Avoided level crossings in the quantization of a mixed regular-chaotic system

The study of avoided level crossings in the spectra of quantum Hamiltonians whose classical counterparts exhibit mixed regular-chaotic dynamics reveals important information about the quantum signatures of such dynamics. Among other topics, one can study delocalization phenomena and exchange of structure in Husimi distributions and compare the quantum dynamics one observes to the dynamics of corresponding classical systems at the same parameter values

Beyond wild walls there is algebraicity and exponential growth (of BPS indices)

textThe BPS spectrum of pure SU(3) four-dimensional super Yang-Mills with N=2 supersymmetry (a theory of class S(A)) exhibits a surprising phenomenon: there are regions of the Coulomb branch where the growth of BPS-indices with the charge is exponential. We show this using spectral networks and, independently, using wall-crossing formulae and quiver methods. The technique using spectral networks hints at a general property dubbed "algebraicity": generating series for BPS-indices in theories of class S(A) (a class of N=2 four-dimensional field theories) are secretly algebraic functions over the rational numbers. Kontsevich and Soibelman have an independent understanding of algebraicity using indirect techniques, however, spectral networks give a distinct reason for algebraicity with the advantage of providing explicit algebraic equations obeyed by generating series; along these lines, we provide a novel example of such an algebraic equation, and explore some relationships to Euler characteristics of Kronecker quiver stable moduli. We conclude by proving that exponential asymptotic growth is a corollary of algebraicity, leading to the slogan "there are either finitely many BPS indices or exponentially many" (in theories of class S(A)).Physic

Women directors on corporate boards: A review and research agenda

Review This review examines how gender diversity on corporate boards influences corporate governance outcomes that in turn impact performance. We describe extant research on theoretical perspectives, characteristics, and impact of women on corporate boards (WOCB) at micro, meso, and macro levels: individual, board, firm, and industry/environment. To the best of our knowledge, this is the first comprehensive review of WOCBs, incorporating and integrating research from over 400 publications in psychology, sociology, leadership, gender, finance, management, law, corporate governance, and entrepreneurship domains. In addition, we organized our findings to provide a new lens enabling the field to be readily examined by level and by theoretical perspective. The review indicates that WOCB research is about improving corporate governance through better use of the whole talent pool's capital, as well as about building more inclusive and fairer business institutions that better reflect their present generation of stakeholders. With only one in 10 papers addressing theoretical development, the predominant perspectives are human and social capital theories and gender schema at the individual level; social identity, token, and social networks theories at board level; resource dependency, institution, and agency theories at the firm level; and institutional, critical, and political theories at the environmental level. We provide a short synopsis of findings at each level, and conclude with an outline of fruitful directions for future research. There are increasing pressures for WOCBs from diverse stakeholders, such as the European Commission, national governments, politicians, employer lobby groups, shareholders, Fortune and FTSE rankings, best places for women to work lists, as well as expectations from highly qualified women who are likely to leave if they see no women board members. Rationales generally draw on the business case; however, the moral justice case is also used by those who seek a fairer gender balance in all aspects of society. From our review, the "Impact" section charts the effect of WOCB at all four levels of analysis