40 research outputs found

    Arnold conjecture over integers

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    For any closed symplectic manifold, we show that the number of 1-periodic orbits of a nondegenerate Hamiltonian thereon is bounded from below by a version of total Betti number over Z of the ambient space taking account of the total Betti number over Q and torsions of all characteristic. The proof is based on constructing a Hamiltonian Floer theory over the Novikov ring with integer coefficients, which generalizes our earlier work for constructing integer-valued Gromov-Witten type invariants. In the course of the construction, we build a Hamiltonian Floer flow category with compatible smooth global Kuranishi charts. This generalizes a recent work of Abouzaid-McLean-Smith, which might be of independent interest.Comment: 168 pages, 2 figures. Comments welcome

    History and the Unconscious

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    This work represents the first truly comprehensive and non-biased history of psychohistory, a vanguard branch of historical scholarship that studies the psychological dimension of the past using principles of psychoanalysis and psychology as its theoretical ground. Tomasz Pawelec is an experienced methodologist and historiographer who systematically examines, reconstructs, and evaluates the major theoretical and methodological guiding assumptions shared by psychohistorians. In effect, he provides the reader with an intriguing portrait of a peculiar research paradigm – and a specific intellectual “monad” – that developed within the twentieth-century American history. At the empirical foundation of his work lies a broad collection of psychohistorical publications

    Perspectives on Platform Regulation

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    Online social media platforms set the agenda and structure for public and private communication in our age. Their influence and power is beyond any traditional media empire. Their legal regulation is a pressing challenge, but currently, they are mainly governed by economic pressures. There are now diverse legislative attempts to regulate platforms in various parts of the world. The European Union and most of its Member States have historically relied on soft law, but are now looking to introduce regulation. Leading researchers of the field analyse the hard questions and the responses given by various states. The book offers legislative solutions from various parts of the world, compares regulatory concepts and assesses the use of algorithms. With contributions by Izumi Aizu, Enni Ala-Mikkula, Alexandre Alaphilippe, Natalie Alkiviadou, Alejandro ArĂ©chiga Morales, Siwal Ashwini, Judit Bayer, Jörg Becker, Konrad Bleyer-Simon, Elda Brogi, Shun-Ling Chen, Poren Chiang, Michael Geist, Gerard Goggin, Giovanni De Gregorio, Sarah Hartmann, Maximilian Hemmert-Halswick, Maria Carolina Herrera Rubio, Bernd Holznagel, Peng Hwa Ang, Richard Janda, Jan Christopher Kalbhenn, Juliya Kharitonova, Kristiina Koivukari, PĂ€ivi Korpisaari, Jacob Mchangama, Trisha Meyer, Kilian MĂŒller, Larissa Sannikova, MĂ„rten Schultz, Nicole Stremlau, Maria L. Vazquez, Kuo-Wei Wu and Lorna Woods

    The Making of the Humanities, Volume III. The Modern Humanities

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    This comprehensive history of the humanities focuses on the modern period (1850-2000). The contributors, including Floris Cohen, Lorraine Daston and Ingrid Rowland, survey the rise of the humanities in interaction with the natural and social sciences, offering new perspectives on the interaction between disciplines in Europe and Asia and new insights generated by digital humanities

    Symplectic Topology of Projective Space: Lagrangians, Local Systems and Twistors

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    In this thesis we study monotone Lagrangian submanifolds of CPn . Our results are roughly of two types: identifying restrictions on the topology of such submanifolds and proving that certain Lagrangians cannot be displaced by a Hamiltonian isotopy. The main tool we use is Floer cohomology with high rank local systems. We describe this theory in detail, paying particular attention to how Maslov 2 discs can obstruct the differential. We also introduce some natural unobstructed subcomplexes. We apply this theory to study the topology of Lagrangians in projective space. We prove that a monotone Lagrangian in CPn with minimal Maslov number n + 1 must be homotopy equivalent to RPn (this is joint work with Jack Smith). We also show that, if a monotone Lagrangian in CP3 has minimal Maslov number 2, then it is diffeomorphic to a spherical space form, one of two possible Euclidean manifolds or a principal circle bundle over an orientable surface. To prove this, we use algebraic properties of lifted Floer cohomology and an observation about the degree of maps between Seifert fibred 3-manifolds which may be of independent interest. Finally, we study Lagrangians in CP(2n+1) which project to maximal totally complex subman- ifolds of HPn under the twistor fibration. By applying the above topological restrictions to such Lagrangians, we show that the only embedded maximal KĂ€hler submanifold of HPn is the totally geodesic CPn and that an embedded, non-orientable, superminimal surface in S4 = HP1 is congruent to the Veronese RP2 . Lastly, we prove some non-displaceability results for such Lagrangians. In particular, we show that, when equipped with a specific rank 2 local system, the Chiang Lagrangian L∆ ⊆ CP3 becomes wide in characteristic 2, which is known to be impossible to achieve with rank 1 local systems. We deduce that L∆ and RP3 cannot be disjoined by a Hamiltonian isotopy

    The Open Anthology of Earlier American Literature

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    This is an anthology of public domain texts from earlier American literature, collected by students, faculty, and alumnae of Plymouth State University as an OER alternative to expensive commercial anthologies. In addition to content from earlier editions, the 2018 edition adds four new sections: Where is American Literature Now?: Contemporary Connections, Earlier American Literature in Music, Female American (1767) Supplementary Readings, and Letters from an American Farmer (1767) Supplementary Readings. This file represents the state of the work at the end of 2018. Visit to see new and updated material visit https://openeal.pressbooks.com

    The Matrix Reproved: Verification Pearl

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    International audienceIn this paper we describe a complete solution for the first challenge of the VerifyThis 2016 competition held at the 18th ETAPS Forum. We present the proof of two variants for the multiplication of matrices: a naive version using three nested loops and Strassen's algorithm. The proofs are conducted using the Why3 platform for deductive program verification and automated theorem provers to discharge proof obligations. In order to specify and prove the two multiplication algorithms, we develop a new Why3 theory of matrices. In order to prove the matrix identities on which Strassen's algorithm is based, we apply the proof by reflection methodology, which we implement using ghost state.To our knowledge, this is the first time such a methodology is used under an auto-active setting

    Yeats's Legacies: Yeats Annual No. 21

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    The two great Yeats Family Sales of 2017 and the legacy of the Yeats family’s 80-year tradition of generosity to Ireland’s great cultural institutions provide the kaleidoscope through which these advanced research essays find their theme. Hannah Sullivan’s brilliant history of Yeats’s versecraft challenges Poundian definitions of Modernism; Denis Donoghue offers unique family memories of 1916 whilst tracing the political significance of the Easter Rising; Anita Feldman addresses Yeats’s responses to the Rising’s appropriation of his symbols and myths, the daring artistry of his ritual drama developed from Noh, his poetry of personal utterance, and his vision of art as a body reborn rather than a treasure preserved amid the testing of the illusions that hold civilizations together in ensuing wars. Warwick Gould looks at Yeats as founding Senator in the new Free State, and his valiant struggle against the literary censorship law of 1929 (with its present-day legacy of Irish anti-blasphemy law still presenting a constitutional challenge). Drawing on Gregory Estate documents, James Pethica looks at the evictions which preceded Yeats’s purchase of Thoor Ballylee in Galway; Lauren Arrington looks back at Yeats, Ezra Pound, and the Ghosts of The Winding Stair (1929) in Rapallo. Having co-edited both versions of A Vision, Catherine Paul offers some profound reflections on ‘Yeats and Belief’. Grevel Lindop provides a pioneering view of Yeats’s impact on English mystical verse and on Charles Williams who, while at Oxford University Press, helped publish the Oxford Book of Modern Verse. Stanley van der Ziel looks at the presence of Shakespeare in Yeats’s Purgatory. William H. O’Donnell examines the vexed textual legacy of his late work, On the Boiler while Gould considers the challenge Yeats’s intentionalism posed for once-fashionable post-structuralist editorial theory. John Kelly recovers a startling autobiographical short story by Maud Gonne. While nine works of current biographical, textual and literary scholarship are reviewed, Maud Gonne is the focus of debate for two reviewers, as are Eva Gore-Booth, Constance and Casimir Markievicz, Rudyard Kipling, David Jones, T. S. Eliot and his presence on the radio
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