We give a complete picture of the interaction between Koszul and Ringel dualities for quasi-hereditary algebras admitting linear tilting (co)resolutions of standard and costandard modules. We show that such algebras are Koszul, that the class of these algebras is closed with respect to both dualities and that on this class these two dualities commute. All arguments reduce to short computations ...

These lectures briefly introduce dualities in four-dimensional quantum field theory, and summarize results found in supersymmetric field theories. The first lecture describes physical aspects of electric-magnetic (EM), strong-weak coupling (S), and infrared (IR) dualities. The second lecture focuses on results and conjectures concerning S-duality in N=2 supersymmetric gauge theories. The third ...

We study the effect of diagram automorphisms on rank-level duality. We create new symplectic rank-level dualities from T. Abe’s symplectic rank-level duality on genus zero smooth curves with marked points and chosen coordinates. We also show that ranklevel dualities for the pair sl(r), sl(s) in genus 0 arising from representation theory can also be obtained from the parabolic strange dualities ...

In this paper I develop a framework for relating dualities and emergence: two notions that are close to each other but also exclude one another. I adopt the conception of duality as ‘isomorphism’, from the physics literature, cashing it out in terms of three conditions. These three conditions prompt two conceptually different ways in which a duality can be modified to make room for emergence; a...

In this paper we survey results related to homomorphism dualities for graphs, and more generally, for finite structures. This is related to some of the classical combinatorial problems, such as colorings of graphs and hypergraphs, and also to recently intensively studied Constraint Satisfaction Problems. On the other side dualities are related to the descriptive complexity and First Order defin...

We provide tests of dualities for three-dimensional N = 4 quiver SCFTs with brane realizations in IIB string theory, by matching their exact partition functions on S3. The dualities are generated by SL(2,Z) transformations and Hanany-Witten 5-brane moves. These contain mirror symmetry as well as dualities identifiying fixed points of Yang-Mills quivers and Chern-Simons theories. The partition f...

Mappings between certain infinite series of N = 2 superconformal coset models are constructed. They make use of level-rank dualities for B, C and D type WZW theories, which are described in some detail. The WZW level-rank dualities do not constitute isomorphisms of the theories; for example, for B and D type WZW theories, only simple current orbits rather than individual primary fields are mapp...

Leadership has a renewed focus in healthcare, and physicians are being increasingly involved in a range of leadership roles. The aim of this paper is to discuss several dualities that exert tensions at the systems and individual levels. Although oppositional, the common dualities of physician leadership are not mutually exclusive but represent a complex, dynamic and interdependent relationship,...