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The art of biography in Antiquity
\"Greek and Roman biography embraces much more than Plutarch, Suetonius and their lost Hellenistic antecedents. In this book Professor Hägg explores the whole range and diversity of ancient biography, from its Socratic beginnings to the Christian acquisition of the form in late antiquity. He shows how creative writers developed the lives of popular heroes like Homer, Aesop and Alexander and how the Christian gospels grew from bare sayings to full lives. In imperial Rome biography flourished in the works of Greek writers: Lucian's satire, Philostratus' full sophistic orchestration, Porphyry's intellectual portrait of Plotinus. Perhaps surprisingly, it is not political biography or the lives of poets that provide the main artery of ancient biography, but various kinds of philosophical, spiritual and ethical lives. Applying a consistent biographical reading to a representative set of surviving texts, this book opens up the manifold but often neglected art of biography in classical antiquity\"-- Provided by publisher.
Book
Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
Motivated by the critical dissipative quasi-geostrophic equation, we prove that drift-diffusion equations with L² initial data and minimal assumptions on the drift are locally Hölder continuous. As an application we show that solutions of the quasi-geostrophic equation with initial L² data and critical diffusion (—Δ) 1/2 are locally smooth for any space dimension.
Journal Article
Rethinking historical distance
\"This volume brings new depth to the analysis of historical distance by looking at its importance in fields that extend far beyond the usual bounds of history, including psychoanalysis and the visual and performing arts. Its sources include 19th century British sculpture, musical theatre, and late 18th and 19th century fashion plates. The book offers general introductory discussions of how historical distance might best be understood in contemporary historiography, of changing ideals of distance and proximity as they have taken shape in Western thought from the Renaissance to modernity and of historical judgments and their meanings. It includes a range of essays that explore the importance of distance in relation to a number of different problems and periods, including how the use of historical distance as a framework might offer new ways of distinguishing literary fictions from histories, or a new understanding of the changing pattern of biography over the past two centuries. The range of forms and media covered by the essays in this collection greatly expands not only ways of thinking about historical distance, but the nature and meaning of history. By incorporating this wide range of different material and an equally wide range of approaches, the volume gives the discussion of historical distance a new breadth, flexibility and importance. \"-- Provided by publisher.
Book
On motivic cohomology with Z/l-coefficients
In this paper we prove the conjecture of Bloch and Kato which relates Milnor's K-theory of a field with its Galois cohomology as well as the related comparisons results for motivic cohomology with finite coefficients in the Nisnevich and étale topologies.
Journal Article
Alexander the Great : his life and his mysterious death
\"More than two millennia have passed, but Alexander the Great is still a household name. His life was an adventure story and took him to every corner of the ancient world. His memory and glamour persist, and his early death at thirty-three has kept him evergreen in our imaginations with a legacy that meant something different to every age: in the Middle Ages he became an exemplar of knightly chivalry, he was a star of Renaissance paintings, and by the early twentieth century he even came to resemble an English gentleman. But who was he in his own time? In Alexander the Great, Anthony Everitt judges Alexander's life against the criteria of his own age and considers all his contradictions. We meet the Macedonian prince who was naturally inquisitive and fascinated by science and exploration, who enjoyed the arts and used the poet Homer's great epic, the Iliad, as a bible. As his empire grew, stretching from Greece and Macedonia to Ancient Egypt and Persia and all the way to India, Alexander exhibited respect for the traditions of his new subjects and careful judgment in administering rule over a vast territory. But his career also had a dark side. An inveterate conqueror, who in his short life built the largest empire to that point in history, Alexander glorified war and was known to commit acts of great cruelty. As debates continue about the meaning of his life, Alexander's death remains an unsolved mystery. Did he die of natural causes, felled by a fever, or did his marshals, angered by his tyrannical behavior, kill him? An explanation of his death can lie only in what we know of his life, and Everitt ventures to solve that puzzle, offering an ending to Alexander's story that has eluded so many for so long\"-- Provided by publisher.
Book
Analyticity of periodic traveling free surface water waves with vorticity
We prove that the profile of a periodic traveling wave propagating at the surface of water above a flat bed in a flow with a real analytic vorticity must be real analytic, provided the wave speed exceeds the horizontal fluid velocity throughout the flow. The real analyticity of each streamline beneath the free surface holds even if the vorticity is only Hölder continuously differentiable.
Journal Article
Australian sociology : fragility, survival, rivalry
\"Sociology in Australia was battered and bruised by the injuries it sustained in the first half of the twentieth century. Most of these were self-inflicted. Through arrogance and overreach its early advocates ruined its chances, such that by the 1930s sociology had been rejected as a distinctive discipline by the only two universities which were prepared to give it a chance, Melbourne and Sydney. But since 1950 the discipline has fought its way back into the academic mainstream and now has a place in most of the nation's universities. This has not been easy; its fortunes seem forever mixed. It has never flourished in all states and territories at the same time and even while it is now on the rise in places like the University of Sydney it is relatively weak at some of its former strongholds in the second tier universities. Despite these mixed fortunes, the discipline has proved itself a survivor\"-- Provided by publisher.
Book
From real affine geometry to complex geometry
We construct from a real affine manifold with singularities (a tropical manifold) a degeneration of Calabi-Yau manifolds. This solves a fundamental problem in mirror symmetry. Furthermore, a striking feature of our approach is that it yields an explicit and canonical order-by-order description of the degeneration via families of tropical trees. This gives complete control of the B-model side of mirror symmetry in terms of tropical geometry. For example, we expect that our deformation parameter is a canonical coordinate, and expect period calculations to be expressible in terms of tropical curves. We anticipate this will lead to a proof of mirror symmetry via tropical methods.
Journal Article
Theoderic and the Roman imperial restoration
\"This book provides a new interpretation of the fall of the Roman Empire and the \"barbarian\" kingdom known conventionally as Ostrogothic Italy. Relying primarily on Italian textual and material evidence, and in particular the works of Cassiodorus and Ennodius, Jonathan J. Arnold argues that contemporary Italo-Romans viewed the Ostrogothic kingdom as the Western Roman Empire and its \"barbarian\" king, Theoderic (r. 489/93-526), as its emperor. Investigating conceptions of Romanness, Arnold explains how the Roman past, both immediate and distant, allowed Theoderic and his Goths to find acceptance in Italy as Romans, with roles essential to the Empire's perceived recovery. Theoderic and the Roman Imperial Restoration demonstrates how Theoderic's careful attention to imperial traditions, good governance, and reconquest followed by the re-Romanization of lost imperial territories contributed to contemporary sentiments of imperial resurgence and a golden age. There was no need for Justinian to restore the Western Empire: Theoderic had already done so\"-- Provided by publisher.
Book
Ricci curvature for metric-measure spaces via optimal transport
We define a notion of a measured length space X having nonnegative N-Ricci curvature, for N ∈ [1, ∞), or having ∞-Ricci curvature bounded below by K, for K ∈ ℝ. The definitions are in terms of the displacement convexity of certain functions on the associated Wasserstein metric space P₂(X) of probability measures. We show that these properties are preserved under measured Gromov-Hausdorff limits. We give geometric and analytic consequences. This paper has dual goals. One goal is to extend results about optimal transport from the setting of smooth Riemannian manifolds to the setting of length spaces. A second goal is to use optimal transport to give a notion for a measured length space to have Ricci curvature bounded below. We refer to [11] and [44] for background material on length spaces and optimal transport, respectively. Further bibliographic notes on optimal transport are in Appendix F. In the present introduction we motivate the questions that we address and we state the main results. To start on the geometric side, there are various reasons to try to extend notions of curvature from smooth Riemannian manifolds to more general spaces. A fairly general setting is that of length spaces, meaning metric spaces (X, d) in which the distance between two points equals the infimum of the lengths of curves joining the points. In the rest of this introduction we assume that X is a compact length space. Alexandrov gave a good notion of a length space having \"curvature bounded below by K\", with K a real number, in terms of the geodesic triangles in X. In the case of a Riemannian manifold M with the induced length structure, one recovers the Riemannian notion of having sectional curvature bounded below by K. Length spaces with Alexandrov curvature bounded below by K behave nicely with respect to the Gromov-Hausdorff topology on compact metric spaces (modulo isometries); they form a closed subset.
Journal Article