455 research outputs found
Interview with Martin Wachs, January 2015
No full textThis document contains the content of an oral history interview and is part of a series of inter-views conducted by the Alan M. Voorhees Transportation Center (VTC). These interviews are personal, experiential, and interpretative, reflecting the memories and associations of individuals. All reasonable attempts are made to ensure accuracy, but statements should not be interpreted as facts endorsed by Rutgers University, the Edward J. Bloustein School, or VTC. The associated website also contains links to other resources, but does not endorse or guarantee their content.Transcrip
Hate Speech thematisieren: (K)eine Aufgabe für eine liberale öffentliche Allgemeinbildung?! Reflexionen zu zwölf Unterrichtsbeispielen aus Japan und Deutschland
No full textKoch-Priewe B. Hate Speech thematisieren: (K)eine Aufgabe für eine liberale öffentliche Allgemeinbildung?! Reflexionen zu zwölf Unterrichtsbeispielen aus Japan und Deutschland. In: Wachs S, Koch-Priewe B, Zick A, eds. Hate Speech - Multidisziplinäre Analysen und Handlungsoptionen. Theoretische und empirische Annäherungen an ein interdisziplinäres Phänomen. Wiesbaden: Springer Fachmedien Wiesbaden; 2021: 191-226.Der Beitrag greift unter Bezug auf einen Lehrkräfteaustausch zwischen Deutschland und Japan zu „Hate Speech als Unterrichtsthema“ mehrere Fragestellungen auf: Sollte anti-diskriminierender Unterricht als eine „Präventions- bzw. Interventionsmaßnahme“ und Demokratieerziehung als eine „schulische Querschnittsaufgabe“ bezeichnet werden? Zum Zusammenhang von Allgemeinbildung, Demokratie und Öffentlichkeit werden Thesen vorgestellt und die Frage verfolgt, welche Konsequenzen für Konzepte der Demokratieerziehung zu ziehen sind, wenn man auf Strategien des Demokratieabbaus in autoritaristischen Systemen wie unter anderem in Japan blickt? In diesem Kontext werden Ergebnisse aus dem interkulturellen Lehrkräfte-Austausch zu „Hate Speech als Unterrichtsthema“ präsentiert. Sie münden in die Frage nach geeigneten Konzepten eines allgemeinbildenden Unterrichts, der auch der Demokratieerziehung dient
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Whitney Homology of Semipure Shellable Posets
No full textWe generalize results of Calderbank, Hanlon and Robinson on the representation of the symmetric group on the homology of posets of partitions with restricted block size. Calderbank, Hanlon and Robinson consider the cases of block sizes that are congruent to 0 mod d and 1 mod d for fixed d. We derive a general formula for the representation of the symmetric group on the homology of posets of partitions whose block sizes are congruent to k mod d for any k and d. This formula reduces to the Calderbank-Hanlon-Robinson formulas when k = 0, 1 and to formulas of Sundaram for the virtual representation on the alternating sum of homology. Our results apply to restricted block size partition posets even more general than the k mod d partition posets. These posets include the lattice of partitions whose block sizes are bounded from below by some fixed k. Our main tools involve the new theory of nonpure shellability developed by Björner and Wachs and a generalization of a technique of Sundaram which uses Whitney homology to compute homology representations of Cohen-Macaulay posets. An application to subspace arrangements is also discussed
On Lie k-Algebras
No full textAbstractWe define the notion of a "Lie k-algebra" to be a (k + 1)-ary skew-symmetric operation on a bigraded vector space which satisfies a certain relation of degree 2k + 1. The notion of Lie 1-algebra coincides with the notion of Lie superalgebra. An ordinary Lie algebra is precisely a Lie 1-algebra with odd elements. We show first that the boundary map in the Koszul complex (constructed as the Koszul complex for ordinary Lie algebras) squares to zero. We then show that the 1nk +1 homogeneous part of the free Lie k-algebra with (nk + 1) even generators is isomorphic, as an Snk+1-module, to the cohomology of Π(1)nk +1, the poset of all partitions of nk + 1 in which every block size is congruent to 1 mod k. This result is analogous to a classical result relating the free Lie algebra with n generators to the cohomology of the partition lattice. We also construct an explicit basis for the 1nk +1 homogeneous part of the free Lie k-algebra with nk + 1 even generators and for the cohomology of Π(1)nk +1. Lastly, we compute the Lie k-algebra homology of the free Lie k-algebra
Crime Victim Stories
No full textCrime Victim Stories looks at the frightening world of urban violence. Eleanor Wachs analyzes stories of muggings and other crime experiences told by native New Yorkers. By using the personal-experience narrative, the author shows how these shocking stories about the danger and violence of city streets reveal attitudes toward crime, urban groups, and life in general in New York City. These true accounts, frequently embedded in social conversations, suggest ways in which city folk plan to thwart future victimization and tell how a candidate for a mugging—almost anyone—can avoid becoming a victim. These narratives reveal that two standard folklore forms, the urban legend and the shaggy dog story, are the underlying models of crime-victim stories. Oral stories about urban crime often differ from their newspaper counterparts, demonstrating the tenacity of oral tradition in a cosmopolitan environment. Readers will be surprised to learn that these horrifying, and sometimes titillating, stories are filled with stock characters such as the trickster mugger and the clever victim who try to outsmart each other. Crime Victim Stories presents oft-told tales of city life that sometimes shock, often entertain, and also enhance our understanding of daily experience in what is believed to be one of America's most dangerous cities
Crime Victim Stories
No full textCrime Victim Stories looks at the frightening world of urban violence. Eleanor Wachs analyzes stories of muggings and other crime experiences told by native New Yorkers. By using the personal-experience narrative, the author shows how these shocking stories about the danger and violence of city streets reveal attitudes toward crime, urban groups, and life in general in New York City. These true accounts, frequently embedded in social conversations, suggest ways in which city folk plan to thwart future victimization and tell how a candidate for a mugging—almost anyone—can avoid becoming a victim. These narratives reveal that two standard folklore forms, the urban legend and the shaggy dog story, are the underlying models of crime-victim stories. Oral stories about urban crime often differ from their newspaper counterparts, demonstrating the tenacity of oral tradition in a cosmopolitan environment. Readers will be surprised to learn that these horrifying, and sometimes titillating, stories are filled with stock characters such as the trickster mugger and the clever victim who try to outsmart each other. Crime Victim Stories presents oft-told tales of city life that sometimes shock, often entertain, and also enhance our understanding of daily experience in what is believed to be one of America's most dangerous cities
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The Topology of k–Equal Partial Decomposition Lattices
No full textThe lattice B_n of subsets of the set {1, 2, ..., n} ordered by inclusion and the lattice \Pi_n of partitions of {1, 2, ..., n} ordered by refinement are two of the most fundamental examples in the theory of partially ordered sets (posets). A natural well-studied q–analogue of the subset lattice is the lattice B_n(q) of subspaces of the n–dimensional vector space F^n_q over the field F_q with q elements ordered by inclusion. There are many justifications for viewing this as a q–analogue. One comes from the fact that the number of maximal chains of B_n is n!, while the number of maximal chains of B_n(q) equals the q–analogue of n! which is defined by [n]_q! := [n]_q[n − 1]_q . . . [1]_q, where [n]_q := 1 + q + · · · + q^{n−1}. Another justification comes from studying the topology of a certain simplicial complex associated with the poset, called the order complex. The order complex associated with B_n is homeomorphic to a single sphere of dimension n−2, while the order complex associated with B_n(q) has the homotopy type of a wedge of q^{\binom{n}{ 2}} spheres of dimension n − 2. It is well-known that the order complex associated with \Pi_n has the homotopy type of a wedge of (n−1)! spheres of dimension n−3. Various q–analogues of the partition lattice \Pi_n have been proposed over the years, starting with the Dowling lattices introduced in a 1973 paper of Dowling. Posets studied by Welker and by Hanlon, Hersh, and Shareshian involve direct sum decompositions of vector spaces over F_q. While these posets have interesting properties analogous to those of \Pi_n, such as having the homotopy type of a wedge of spheres, none have the desirable property that the number of spheres is a q–analogue of (n−1)!. The q–analogue proposed in this thesis is the poset \Pi_n(q) of direct sum decompositions of subspaces of F^n_q whose summands all have dimension at least 2, ordered by inclusion of summands. This is actually a q–analogue of a poset that is isomorphic to \Pi_n, namely the poset of partitions of subsets of {1, 2, ..., n} in which each block has size at least 2. We show that the order complex associated with \Pi_n(q) has the homotopy type of a wedge of f(q)[n−1]_q! spheres of dimension n − 3 where f(q) is a polynomial in q that is equal to 1 when q is set equal to 1. In order to prove this result, we initiate a study of a much more general class of posets, which includes \Pi_n, \Pi_n(q), and the k–equal partition lattices introduced by Björner, Lovász, and Yao in 1992. The k–equal partition lattice \Pi^{=k}_ n is the subposet of \Pi_n consisting of partitions for which each block has size at least k or 1. In this general class, the roles of B_n and B_n(q) in the definitions of \Pi_n and \Pi_n(q) are played by an arbitrary geometric lattice L. We use shellability theory to prove that the order complex associated with a general k–equal decomposition lattice \Pi^{=k}_ L has the homotopy type of a wedge of spheres in varying dimensions when k > 2 and just in dimension n − 3 when k = 2. Shellability theory also enables us to derive a complicated formula for the number of spheres in each dimension. The nontrivial step of reducing the complicated formula in the case of \Pi^{=2}_{ Bn(q)} = \Pi_n(q) to the desired f_n(q)[n − 1]_q! formula uses Stanley’s theory of exponential structures.</p
ON THE PROPERTY M CONJECTURE FOR THE HEISENBERG LIE ALGEBRA
No full textAbstract. We prove a fundamental case of a conjecture of the first author which expresses the homology of the extension of the Heisenberg Lie algebra by C[t]/(t k+1) in terms of the homology of the Heisenberg Lie algebra itself. More specifically, we show that both the 0 th and k +1 st x-graded components of homology of this extension of the 3-dimensional Heisenberg Lie algebra have dimension 3 k+1 by constructing a simple basis for cohomology. 1
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Dimension filtration, sequential Cohen-Macaulayness and a new polynomial invariant of graded algebras
No full textLet k be a field and let A be a standard N-graded k-algebra. Using numerical information of some invariants in the primary decomposition of 0 in A, namely the so-called dimension filtration, we associate a bivariate polynomial BW(A;t,w), that we call the Björner-Wachs polynomial, to A.It is shown that the Björner-Wachs polynomial is an algebraic counterpart to the combinatorially defined h-triangle of finite simplicial complexes introduced by Björner & Wachs. We provide a characterisation of sequentially Cohen-Macaulay algebras in terms of the effect of the reverse lexicographic generic initial ideal on the Björner-Wachs polynomial. More precisely, we show that a graded algebra is sequentially Cohen-Macaulay if and only if it has a stable Björner-Wachs polynomial under passing to the reverse lexicographic generic initial ideal. We conclude by discussing some connections with the Hilbert series of local cohomology modules, extremal Betti numbers and combinatorial Alexander duality.</p
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