Hilbert-Smith Conjecture for K - Quasiconformal Groups

MSC 2010: 30C60

RIEMANN ZETA ZEROS AND PRIME NUMBER SPECTRA IN QUANTUM FIELD THEORY

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Minimal Hilbert series for quadratic algebras and the Anick conjecture

We study the question on whether the famous Golod–Shafarevich estimate, which gives a lower bound for the Hilbert series of a (noncommutative) algebra, is attained. This question was considered by Anick in his 1983 paper ‘Generic algebras and CW-complexes’, Princeton Univ. Press, where he proved that the estimate is attained for the number of quadratic relations $d\leq n^2/4$
and $d\geq n^2/2$, and conjectured that it is the case for any number of quadratic relations. The particular point where the number of relations is equal to $n(n-1)/2$ was addressed by Vershik. He conjectured that a generic algebra with this number of relations is finite dimensional. We announce here the result that over any infinite field, the Anick conjecture holds for $d \geq 4(n2+n)/9$ and an arbitrary number of generators. We also discuss the result that confirms the Vershik conjecture over any field of characteristic 0, and a series of related
asymptotic results.

Graphs of relations and Hilbert series

We are discussing certain combinatorial and counting problems related to quadratic algebras. First we give examples which confirm the Anick conjecture on the minimal Hilbert series for algebras given by $n$ generators and $\frac {n(n-1)}{2}$ relations for $n \leq 7$. Then we investigate combinatorial structure of colored graph associated to relations of RIT algebra. Precise descriptions of graphs (maps) corresponding to algebras with maximal Hilbert series are given in certain cases. As a consequence it turns out, for example, that RIT algebra may have a maximal Hilbert series only if components of the graph associated to each color are pairwise 2-isomorphic.

Toward Clemens' Conjecture in Degrees between 10 and 24

1 Supported in part by the Norwegian Research Council for Science and the Humanities. It is a pleasure for this author to thank the Department of Mathematics of the University of Sofia for organizing the remarkable conference in Zlatograd during the period August 28-September 2, 1995. It is also a pleasure to thank the M.I.T. Department of Mathematics for its hospitality from January 1 to July 31, 1993, when this work was started. 2Supported in part by NSF grant 9400918-DMS.

Gemma Smith and the intuitive abstract

This article examines the work of Brisbane artist Gemma Smith. It investigates the artist's career and her developmental abstract paintings and sculptures. It argues that the artist is fundamentally intuitive in her approach to the genre and also employs mimicry of certain abstract styles as a means through which to develop her own creative outcomes.

Adam Smith's Dinner

The Future of Financial Regulation is an edited collection of papers presented at a major conference at the University of Glasgow in Spring 2009. It draws together a variety of different perspectives on the international financial crisis which began in August 2007 and later turned into a more widespread economic crisis following the collapse of Lehman Brothers in the Autumn of 2008. Spring 2009 was in many respects the nadir since valuations in financial markets had reached their low point and crisis management rather than regulatory reform was the main focus of attention. The conference and book were deliberately framed as an attempt to re-focus attention from the former to the latter. The first part of the book focuses on the context of the crisis, discussing the general characteristics of financial crises and the specific influences that were at work during this time. The second part focuses more specifically on regulatory techniques and practices implicated in the crisis, noting in particular an over-reliance on the capacity of regulators and financial institutions to manage risk and on the capacity of markets to self-correct. The third part focuses on the role of governance and ethics in the crisis and in particular the need for a common ethical framework to underpin governance practices and to provide greater clarity in the design of accountability mechanisms. The final part focuses on the trajectory of regulatory reform, noting the considerable potential for change as a result of the role of the state in the rescue and recuperation of the financial system and stressing the need for fundamental re-appraisal of business and regulatory models. This informative book will be of interest to financial regulators and theorists, commercial and financial law practitioners, and academics involved in the law and economics of regulation.

Adam Smith's dinner

In 1961, the East German government erected what they claimed was an anti-capitalist barricade. In 1989, this barricade was dismantled by those whom it was supposed to keep apart: the forces it was intended to contain had overwhelmed it. In the aftermath, the victims of Stalinist oppression and the planned economy opted for radical change. Some might have hoped that they would intellectually march resolutely westwards towards the forms of social democracy that had proven so successful in their nearest neighbours – Scandinavia, Germany and Austria – and stop when they had reached a point on the political spectrum with which they felt comfortable, and which worked for them. Unfortunately, they went to the opposite end of political economy. That choice was celebrated by those theorists who wanted our own countries to move in the same direction. Eastern Europe suffered a decline of 50% in its GDP. Much earlier in 1653, Peter Stuyvesant had erected an earth and wooden wall to protect the westernmost settlement of a great commercial nation from those they imagined to be barbarians. In 1699 Stuyvesant’s barrier was dismantled by the British, who replaced it with a street named after the wall. So it came to be that one of the most inconsequential walls in history became one of history’s most famous streets. I am not sure if the Dutch had left some tulip bulbs on either side of the wall, perhaps as a reminder of capitalism’s first bubble, and an inspiration to later bubbles. However, many of the victims of the latest burst bubble are pretty keen to tear down that Wall.1 As in 1989, they want to take action against the guardians of the system that failed them. And the more they suffer, the more likely it is that they will demand radical change, and the more likely that the resulting change will go too far – as seems to have been the case in Eastern Europe after the terminal crisis of communism, and in the majority of democracies that fell in the dozen years following the Great Crash. The current reaction is so strong that some are even wondering what role there will be for markets. I was invited to address a conference in the EU Parliament last November on the topic ‘Capitalism: Quo Vadis?’, where I apologized to the international audience that the topic was posed in a dead European language because the answer to this question is not going to be determined by the west alone. The problems we have been addressing emerged in the west and have affected the rest. However, the answers will not come, solely from the west, and may even come primarily from the south and the east.

Review ["Telling the Evolutionary Time : Molecular Clocks and the Fossil Record" edited by Philip C. J. Donoghue and M. Paul Smith]

Determining the temporal scale of biological evolution has traditionally been the preserve of paleontology, with the timing of species originations and major diversifications all being read from the fossil record. However, the ages of the earliest (correctly identified) records will underestimate actual origins due to the incomplete nature of the fossil record and the necessity for lineages to have evolved sufficiently divergent morphologies in order to be distinguished. The possibility of inferring divergence times more accurately has been promoted by the idea that the accumulation of genetic change between modern lineages can be used as a molecular clock (Zuckerkandl and Pauling, 1965). In practice, though, molecular dates have often been so old as to be incongruent even with liberal readings of the fossil record. Prominent examples include inferred diversifications of metazoan phyla hundreds of millions of years before their Cambrian fossil record appearances (e.g., Nei et al., 2001) and a basal split between modern birds (Neoaves) that is almost double the age of their earliest recognizable fossils (e.g., Cooper and Penny, 1997).

"What is contemporary art? A review of two books by Terry Smith'

What is contemporary art and what are the key components of contemporary culture? This review demonstrates where Terry Smith provides important answers to this question. The books thus help to improve understanding of how art has changed in recent decades and how a global culture now shapes its parameters. This review does not however concur that Smith provides a convincing case for a complete cultural paradigm transformation.