Milnor numbers of projective hypersurfaces and the chromatic polynomial of graphs

The chromatic polynomial of a graph G counts the number of proper colorings of G. We give an affirmative answer to the conjecture of Read and Rota-Heron-Welsh that the absolute values of the coefficients of the chromatic polynomial form a log-concave sequence. We define a sequence of numerical invariants of projective hypersurfaces analogous to the Milnor number of local analytic hypersurfaces. Then we give a characterization of correspondences between projective spaces up to a positive integer multiple which includes the conjecture on the chromatic polynomial as a special case. As a byproduct of our approach, we obtain an analogue of Kouchnirenko's theorem relating the Milnor number with the Newton polytope.Comment: Improved readability. Final version, to appear in J. Amer. Math. So

Thoughts From A Public Librarian

I am fairly new to the Association of Christian Librarians and librarianship. This year, the 43rd conference, was my fourth ACL conference. I have been a reference librarian for about the same number of years. I felt a bit lost at my first conference. I would imagine most people do. I was just beginning to pursue my MLS and, most of my experience had been in public libraries. So, classes that focused on academic issues didn\u27t mean too much to me. However, other conference goers helped me choose a few subjects that could be adapted to public library service and it was clear sailing from then on. Now I choose subjects that I know will either expose me to something that will soon become a part of the public library scene, or a training session in some technical area that I can adapt to my needs

Book review: Unlocking Minds in Lockup

Education is a powerful tool that not only opens doors within prisons, but international research would indicate education also, and more crucially, prevents men and women from re-entering those same doors back to prison. Therefore Jan Walker’s recently published Unlocking Minds in Lockup: Prison Education Opens Doors is a welcome addition to the already rich literature on this subject

Book Review: Interpreting Ramakrishna: Kali\u27s Child Revisited

A review of Interpreting Ramakrishna: Kali\u27s Child Revisited by Swami Tyagananda and Pravrajika Vrajaprana

Family learning: "What's the score?"

Family Learning through Football and Coaching (FLTFC) was developed with Sunderland Association Football Club (SAFC) Foundation, an adult basic skills provider, a primary school and the Open College Network. Ten years on this programme has high participation rates and is recognised for its capacity to engage the ‘hard-to-reach’ in learning. This paper provides a focused historical analysis and attempts to locate family learning in relation to policy, local authority structures and educational discourse. As cuts to public services continue, there is an expectation that the third sector, including social enterprises such as SAFC Foundation, will step in to fill the gap. The success of FLTFC could be presented as evidence of the effectiveness of the Big Society agenda however taking the long view it is evident that partnership with the public sector is an essential element in the development and continuity of successful provision. The theoretical framework which informs the paper incorporates brief consideration of the concept of lifelong learning and an examination of informal learning in the context of the family. The emerging localism agenda and issues relating to the current Coalition government's Big Society concept also inform the discussion. The paper will contribute to understanding of support for learning within families by providing a historical analysis of the endurance and success of a specific family learning programme. The findings of this study have the potential to contribute to the implementation of policy arising from the current review of adult informal community learning (BIS, 2011)