Informal notes for a talk at UNCG on reciprocity laws (such as quadratic reciprocity and Shimura-Taniyama). This material is from Fearless Symmetry by Ash and Gross [1] and Galois Representations and Modular Forms by Ribet [2].

The standard theories of cooperation in humans, which depend on repeated interaction and reputation effects among self-regarding agents, are inadequate. Strong reciprocity, a predisposition to participate in costly cooperation and the punishment, fosters cooperation where self-regarding behaviors fail. The effectiveness of socially coordinated punishment depends on individual motivations to par...

This paper surveys the evolutionary game theoretic literature on reciprocity in human interactions, dealing both with long-term relationships and with sporadic interactions. Four basic themes, repetition, commitment, assortation, and parochialism, appear repeatedly throughout the literature. Repetition can give rise to the evolution of behavior that exhibits reciprocity-like features but a vast...

The purpose of this paper is to give a reciprocity between Uq(h) and Hn,r, the Hecke algebra of (Z/rZ) ≀ Sn introduced by Ariki and Koike [1]. The Schur-Weyl reciprocity was originally discovered for GL(m) and Sn [17, p.130]. This is the first example of dual pairs and has been generalized to various pairs of groups and algebras. Jimbo [10] proved a q-analogue of the original reciprocity, namel...

BACKGROUND The persistent lack of evidence on causal mechanisms between social capital and health threatens the credibility of the social capital-health association. The present study aims to address this ongoing problem by investigating whether health behaviours (i.e. smoking, alcohol consumption, and physical activity) mediate the prospective relation between workplace reciprocity and future ...

Objective: The ways people use for social rank (dominance vs prestige) could explain difference attitude toward five moral foundations. The aim of this study was to investigate the differential relationship between prestige, dominance and moral foundations. Methods: This study conducted with 150 participants who respond to the moral foundation questionnaire and dominance-prestige scale. Multip...