Symplectic resolutions of quiver varieties

In this article, we consider Nakajima quiver varieties from the point of view of symplectic algebraic geometry. We prove that they are all symplectic singularities in the sense of Beauville and completely classify which admit symplectic resolutions. Moreover we show that the smooth locus coincides with the locus of canonically $$\theta $$ θ -polystable points, generalizing a result of Le Bruyn; we study their étale local structure and find their symplectic leaves. An interesting consequence of our results is that not all symplectic resolutions of quiver varieties appear to come from variation of GIT.

Epistemic injustice in psychiatric practice: epistemic duties and the phenomenological approach

Epistemic injustice is a kind of injustice that arises when one’s capacity as an epistemic subject (eg, a knower, a reasoner) is wrongfully denied. In recent years it has been argued that psychiatric patients are often harmed in their capacity as knowers and suffer from various forms of epistemic injustice that they encounter in psychiatric services. Acknowledging that epistemic injustice is a multifaceted problem in psychiatry calls for an adequate response. In this paper I argue that, given that psychiatric patients deserve epistemic respect and have a certain epistemic privilege, healthcare professionals have a pro tanto epistemic duty to attend to and/or solicit reports of patients’ first-person experiences in order to prevent epistemic losses. I discuss the nature and scope of this epistemic duty and point to one interesting consequence. In order to prevent epistemic losses, healthcare professionals may need to provide some patients with resources and tools for expressing their experiences and first-person knowledge, such as those that have been developed within the phenomenological approach. I discuss the risk of secondary testimonial and hermeneutical injustice that the practice of relying on such external tools might pose and survey some ways to mitigate it.

What Does it Mean to "Throw Away the Ladder"?

In this paper, I will demonstrate via reductio ad absurdum that a resolute reading of Wittgenstein’s Tractatus should reconsider their equation of “throwing away the ladder” with the “end of philosophy.” To do this, I will show that an inconsistency arises in Wittgenstein’s view regarding the relationship of philosophy and science since he associates “the correct method of philosophy” with the propositions of science at the end of the aforementioned text. Due to this, I will maintain that it is reasonable to posit that the sharp distinction that Wittgenstein makes between philosophy and science in the Tractatus is merely illusory. An interesting consequence of this is that if this interpretation holds then this provides sufficient grounds to maintain that what some scholars refer to as “the end of philosophy” may actually be the beginning of “Wittgenstein’s naturalism.”

A note on automorphism groups of symmetric cubic graphs

We study [Formula: see text]-arc-transitive cubic graph [Formula: see text], and give a characterization of minimal normal subgroups of the automorphism group. In particular, each [Formula: see text] with quasi-primitive automorphism group is characterized. An interesting consequence of this characterization states that a non-solvable minimal normal subgroup [Formula: see text] contains at most 2 copies of non-abelian simple group when it acts transitively on arcs, or contains at most 6 copies of non-abelian simple group when it acts regularly on vertices.

Aristotle’s Methodology for Natural Science in Physics 1-2: a New Interpretation

In this essay I will argue for an interpretation of the remarks of Physics 1.1 that both resolves some of the confusion surrounding the precise nature of methodology described there and shows how those remarks at 184a15-25 serve as important programmatic remarks besides, as they help in the structuring of books 1 and 2 of the Physics. I will argue that “what is clearer and more knowable to us” is what Aristotle goes on to describe in 1.2—namely, that nature exists and that natural things change—his basic starting-point for natural science. This, I shall hope to show, is the kind of “immediate” sense datum which Aristotle thinks must be further analyzed in terms of principles (archai) and then causes (aitia) over the course of Physics books 1 and 2 to lead to knowledge about the natural world.[1] Such an analysis arrives at, as I shall show, a definition (horismos) of nature not initially available from the starting-point just mentioned (i.e., it is in need of further analysis), and which is clearer by nature.[2] It is not my aim here to resolve longstanding debates surrounding Aristotle’s original intent in the ordering and composition of the first two books of the Physics, nor how the Physics is meant to fit into the Aristotelian corpus taken as a coherent whole, but rather to show that the first two books of the Physics, as they stand, fit with the picture of methodology for natural science presented to us in 1.1. [1] An interesting consequence of this, and one which I shall not pursue in this paper at any length, is that the progression from what is clearer to us and what is clearer by nature is by necessity a form of revision: i.e., the Physics should not be seen as a work validating the “starting-point” of 1.2 contra the monists, but a work which gradually builds to the language of matter and form as what is clearer by nature. [2] Viz., what we find at the beginning of 2.1: “this suggests that nature is a sort of source (arche) and cause (aition) of change and remaining unchanged in that to which it belongs primarily of itself, that is, not by virtue of concurrence” (192b20-22).

The polylog quotient and the Goncharov quotient in computational Chabauty–Kim Theory I

Polylogarithms are those multiple polylogarithms that factor through a certain quotient of the de Rham fundamental group of the thrice punctured line known as the polylogarithmic quotient. Building on work of Dan-Cohen, Wewers, and Brown, we push the computational boundary of our explicit motivic version of Kim’s method in the case of the thrice punctured line over an open subscheme of [Formula: see text]. To do so, we develop a greatly refined version of the algorithm of Dan-Cohen tailored specifically to this case, and we focus attention on the polylogarithmic quotient. This allows us to restrict our calculus with motivic iterated integrals to the so-called depth-one part of the mixed Tate Galois group studied extensively by Goncharov. We also discover an interesting consequence of the symmetry-breaking nature of the polylog quotient that forces us to symmetrize our polylogarithmic version of Kim’s conjecture. In this first part of a two-part series, we focus on a specific example, which allows us to verify an interesting new case of Kim’s conjecture.

Ordered models for concept representation

Basic notions linked with concept theory can be accounted for by partial order relations. These orders translate the fact that, for an agent, an object may be seen as a better or a more typical exemplar of a concept than anyother. They adequately model notions linked with categorial membership, typicality and resemblance, without any of the drawbacks that are classically encountered in conjunction theory. An interesting consequence of such a concept representation is the possibility of using the tools of non-monotonic logic to address some well-known problems of cognitive psychology. Thus, conceptual entailment and concept induction can be reexamined in the framework of preferential inference relations. This leads to a rigorous definition of the basic notions used in the study of category-based induction.

The Kobayashi–Royden metric on punctured spheres

This paper gives an explicit formula of the asymptotic expansion of the Kobayashi–Royden metric on the punctured sphere {\mathbb{CP}^{1}\setminus\{0,1,\infty\}} in terms of the exponential Bell polynomials. We prove a local quantitative version of the Little Picard’s Theorem as an application of the asymptotic expansion. Furthermore, the approach in the paper leads to the interesting consequence that the coefficients in the asymptotic expansion are rational numbers. Furthermore, the explicit formula of the metric and the conclusion regarding the coefficients apply to more general cases of {\mathbb{CP}^{1}\setminus\{a_{1},\ldots,a_{n}\}}, {n\geq 3}, as well, and the metric on {\mathbb{CP}^{1}\setminus\{0,\frac{1}{3},-\frac{1}{6}\pm\frac{\sqrt{3}}{6}i\}} will be given as a concrete example of our results.

The Truth in Modalism

This chapter takes up two further issues about Frege’s attitude towards modality. First, Frege doesn’t simply reject the relativization of truth. He gives amodalist explanations of linguistic phenomena that seem to show that truth is relative to time, and of talk of truth in various circumstances. Second, Frege’s truth-absolutism is not incompatible with two analyses of modality prominent in the history of philosophy: in terms of a priori knowledge and in terms of analytic truth. But Frege construes apriority and analyticity in logical terms. Thus, ultimately, Frege’s view is that if there are any modal distinctions, they amount to nothing more than logical distinctions. An interesting consequence of Frege’s accounts of apriority, analyticity, and modality is that they allow not only for synthetic a priori truths, but also necessary a posteriori and contingent a priori truths.

Spacetime can be neither discrete nor continuous

We show that our recent Bohr-like approach to black hole (BH) quantum physics implies that spacetime quantization could be energy-dependent. Thus, in a certain sense, spacetime can be neither discrete nor continuous. Our approach also permits to show that the “volume quantum” of the Schwarzschild spacetime increases with increasing energy during BH evaporation and arrives at a maximum value when the Planck scale is reached and the generalized uncertainty principle (GUP) prevents the total BH evaporation. Remarkably, this result does not depend on the BH original mass. The interesting consequence is that the behavior of BH evaporation should be the same for all Schwarzschild BHs when the Planck scale is approached.