The Functional Equation and Beyond Endoscopy

In his paper "Beyond Endoscopy," Langlands tries to understand functoriality via poles of L-functions. The following paper further investigates the analytic continuation of a L-function associated to a $GL_2$ automorphic form through the trace formula. Though the usual way to obtain the analytic continuation of an L-function is through its functional equation, this paper shows that by simply assuming the trace formula, the functional equation of the L-function may be recovered. This paper is a step towards understanding the analytic continuation of the L-function at the same time as capturing information about functoriality. From an analytic number theory perspective, obtaining the functional equation from the trace formula implies that Voronoi summation should in general be also a consequence of the trace formula.Comment: 13 pgs. Dedicated to Jonathan Rogawsk

Polytheism and the Euthyphro

In this reading of the Euthyphro, Socrates and Euthyphro are seen less in a primordial conflict between reason and devotion, than as sincere Hellenic polytheists engaged in an inquiry based upon a common intuition that, in addition to the irreducible agency of the Gods, there is also some irreducible intelligible content to holiness. This reading is supported by the fact that Euthyphro does not claim the authority of revelation for his decision to prosecute his father, but rather submits it to elenchus, and that Euthyphro does not embrace the ‘solution’ of theological voluntarism when Socrates explicitly offers it. Since the goal of this inquiry is neither to eliminate the noetic content of the holy, nor to eliminate the Gods’ agency, the purpose of the elenchus becomes the effort to articulate the results of this productive tension between the Gods and the intelligible on the several planes of Being implied by each conception of the holy which is successively taken up and dialectically overturned to yield the conception appropriate to the next higher plane, a style of interpretation characteristic of the ancient Neoplatonists

"Allegro Barbaro" for band

Thesis (M.M.E.)--Boston Universit

Transformation and Individuation in Giordano Bruno's Monadology

The essay explores the systematic relationship in the work of Giordano Bruno (1548-1600) between his monadology, his metaphysics as presented in works such as De la causa, principio et uno, the mythopoeic cosmology of Lo spaccio de la bestia trionfante, and practical works like De vinculis in genere. Bruno subverts the conceptual regime of the Aristotelian substantial forms and its accompanying cosmology with a metaphysics of individuality that privileges individual unity (singularity) over formal unity and particulars over substantial forms without sacrificing a metaphysical perspective on the cosmos. The particular is individuated as a unique site of desire, continually transforming but able to entrain itself and others through phantasmatic ‘bonding’, the new source of regularity in Bruno’s polycentric universe. Bruno thus tries to do justice to the demands of intelligibility as well as transformative eros. The essay concludes with a note on Bruno’s geometry as it relates to his general conception of form