Generalizing Tanisaki's ideal via ideals of truncated symmetric functions

We define a family of ideals $I_h$ in the polynomial ring $\mathbb{Z}[x_1,...,x_n]$ that are parametrized by Hessenberg functions $h$ (equivalently Dyck paths or ample partitions). The ideals $I_h$ generalize algebraically a family of ideals called the Tanisaki ideal, which is used in a geometric construction of permutation representations called Springer theory. To define $I_h$, we use polynomials in a proper subset of the variables ${x_1,...,x_n}$ that are symmetric under the corresponding permutation subgroup. We call these polynomials {\em truncated symmetric functions} and show combinatorial identities relating different kinds of truncated symmetric polynomials. We then prove several key properties of $I_h$, including that if $h>h'$ in the natural partial order on Dyck paths then $I_{h} \subset I_{h'}$, and explicitly construct a Gr\"{o}bner basis for $I_h$. We use a second family of ideals $J_h$ for which some of the claims are easier to see, and prove that $I_h = J_h$. The ideals $J_h$ arise in work of Ding, Develin-Martin-Reiner, and Gasharov-Reiner on a family of Schubert varieties called partition varieties. Using earlier work of the first author, the current manuscript proves that the ideals $I_h = J_h$ generalize the Tanisaki ideals both algebraically and geometrically, from Springer varieties to a family of nilpotent Hessenberg varieties.Comment: v1 had 27 pages. v2 is 29 pages and adds Appendix B, where we include a recent proof by Federico Galetto of a conjecture given in the previous version. We also add some connections between our work and earlier results of Ding, Gasharov-Reiner, and Develin-Martin-Reiner. v3 corrects a typo in Valibouze's citation in the bibliography. To appear in Journal of Algebraic Combinatoric

A Tonnetz Model for pentachords

This article deals with the construction of surfaces that are suitable for representing pentachords or 5-pitch segments that are in the same $T/I$ class. It is a generalization of the well known \"Ottingen-Riemann torus for triads of neo-Riemannian theories. Two pentachords are near if they differ by a particular set of contextual inversions and the whole contextual group of inversions produces a Tiling (Tessellation) by pentagons on the surfaces. A description of the surfaces as coverings of a particular Tiling is given in the twelve-tone enharmonic scale case.Comment: 27 pages, 12 figure

Micropolitical dynamics of interlingual translation processes in an MNC subsidiary

An analysis of the process whereby a Polish subsidiary of a North American pharmaceutical company translated a set of corporate values into Polis

From littérature engagée to engaged translation : staging Jean-Paul Sartre’s theatre as a challenge to Franco’s rule in Spain

The practice of creating translations that ‘rouse, inspire, witness, mobilize, and incite to rebellion’ is described by Maria Tymoczko, following Jean-Paul Sartre's littérature engagée, as ‘engaged translation’. In Spain, under the Franco dictatorship (1939–1975), the theatre became a site of opposition to his rule and the creation of ‘engaged’ translations of foreign plays was one of the ways in which alternative social and political realities were transmitted to local audiences. This was particularly evident during the so-called apertura period (1962–1969), when Spain's political leaders embraced more liberal and outward-facing cultural policies as part of their efforts to ensure the regime's continuity. Drawing on archival evidence from the state censorship files held at Archivo General de la Administración (AGA) in Alcalá de Henares, this article considers how ‘engaged’ translations of Sartre's theatre were employed as instruments of cultural opposition to the Spanish dictatorship. It also argues that an analysis of the files both helps us to understand the role of censorship in shaping an official version of the past, and shines a light on the memory of a little-studied aspect of cultural activism in the Spanish theatre.PostprintPeer reviewe

Cohomology of GKM Fiber Bundles

The equivariant cohomology ring of a GKM manifold is isomorphic to the cohomology ring of its GKM graph. In this paper we explore the implications of this fact for equivariant fiber bundles for which the total space and the base space are both GKM and derive a graph theoretical version of the Leray-Hirsch theorem. Then we apply this result to the equivariant cohomology theory of flag varieties.Comment: The paper has been accepted by the Journal of Algebraic Combinatorics. The final publication is available at springerlink.co

Living between languages: The politics of translation in Leila Aboulela’s Minaret and Xiaolu Guo’s A Concise Chinese-English Dictionary for Lovers

This is the author's final draft post-refereeing as published in The Journal of Commonwealth Literature 2012 47: 207 DOI:10.1177/0021989412440433. The online version of this article can be found at: http://jcl.sagepub.com/content/47/2/20

Teaching Intercultural Competence in Translator Training

In this position paper we define an interculturally competent translator as one that demonstrates a high level of intercultural knowledge, skills, attitude and flexibility throughout his or her professional engagements. We argue that to attain this goal in translator training intercultural competence needs to be introduced into the curriculum explicitly and in a conceptually clear manner. In this article we provide an overview of earlier attempts at discussing the role of intercultural communication in translator training curricula and we discuss the various pedagogical and practical challenges involved. We also look at some future challenges, identifying increasing societal diversity as both a source of added urgency into intercultural training and a challenge for traditional biculturally based notions of translators’ intercultural competence and we argue for the central role of empathy. Finally, and importantly, we introduce the contributions to the special issue

Reoccurring patterns in hierarchical protein materials and music: The power of analogies

Complex hierarchical structures composed of simple nanoscale building blocks form the basis of most biological materials. Here we demonstrate how analogies between seemingly different fields enable the understanding of general principles by which functional properties in hierarchical systems emerge, similar to an analogy learning process. Specifically, natural hierarchical materials like spider silk exhibit properties comparable to classical music in terms of their hierarchical structure and function. As a comparative tool here we apply hierarchical ontology logs (olog) that follow a rigorous mathematical formulation based on category theory to provide an insightful system representation by expressing knowledge in a conceptual map. We explain the process of analogy creation, draw connections at several levels of hierarchy and identify similar patterns that govern the structure of the hierarchical systems silk and music and discuss the impact of the derived analogy for nanotechnology.Comment: 13 pages, 3 figure

How Mathematicians Obtain Conviction: Implications for Mathematics Instruction and Research on Epistemic Cognition

This is an Accepted Manuscript of an article published by Taylor & Francis in Educational Psychologist on 16th January 2014, available online: http://wwww.tandfonline.com/10.1080/00461520.2013.865527The received view of mathematical practice is that mathematicians gain certainty in mathematical assertions by deductive evidence rather than empirical or authoritarian evidence. This assumption has influenced mathematics instruction where students are expected to justify assertions with deductive arguments rather than by checking the assertion with specific examples or appealing to authorities. In this paper, we argue that the received view about mathematical practice is too simplistic; some mathematicians sometimes gain high levels of conviction with empirical or authoritarian evidence and sometimes do not gain full conviction from the proofs that they read. We discuss what implications this might have, both for for mathematics instruction and theories of epistemic cognition