On the image of the Lawrence-Krammer representation

A non-singular sesquilinear form is constructed that is preserved by the Lawrence-Krammer representation. It is shown that if the polynomial variables q and t of the Lawrence-Krammer representation are chosen to be appropriate algebraically independant unit complex numbers, then the form is negative-definite Hermitian. Since unitary matrices diagonalize, the conjugacy class of a matrix in the unitary group is determined by its eigenvalues. It is shown that the eigenvalues of a Lawrence-Krammer matrix satisfy some symmetry relations. Using the fact that non-invertible knots exist, the symmetry relations imply that there are matrices in the image of the Lawrence-Krammer representation that are conjugate in the unitary group, yet the braids that they correspond to are not conjugate. The two primary tools involved in constructing the form are Bigelow's interpretation of the Lawrence-Krammer representation, together with Morse theory on manifolds with corners.Comment: 17 pages, 11 figure

Applying Lawrence: Teenagers and the Crime against Nature

The Supreme Court\u27s decision striking down a Texas statute prohibiting homosexual conduct in Lawrence v. Texas is vague in many ways. The opinion failed to articulate both the contours of the right the Court was recognizing and the level of scrutiny courts should apply when enforcing the right. When a question concerning the rights of minors arises under Lawrence, the answer is even more obscure. The Supreme Court of North Carolina faced precisely this question in a 2007 decision, in which the court considered whether Lawrence prohibited the state from prosecuting a minor for engaging in nontraditional sexual activity when the minor legally could have engaged in traditional, vaginal intercourse. This Note argues for an extension of Lawrence\u27s right to sexual privacy to minors when those minors may otherwise lawfully consent to sexual activity. Lawrence held the state may only infringe an adult\u27s right to sexual privacy when the state has some interest other than moral aversion to the sexual act itself. The Supreme Court has also held that minors generally share an adult\u27s right to privacy unless the state has a significant interest unique to the context of minors to justify the infringement. Because the state has no interest other than moral aversion when regulating the form of a minor\u27s sexual activity, this Note argues Lawrence should also protect minors

Lawrence K. Williams

[Excerpt] In 1952, Professor Williams graduated cum laude from Tufts University. He received his Masters Degree in 1954 from the University Illinois. In 1960, he earned a PhD in psychology from the University of Michigan. Professor Williams served in the U.S. Army from 1954-56, and worked as a research psychologist. In 1961 he came to Cornell University as an assistant professor, and became a full professor in 1969. When he retired in 1999, his colleagues awarded him an emeritus professorship. During his long career, Professor Williams served for a period as chairman of the Department of Organizational Behavior and for 25 years was the director of graduate studies for the school of Industrial and Labor Relations. He served on the committees of over 250 graduate students and was chairman for more than 70 students. He was also one of the founders and directors of GOALS, a foundation to support under represented minority graduate students in Human Resources and Industrial Relations. Professor Williams was also a Fulbright scholar in Peru during 1967-72

Germany's Stephen Lawrence

Campaigners in Germany, protesting at the suspicious death in custody of Oury Jalloh in 2005 and the subsequent cover-up by the criminal justice system, are looking to the Lawrence trial, the Macpherson Report and other British institutional responses to see how Germany could learn from the British experience

Living with Lawrence

This Article will proceed in three steps. First, I will examine the Court\u27s treatment of liberty. I see Lawrence as marking the emergence of a new approach to substantive due process analysis, one that has been simmering in the concurring opinions of Justices Souter, Stevens, and Kennedy for the last decade. These three Justices apparently now have a majority for extending meaningful constitutional protection to liberty interests without denominating them as fundamental rights. They also appear to be jettisoning, at least prospectively, a special category for privacy rights. Second, I will turn my attention to the ramifications of Lawrence\u27s equality subtext. The only equal protection opinion per se is the concurring opinion of Justice O\u27Connor, which is significant for its elaboration and clarification of the heightened rational-basis review standard the Court used in Romer v. Evans. Justice O\u27Connor\u27s opinion explicitly adopts a new form of rational-basis review triggered by indicia of animus toward the group being subjected to adverse treatment. Third, I aspire to read between all its lines and unravel the larger meanings of the liberty-equality dialogue embedded in the decision. In my view, the Lawrence opinion is in perfect tune with its times, articulating a new principle of equal liberty and resonating with a neoliberal political vision of civil rights

Higher Lawrence configurations

Any configuration of lattice vectors gives rise to a hierarchy of higher-dimensional configurations which generalize the Lawrence construction in geometric combinatorics. We prove finiteness results for the Markov bases, Graver bases and face posets of these configurations, and we discuss applications to the statistical theory of log-linear models.Comment: 12 pages. Changes from v1 and v2: minor edits. This version is to appear in the Journal of Combinatorial Theory, Ser.