The B(G)-parametrization of the local Langlands correspondence

This article is on the parametrization of the local Langlands correspondence over p-adic fields for non-quasi-split groups according to the philosophy of Vogan. We show that a parametrization indexed by the basic part of the Kottwitz set (which is an extension of the set of pure inner twists) implies a parametrization indexed by the full Kottwitz set. On the Galois side, we consider irreducible algebraic representations of the full centralizer group of the L-parameter (i.e not a component group). These yield sheaves on the stack of Langlands parameters.Comment: 15 page

The stable trace formula for Igusa varieties, II

Assuming the trace formula for Igusa varieties in characteristic p, which is known by Mack-Crane in the case of Hodge type with good reduction at p, we stabilize the formula via Kaletha's theory of rigid inner twists when the reductive group in the underlying Shimura datum is quasi-split at p. This generalizes our earlier work under more restrictive hypotheses.Comment: 49 pages, comments welcom

Teleology and Realism in Leibniz's Philosophy of Science

This paper argues for an interpretation of Leibniz’s claim that physics requires both mechanical and teleological principles as a view regarding the interpretation of physical theories. Granting that Leibniz’s fundamental ontology remains non-physical, or mentalistic, it argues that teleological principles nevertheless ground a realist commitment about mechanical descriptions of phenomena. The empirical results of the new sciences, according to Leibniz, have genuine truth conditions: there is a fact of the matter about the regularities observed in experience. Taking this stance, however, requires bringing non-empirical reasons to bear upon mechanical causal claims. This paper first evaluates extant interpretations of Leibniz’s thesis that there are two realms in physics as describing parallel, self-sufficient sets of laws. It then examines Leibniz’s use of teleological principles to interpret scientific results in the context of his interventions in debates in seventeenth-century kinematic theory, and in the teaching of Copernicanism. Leibniz’s use of the principle of continuity and the principle of simplicity, for instance, reveal an underlying commitment to the truth-aptness, or approximate truth-aptness, of the new natural sciences. The paper concludes with a brief remark on the relation between metaphysics, theology, and physics in Leibniz