Creating Work That Matters: Memphis Choreographs to the Soul of a City

Explores the artistic development of Ballet Memphis -- how it became a thriving company within a community that had not historically supported ballet, and how it continues to evolve artistically while remaining relevant to the community

Going Beyond the Kantian Philosophy: On McDowell's Hegelian Critique of Kant

The Kant-Hegel relation has a continuing fascination for commentators on Hegel, and understandbly so: for, taking this route into the Hegelian jungle can promise many advantages. First, it can set Hegel's thought against a background with which we are fairly familiar, and in a way that makes its relevance clearly apparent; second, it can help us locate Hegel in the broader philisophical tradition, making us see that the traditional "analytic jump from Kant to Frege leaves out a crucial period in post-Kantian thought, third, it can show Hegel in a progressive light, as attempting to take that tradition further forward; fourth, it can help us locate familiar philisophical issues in Hegelian thought that other-wise can appear whooly sui generis; and finally, and perhaps most importantly of all, focusing on this relation can help raise and crystalise some of the fascinating ambiguties concerning Hegel's outlook, regarding whether Hegel's response to Kant shows him to have been a reactionary, Romantic, pre-critical thinker, who sought to turn the philosophical clock back to a time before Kant had written, or a modernist, Enlightented and essentially critical one, who remained true to the spirit if not the letter of Kant's philosophy

Banach space projections and Petrov-Galerkin estimates

We sharpen the classic a priori error estimate of Babuska for Petrov-Galerkin methods on a Banach space. In particular, we do so by (i) introducing a new constant, called the Banach-Mazur constant, to describe the geometry of a normed vector space; (ii) showing that, for a nontrivial projection $P$, it is possible to use the Banach-Mazur constant to improve upon the naive estimate $\| I - P \| \leq 1 + \| P \|$; and (iii) applying that improved estimate to the Petrov-Galerkin projection operator. This generalizes and extends a 2003 result of Xu and Zikatanov for the special case of Hilbert spaces.Comment: 9 pages; v2: added new section on application to Lp and Sobolev space

Remarks on an Exact Seiberg-Witten map

We obtain the leading derivative corrections to an expression for the Seiberg-Witten map given by Banerjee and Yang and show how they affect the noncommutative deformation of the Maxwell action, as well as the matter coupling in noncommutative emergent gravity.Comment: 8 page