa-special-seminar/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170321T122800
DTEND;TZID=America/New_York:20170321T122800
DTSTAMP:20260517T155126
CREATED:20240213T091532Z
LAST-MODIFIED:20240213T091532Z
UID:10002307-1490099280-1490099280@cmsa.fas.harvard.edu
SUMMARY:3-21-2017 Social Science Applications Forum
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/3-21-2017-social-science-applications-forum/
CATEGORIES:Seminars
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=America/New_York:20170310T122700
DTEND;TZID=America/New_York:20170310T122700
DTSTAMP:20260517T155126
CREATED:20240213T091725Z
LAST-MODIFIED:20240213T091725Z
UID:10002310-1489148820-1489148820@cmsa.fas.harvard.edu
SUMMARY:3-10-2017 Special Lecture Series
DESCRIPTION:
URL:https://cmsa.fas.harvard.edu/event/3-10-2017-special-lecture-series/
CATEGORIES:Seminars
END:VEVENT
END:VCALENDAR