Configuration of points and strings

Let $X$ be a smooth projective variety of dimension $n\geq 2$. It is shown that a finite configuration of points on $X$ subject to certain geometric conditions possesses rich inner structure. On the mathematical level this inner structure is a variation of Hodge-like structure. As a consequence one can attach to such point configurations: (i) Lie algebras and their representations (ii) Fano toric variety whose hyperplane sections are Calabi-Yau varieties. These features lead to a picture which is very suggestive of quantum gravity according to string theory.Comment: 32 pages, 1 figure this version will appear in Journal of Geometry and Physic

Nonabelian Jacobian of smooth projective surface : a survey

The nonabelian Jacobian J(X; L, d) of a smooth projective surface X is inspired by the classical theory of Jacobian of curves. It is built as a natural scheme interpolating between the Hilbert scheme X [d] of subschemes of length d of X and the stack M X (2, L, d) of torsion free sheaves of rank 2 on X having the determinant O X (L) and the second Chern class (= number) d. It relates to such influential ideas as variations of Hodge structures, period maps, nonabelian Hodge theory, Homological mirror symmetry, perverse sheaves, geometric Langlands program. These relations manifest themselves by the appearance of the following structures on J(X; L, d): a sheaf of reductive Lie algebras (singular) Fano toric varieties whose hyperplane sections are (singular) Calabi-Yau varieties trivalent graphs. This is an expository paper giving an account of most of the main properties of J(X; L, d) uncovered in Reider 2006 and ArXiv:1103.4794v1

Western European Architecture Studies

STEP Category: Education AbroadPresentation of 4-week summer session 1, "Maymester" study abroad for Western European Architecture Studies.The Ohio State University Second-year Transformational Experience Program (STEP)Academic Major: Architectur

Nonabelian Jacobian of Projective Surfaces : Geometry and Representation Theory

The Jacobian of a smooth projective curve is undoubtedly one of the most remarkable and beautiful objects in algebraic geometry. This work is an attempt to develop an analogous theory for smooth projective surfaces - a theory of the nonabelian Jacobian of smooth projective surfaces. Just like its classical counterpart, our nonabelian Jacobian relates to vector bundles (of rank 2) on a surface as well as its Hilbert scheme of points. But it also comes equipped with the variation of Hodge-like structures, which produces a sheaf of reductive Lie algebras naturally attached to our Jacobian. This constitutes a nonabelian analogue of the (abelian) Lie algebra structure of the classical Jacobian. This feature naturally relates geometry of surfaces with the representation theory of reductive Lie algebras/groups. This work’s main focus is on providing an in-depth study of various aspects of this relation. It presents a substantial body of evidence that the sheaf of Lie algebras on the nonabelian Jacobian is an efficient tool for using the representation theory to systematically address various algebro-geometric problems. It also shows how to construct new invariants of representation theoretic origin on smooth projective surfaces

An unconfined, large-volume hydrogen/air explosion

Cause and results of the autoignition of 283 cubic meters of hydrogen gas, of which only about 10 percent exploded, are given. Results indicate that autoignition produces an explosion which could be described as a deflagration of explosive velocity, with a shock wave of sonic velocity and minor damage potential

Shutendôji: oniwith a righteous tongue

Numa das mais famosas lendas de seres demoníacos, o herói guerreiro Minamoto no Raiko (? - 1021) derrota o diabólico oni, Shuten dôji, por manha e engano. Remontada ao Japão medieval, a história sugere que, com a ajuda das divindades os guerreiros podem derrotar até os mais monstruosos vilões. Misto de entertenimento e edificação moral /religiosa, “Shuten dôji” pertence ao género otogi zôshi. Adequadamente ao género, no momento da derrota mortal do demónio, Shuten dôji exclama, “Que tristeza, sacerdotes! Dizeis que não mentis: Não há injustiça nas palavras dos demónios”. Trata-se dum lamento justificado; vindo de um demónio que rapta e come raparigas, parece incongruente e mesmo cândido que um personagem tão diabólico não espere subterfúgios para o derrotar. Ao mesmo tempo a exclamação cria uma súbita mudança de simpatias — de pró-guerreiros para pró-oni — na narração da lenda. Esta transferência detém o fluir da história. Em última análise, põe-se, em termos de um dilema, o problema “até que ponto se pode ser corrupto na demanda de um alvo virtuoso?” Ao examinar o oni, o meu artigo explora o significado da razão de Shuten dôji

Do imaging studies aid diagnosis of acute sinusitis?

Accurate diagnosis of acute sinusitis in both children and adults depends on the history and clinical examination of the patient. While the clinical signs and symptoms of acute sinusitis are often difficult to distinguish from viral upper respiratory infection, such an assessment remains the best approach to diagnosing acute sinusitis (strength of recommendation [SOR]: A). There is no role for imaging in the diagnosis of acute sinusitis. For patients who have persistent symptoms, or those for whom surgery is being considered, some guidelines suggest that coronal computed tomography (CT) scan of the paranasal sinuses be considered (SOR: C, expert opinion)