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Groups Combinatorics & Geometry
Over the past 20 years, the theory of groups in particular simplegroups, finite and algebraic has influenced a number of diverseareas of mathematics. Such areas include topics where groups have beentraditionally applied, such as algebraic combinatorics, finitegeometries, Galois theory and permutation groups, as well as severalmore recent developments.
Symmetric Functions 2001: Surveys of Developments and Perspectives
Proceedings of the NATO Advanced Study Institute, held in Cambridge, UK, from 25th June to 6th July, 2001
The Future Public Health
This is a public health text aimed at bridging the gap between current public health values and skills and those required to tackle future challenges.
New Perspectives in Algebraic Combinatorics
This text contains expository contributions by respected researchers on the connections between algebraic geometry, topology, commutative algebra, representation theory, and convex geometry.
The Gun Ringer
None
Chasing Phil
‘Christ! You guys look like a couple of Feds.’ 1977, the Thunderbird Motel. J.J. Wedick and Jack Brennan - Two fresh-faced FBI agents were about to go undercover. Their target: the charismatic, globe-trotting con man Phil Kitzer, who was responsible for swindling (and spending) millions of dollars and who some called the world’s greatest. One problem, the FBI under J Edgar Hoover didn’t really do undercover operations or fraud investigations. So they did it anyway, making it up as they went along. As the young agents became entangled in Kitzer’s outrageous schemes, meeting other members of Kitzer's crime syndicate and powerful politicians and businessmen he fooled at each stop, they also grew to respect him - even care for him. And Kitzer began to think of Wedick and Brennan like sons, schooling them in everything from writing bad checks to picking up women. Chasing Phil by journalist and author David Howard is the story of an incredible round the world manhunt, a charismatic conman and a friendship that changed crime forever.
An Index of a Graph with Applications to Knot Theory
There are three chapters to the memoir. The first defines and develops the notion of the index of a graph. The next chapter presents the general application of the graph index to knot theory. The last section is devoted to particular examples, such as determining the braid index of alternating pretzel links. A second result shows that for an alternating knot with Alexander polynomial having leading coefficient less than 4 in absolute value, the braid index is determined by polynomial invariants.
A Topological Chern-Weil Theory
We examine the general problem of computing characteristic invariants of principal bundles whose structural group [italic capital]G is a topological group. Under the hypothesis that [italic capital]G has real cohomology finitely generated as an [bold]R-module, we are able to give a completely topological, local method for computing representative cocycles for real characteristic classes; our method applies, for example, to the (homologically) 10-dimensional non-Lie group of Hilton-Roitberg-Stasheff.
Diagram Cohomology and Isovariant Homotopy Theory
Obstruction theoretic methods are introduced into isovariant homotopy theory for a class of spaces with group actions; the latter includes all smooth actions of cyclic groups of prime power order. The central technical result is an equivalence between isovariant homotopy and specific equivariant homotopy theories for diagrams under suitable conditions. This leads to isovariant Whitehead theorems, an obstruction-theoretic approach to isovariant homotopy theory with obstructions in cohomology groups of ordinary and equivalent diagrams, and qualitative computations for rational homotopy groups of certain spaces of isovariant self maps of linear spheres. The computations show that these homotopy groups are often far more complicated than the rational homotopy groups for the corresponding spaces of equivariant self maps. Subsequent work will use these computations to construct new families of smooth actions on spheres that are topologically linear but differentiably nonlinear.
A Proof of the $q$-Macdonald-Morris Conjecture for $BC_n$
Macdonald and Morris gave a series of constant term [italic]q-conjectures associated with root systems. Selberg evaluated a multivariable beta-type integral which plays an important role in the theory of constant term identities associated with root systems. K. Aomoto recently gave a simple and elegant proof of a generalization of Selberg's integral. Kadell extended this proof to treat Askey's conjectured [italic]q-Selberg integral, which was proved independently by Habsieger. We use a constant term formulation of Aomoto's argument to treat the [italic]q-Macdonald-Morris conjecture for the root system [italic capitals]BC[subscript italic]n. We show how to obtain the required functional equations using only the q-transportation theory for [italic capitals]BC[subscript italic]n.
