Representational Arts Research Articles

The number of $D_4$-fields ordered by conductor

We consider families of quartic number fields whose normal closures over \mathbb{Q} have Galois group isomorphic to D_4 , the symmetries of a square. To any such field L , one can associate the Artin conductor of the corresponding 2-dimensional irreducible Galois representation with image D_4 . We determine the asymptotic number of such D_4 -quartic fields ordered by conductor, and compute the leading term explicitly as a mass formula, verifying heuristics of Kedlaya and Wood. Additionally, we are able to impose any local splitting conditions at any finite number of primes (sometimes, at an infinite number of primes), and as a consequence, we also compute the asymptotic number of order-4 elements in class groups and narrow class groups of quadratic fields ordered by discriminant. Traditionally, there have been two approaches to counting quartic fields, using arithmetic invariant theory in combination with geometry-of-number techniques, and applying Kummer theory together with L -function methods. Both of these strategies fail in the case of D_4 -quartic fields ordered by conductor since counting quartic fields containing a quadratic subfield with large discriminant is difficult. However, when ordering by conductor, we utilize additional algebraic structure arising from the outer automorphism of D_4 combined with both approaches mentioned above to obtain exact asymptotics.

On a canonical lift of Artin's representation to loop braid groups

Each pointed topological space has an associated π-module , obtained from action of its first homotopy group on its second homotopy group. For the 3-ball with a trivial link with n -components removed from its interior, its π -module M n is of free type . In this paper we give an injection of the (extended) loop braid group into the group of automorphisms of M n . We give a topological interpretation of this injection, showing that it is both an extension of Artin's representation for braid groups and of Dahm's homomorphism for (extended) loop braid groups.

RECIPROCITY SHEAVES AND THEIR RAMIFICATION FILTRATIONS

AbstractWe define a motivic conductor for any presheaf with transfersFusing the categorical framework developed for the theory of motives with modulus by Kahn, Miyazaki, Saito and Yamazaki. IfFis a reciprocity sheaf, this conductor yields an increasing and exhaustive filtration on$F(L)$, whereLis any henselian discrete valuation field of geometric type over the perfect ground field. We show that ifFis a smooth group scheme, then the motivic conductor extends the Rosenlicht–Serre conductor; ifFassigns toXthe group of finite characters on the abelianised étale fundamental group ofX, then the motivic conductor agrees with the Artin conductor defined by Kato and Matsuda; and ifFassigns toXthe group of integrable rank$1$connections (in characteristic$0$), then it agrees with the irregularity. We also show that this machinery gives rise to a conductor for torsors under finite flat group schemes over the base field, which we believe to be new. We introduce a general notion of conductors on presheaves with transfers and show that on a reciprocity sheaf, the motivic conductor is minimal and any conductor which is defined only for henselian discrete valuation fields of geometric type withperfectresidue field can be uniquely extended to all such fields without any restriction on the residue field. For example, the Kato–Matsuda Artin conductor is characterised as the canonical extension of the classical Artin conductor defined in the case of a perfect residue field.

Stark points on elliptic curves via Perrin-Riou’s philosophy

In the early 90’s, Perrin-Riou (Ann Inst Fourier 43(4):945–995, 1993) introduced an important refinement of the Mazur–Swinnerton-Dyer p-adic L-function of an elliptic curve E over $$\mathbb {Q}$$ , taking values in its p-adic de Rham cohomology. She then formulated a p-adic analogue of the Birch and Swinnerton-Dyer conjecture for this p-adic L-function, in which the formal group logarithms of global points on E make an intriguing appearance. The present work extends Perrin-Riou’s construction to the setting of a Garret–Rankin triple product (f, g, h), where f is a cusp form of weight two attached to E and g and h are classical weight one cusp forms with inverse nebentype characters, corresponding to odd two-dimensional Artin representations $$\varrho _g$$ and $$\varrho _h$$ respectively. The resulting p-adic Birch and Swinnerton-Dyer conjecture involves the p-adic logarithms of global points on E defined over the field cut out by $$\varrho _g\otimes \varrho _h$$ , in the style of the regulators that arise in Darmon et al. (Forum Math 3(e8):95, 2015), and recovers Perrin-Riou’s original conjecture when g and h are Eisenstein series.

İSTANBUL HALKEVLERİ GÜZEL SANATLAR VE TEMSİL ŞUBELERİNİN FAALİYETLERİ (1939-1951)

Kurtuluş Savaşı’ndan sonra gerçekleşen inkılâp hareketlerinin ortak amacı, Türk toplumunu her alanda çağdaş ve akılcı bir yöntemle modern bir toplum haline getirmekti. Bu amaçla 19 Şubat 1932 tarihinde “kültür kurumu” olarak adlandırılan halkevleri açıldı. 1932-1951 döneminde halkevleri; güzel sanatlar, temsil, dil ve edebiyat, spor, sosyal yardım, halk dershaneleri ve kurslar, kütüphane ve yayın, köycülük ile tarih ve müze şubesi olmak üzere toplam 9 şube ve bu şubelere bağlı birçok kol aracılığıyla faaliyet gösterdi. Güzel sanatlar şubesinin amacı; müzik, resim, heykel, mimari ve süsleme sanatları alanında amatör ve profesyonel unsurları bir araya toplamak, genç kabiliyetleri korumak ve bunların yetişmelerini sağlamaktı. Temsil şubesinin amacı da temsil sanatına istekli ve kabiliyetli üyelerden oluşan bir temsil grubu oluşturmaktı.
 İstanbul halkevlerinin güzel sanatlar şubeleri müzik faaliyetleri içinde daha çok Türk müziğine yönelik koro faaliyetleri ve konserler üzerinde durmaktaydı. Eminönü, Kadıköy, Şişli ve Beyoğlu halkevlerinin kendilerine ait orkestraları vardı. Sergi faaliyetleri resim ve fotoğraf ağırlıklı olup ülkenin ilk “diyaroma sergisi” nin açılışı bu dönemde Eminönü Halkevi tarafından yapıldı. Temsil şubelerinin faaliyetleri de piyes, bale, opera, revü, kanto, kukla-karagöz, meddah, hokkabaz, orta oyunu, sinema ve film gösterilerinden oluşmaktaydı.
 İstanbul’da 1932-1935 tarihleri arasında sadece İstanbul Halkevi faaliyet gösterdi ve 1935 yılında yeniden yapılandırmaya gidilerek halkevinin faaliyetlerine son verildi. Aynı yıl İstanbul’da Eminönü, Şehremini, Beyoğlu, Beşiktaş, Kadıköy, Üsküdar ve Şişli halkevleri açıldı. Bu halkevlerini 1938 yılında Fatih, Bakırköy ve Eyüp halkevleri, 1939 yılında Şile, 1940’da Sarıyer halkevlerinin açılması izledi. 1945 yılında Kartal, Yalova ve 1946 yılında da Çatalca, Beykoz ve Yeşilköy halkodaları halkevlerine dönüştürüldü.
 Bu çalışmada 1939-1951 döneminde İstanbul’da faaliyet gösteren 17 halkevine bağlı güzel sanatlar ve temsil şubelerinin faaliyetleri; “müzik, sergi ve temsil” alt başlıkları altında incelendi.

Vision as make-believe: how narratives and models represent sociotechnical futures

ABSTRACT When prominent experiments, simulations, and prototypes fail, sociotechnical futures become contested. This paper discusses the negotiation of visions as make-believe to give the considered feasibility of future narratives a more significant account in explaining innovation dynamics. Following Kendall Walton's theory of representational arts, I propose that imagined futures depend on both material and socio-cultural constraints. On the one hand, the considered data, models, and artifacts give make-believe futures a veto right and a certain kind of objectivity. On the other hand, sociotechnical imaginaries prompt promissory considerations and implications. The contingency of employed objects allows accounting responsibility for fictional truths to imagining subjects. Drawing from a scenario workshop on microalgae nutrition, I demonstrate how stakeholders use uncertain props and imaginaries to negotiate the ambiguous boundaries for the assessment of the unproven technology. I argue that the non-fixity of both authorized sources and promissory narratives explains the uncertainty of innovation dynamics.

On a BSD-type formula for L-values of Artin twists of elliptic curves

Abstract This is an investigation into the possible existence and consequences of a Birch–Swinnerton-Dyer-type formula for L-functions of elliptic curves twisted by Artin representations. We translate expected properties of L-functions into purely arithmetic predictions for elliptic curves, and show that these force some peculiar properties of the Tate–Shafarevich group, which do not appear to be tractable by traditional Selmer group techniques. In particular, we exhibit settings where the different p-primary components of the Tate–Shafarevich group do not behave independently of one another. We also give examples of “arithmetically identical” settings for elliptic curves twisted by Artin representations, where the associated L-values can nonetheless differ, in contrast to the classical Birch–Swinnerton-Dyer conjecture.

Twist‐minimal trace formulas and the Selberg eigenvalue conjecture

We derive a fully explicit version of the Selberg trace formula for twist-minimal Maass forms of weight 0 and arbitrary conductor and nebentypus character, and apply it to prove two theorems. First, conditional on Artin's conjecture, we classify the even 2-dimensional Artin representations of small conductor; in particular, we show that the even icosahedral representation of smallest conductor is the one found by Doud and Moore, of conductor 1951. Second, we verify the Selberg eigenvalue conjecture for groups of small level, improving on a result of Huxley from 1985.

Graph-Based Text Representation and Matching: A Review of the State of the Art and Future Challenges

Graph-based text representation is one of the important preprocessing steps in data and text mining, Natural Language Processing (NLP), and information retrieval approaches. The graph-based methods focus on how to represent text documents in the shape of a graph to exploit the best features of their characteristics. This study reviews and lists the advantages and disadvantages of such methods employed or developed in graph-based text representations. The literature shows that some of the proposed graph-based methods suffer from a lack of representing texts in certain situations. Currently, several techniques are commonly used in graph-based text representation. However, there are still some weaknesses and shortages in these techniques and tools that significantly affect the success of graph representation and graph matching. In this review, we conduct an inclusive survey of the state of the art in graph-based text representation and learning. We provide a formal description of the problem of graph-based text representation and introduce some basic concepts. More significantly, this study proposes a new taxonomy of graph-based text representation, categorizing the existing studies based on representation characteristics and scheme techniques. In terms of the representation scheme taxonomy, we introduce four main types of conceptual graph schemes and summarize the challenges faced in each scheme. The main issues of graph representation, such as research topics and the sub-taxonomy of graph models for web documents, are introduced and categorized. This research also covers some tasks of understanding natural language processing (NLP) that depend on different types of graph structures. In addition, the graph matching taxonomy implements three main categories based on the matching approach, including structural-, semantic-, and similarity-based approaches. Moreover, a deep comparison of these approaches is discussed and reported in terms of methods and tools, the concepts of matching and locality, and the application domains that use these tools. Finally, the paper recommends seven promising future study directions in the graph-based text representation field. These recommendation points are summarized and highlighted as open problems and challenges of graph-based text representation and learning to facilitate and fill the research gaps for scientific researchers in this field.

A mod-p Artin–Tate conjecture, and generalizing the Herbrand–Ribet theorem

Following the natural instinct that when a group operates on a number field then every term in the class number formula should factorize `compatibly' according to the representation theory (both complex and modular) of the group, we are led to some natural questions about the $p$-part of the classgroup of any CM Galois extension of $\Q$ as a module for $\Gal(K/Q)$, in the spirit of Herbrand-Ribet's theorem on the $p$-component of the class number of $Q(\zeta_p)$. In trying to formulate these questions, we are naturally led to consider $L(0,\rho)$, for $\rho$ an Artin representation, in situations where this is known to be nonzero and algebraic, and it is important for us to understand if this is $p$-integral for a prime $\p$ of the ring of algebraic integers $\bar{Z}$ in $C$, that we call {\it mod-$p$ Artin-Tate conjecture}. The most minor term in the class number formula, the number of roots of unity, plays an important role for us --- it being the only term in the denominator, is responsible for all poles!

Przed dziełem sztuki. Wspomnienia ze studiów

The present essay includes the author’s memories of his university studies and the intellectual formation that he received as a student of art history at the University of Poznań in 1949-1954. His first professor who opened to him the door to art history and exerted on him a strong intellectual influence, was Szczęsny Dettloff, a disciple of Heinrich Wölfflin in Munich and Max Dvořák in Vienna. Dettloff taught his students that the foundation of studying art in history is the study of the form of an individual artwork He believed that without a proper analysis of form it is impossible to construct appropriate series of the works of art and specify their position in the culture of the times of their origin. Similar sensitivity to form and the understanding of its significance for the art historian’s work were represented by two other professors important for the author, both educated by Dettloff already before World War II: Gwido Chmarzyński and Zdzisław Kępiński. When in 1957–1968 the author was a postgraduate student in the Centre d’Études Supérieures de Civilisation Médiévale at the University of Poitiers (CÉSCM), it turned out that the local methodological tradition was similar to what he had learned in Poznań before. The CÉSCM was founded as a multidisciplinary institute for the study of the Middle Ages, combining history, art history, literary history, and the history of ideas. It was important that one of them could shed light on an object studied by another, but each of them, including art history, kept its material and methodological identity. In the French tradition, art history had an “autonomous” status, focusing on artistic creation as a special sphere of human activity. That idea influenced also quite strongly the study of medieval architecture, originated in the early 19th century by Arcisse de Caumont, and continued until today by many generations of French scholars. What is characteristic of their research is meticulous analysis of form, articulated with a precise, detailed, and comprehensive specialist vocabulary. The lectures of French scholars on medieval architecture, which the author attended in Paris and Poitiers, taught him precision in the analysis of the artwork’s structure and its components, as well as responsibility for every single statement made on art. For a young art historian who did not specialize in architecture but in representational arts, that French experience was a lesson of methodological rigor necessary in the intellectual pursuits of the humanities scholar.

Facing the Work of Art. Memories of My Student Years

The present essay includes the author’s memories of his university studies and the intellectual formation that he received as a student of art history at the University of Poznań in 1949-1954. His first professor who opened to him the door to art history and exerted on him a strong intellectual influence, was Szczęsny Dettloff, a disciple of Heinrich Wölfflin in Munich and Max Dvořák in Vienna. Dettloff taught his students that the foundation of studying art in history is the study of the form of an individual artwork He believed that without a proper analysis of form it is impossible to construct appropriate series of the works of art and specify their position in the culture of the times of their origin. Similar sensitivity to form and the understanding of its significance for the art historian’s work were represented by two other professors important for the author, both educated by Dettloff already before World War II: Gwido Chmarzyński and Zdzisław Kępiński. When in 1957-1968 the author was a postgraduate student in the Centre d’Études Supérieures de Civilisation Médiévale at the University of Poitiers (CÉSCM), it turned out that the local methodological tradition was similar to what he had learned in Poznań before. The CÉSCM was founded as a multidisciplinary institute for the study of the Middle Ages, combining history, art history, literary history, and the history of ideas. It was important that one of them could shed light on an object studied by another, but each of them, including art history, kept its material and methodological identity. In the French tradition, art history had an “autonomous” status, focusing on artistic creation as a special sphere of human activity. That idea influenced also quite strongly the study of medieval architecture, originated in the early 19th century by Arcisse de Caumont, and continued until today by many generations of French scholars. What is characteristic of their research is meticulous analysis of form, articulated with a precise, detailed, and comprehensive specialist vocabulary. The lectures of French scholars on medieval architecture, which the author attended in Paris and Poitiers, taught him precision in the analysis of the artwork’s structure and its components, as well as responsibility for every single statement made on art. For a young art historian who did not specialize in architecture but in representational arts, that French experience was a lesson of methodological rigor necessary in the intellectual pursuits of the humanities scholar.

Dynamical systems and operator algebras associated to Artin's representation of braid groups

Artin's representation is an injective homomorphism from the braid group Bn on n strands into AutFn, the automorphism group of the free group Fn on n generators. The representation induces maps Bn→AutC∗r(Fn) and Bn→AutC∗(Fn) into the automorphism groups of the corresponding group C∗-algebras of Fn. These maps also have natural restrictions to the pure braid group Pn. In this paper, we consider twisted versions of the actions by cocycles with values in the circle, and discuss the ideal structure of the associated crossed products. Additionally, we make use of Artin's representation to show that the braid groups B∞ and P∞ on infinitely many strands are both C∗-simple.

Irreducible characters with bounded root Artin conductor

In this work, we prove that the growth of the Artin conductor is at most, exponential in the degree of the character.

Pages from Memory – Maeterlinck and the Russian Theatre Creators

AbstractThe dramaturgy and the essays of Maurice Maeterlinck are the starting point for essential changes in the art of theatre representation, marking the transition from realism, which had become naturalist, towards a theatre in which the essence and theatricality conduct to a revitalization of the theatre. The Russian directors V.E. Meyerhold and K.S. Stanislavsky are two of the most important theatre personalities who have searched for the new forms of theatre. Analyzing the first steps of Meyerhold’s directing, it is easy to see that the symbolist roots of theatre making can be found in the French theatre art, also inspired by Maeterlinck. Stanislavsky, the master from The Moscow Art Theatre, was also the first director to stageThe Blue Bird, before the text was even published. We shall follow, in the next pages, fragments from the Russian theatre which refer to these episodes.

Why Do We Need Memory?

Abstract A fundamental question for the study of everything, including of the scenic movement in theatre. A necessary question in any artistic endeavour and nonetheless, continuously endangered by the pressure of information, of the speed of technology, of the necessity of the NOW, the god of the time of globalization and consumer age. What we are aiming at in our applied studies of theatre anthropology, would be the discovery of a line of personal expression distinguishable in the art of theatre representation, which could be subsequently returned to and cultivated by the actor at various levels of artistic maturity. Memory, training and attention allow us to eliminate samples of stage movement and thinking. Memory helps us in the appropriation of skills and knowledge in our work. It helps us change at any time the manner of thinking, in order to become more aware. At the end of the day, in the absence of subjective memory, it becomes impossible to move being aware in the time and space of our own lives...

Explicit root numbers of abelian varieties

The Birch and Swinnerton-Dyer conjecture predicts that the parity of the algebraic rank of an abelian variety over a global field should be controlled by the expected sign of the functional equation of its L L -function, known as the global root number. In this paper, we give explicit formulae for the local root numbers as a product of Jacobi symbols. This enables one to compute the global root number, generalising work of Rohrlich, who studies the case of elliptic curves. We provide similar formulae for the root numbers after twisting the abelian variety by a self-dual Artin representation. As an application, we find a rational genus two hyperelliptic curve with a simple Jacobian whose root number is invariant under quadratic twist.

The Texture of Rare and Common Lesions in Soemmerring and Baillie.

The publications on morbid anatomy by Matthew Baillie and Samuel Thomas Soemmerring put pathological preparations and images center stage. A comparison between their works highlights major shifts from exceptional to more representative cases and significant differences in the art of representation. Initially Baillie provided careful descriptions of internal postmortem lesions (1793). Then Soemmerring's prompt German translation added a wealth of references to the literature and specifically to pathological images available in print (1794). Soon after a second unillustrated edition incorporating some of Soemmerring's comments (1797), Baillie issued ten installments with dozens of pathological plates (1799-1803). His plates differed from those referred to by Soemmerring for their broader scope, representing common and rare conditions alike, and specific attention to the fine changes of texture of the affected parts. Their works document the crucial status of pathological preparations and images at the time and highlight the achievement of Baillie's work at an artistic as well as at an intellectual level.

Quaternionic Artin representations and nontraditional arithmetic statistics

We classify and then attempt to count the real quadratic fields (ordered by the size of the totally positive fundamental unit, as in Sarnak’s work) from which quaternionic Artin representations of minimal conductor can be induced. Some of our results can be interpreted as criteria for a real quadratic field to be contained in a Galois extension of Q \mathbb {Q} with controlled ramification and Galois group isomorphic to a generalized quaternion group.

Almost Abelian Artin Representations of Q

Almost Abelian Artin Representations of Q