 Thesis
Authors: Yuncken, Robert (2006)  If G is a connected Lie group, the Kasparov representation ring KKG(C, C) contains a singularly important element—the 'yelement—which is an idempotent relating the Kasparov representation ring of G with the representation ring of its maximal compact subgroup K. In the proofs of the BaumConnes conjecture with coefficients for the groups G = SO0(n, 1) ([Kas84]) and G = SU(n, 1) ([JK95]), a key component is an explicit construction of the 'yelement as an element of Gequivariant Khomology for the space G/B, where B is the Borel subgroup of G.
In this thesis, we describe some analytical constructions which may be useful for such a construction of y in the case of the ranktwo Lie group G = SL(3, C). The inspiration is the BernsteinGel’fandGel’fand complex—a natural differential ...

 Thesis
Authors: Arnold, Trevor S. (2006)  

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Authors: Durocher, Stephane (2006)  The traditional problems of facility location are defined statically; a set (or multiset) of n points is given as input, corresponding to the positions of clients, and a solution is returned consisting of set of k points, corresponding to the positions of facilities, that optimizes some objective function of the input set. In the kcentre problem, the objective is to select k points for locating facilities such that the maximum distance from any client to its nearest facility is mini¬mized. In the kmedian problem, the objective is to select k points for locating facilities such that the average distance from each client to its nearest facility is minimized. A common setting for these problems is to model clients and facilities as points in Euclidean space and to measure distances b...

 Thesis
Authors: Howse, Samuel (2006)  NummSquared Explained is the thesis version of the comprehensive formal docu¬ment NummSquared 2006a0 Done Formally, which is available at http / /nummist . com/poohbist/.
Set theory is the standard foundation for mathematics, but often does not include rules of reduction for function calls. Therefore, for computer science, the untyped lambda calculus or type theory is usually preferred. The untyped lambda calculus (and several improvements on it) make functions fundamental, but suffer from nonterminating reductions and have partially nonclassical logics. Type theory is a good foundation for logic, mathematics and computer science, except that, by making both types and functions fundamental, it is more complex than either set theory or the un¬typed lambda calculus. This document p...

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Authors: Clement, Anthony E. (2006)  

 Thesis
Authors: Navilarekallu, Tejaswi (2006)  For a finite Galois extension K/Q of number fields with Galois group G and a motive M = M' h°(Spec(K))(O) with coefficients in Q[G], the equivariant Tamagawa number conjecture relates the special value L* (M, 0) of the motivic Lfunction to an element of Ko(Z[G];R) constucted via complexes associated to M. The conjecture for nonabelian groups G is very much unexplored. In this thesis, we will develop some techniques to verify the conjecture for Artin motives and motives attached to elliptic curves. In particular, we consider motives h°(Spec(K))(0) for an A4extension K/Q and, hi (E x Spec(L))(1) for an S3extension L/Q and an elliptic curve E/Q.

 Thesis
Authors: Pasol, Vicentiu (2006)  In this thesis I study the relation between the (CM) Elliptic Construction and the Mod¬ular Construction of padic Lfunctions in two variables which interpolate special values of Hecke Lfunctions.
The first construction, due to N. Katz, and then R. Yager, is very explicit in terms of elliptic units using Iwasawa theory on formal groups. However, this construction does not imply the construction of a modular symbol for which the attached Lfunction is exactly this padic Lfunction.
The Modular construction, developed by R. Greenberg and G. Stevens, is more general. They attach to any Hida family of pstabilized modular forms a padic modular symbol with values in the space of two variable padic distributions. However, this construction is not explicit.
We use padic methods to...

 Thesis
Authors: McCarthy, Anne E. (2006)  This thesis investigates dynamical properties of actions of abelianbycyclic groups on compact manifolds. For a nonsingular integer matrix A, let FA be the fundamental group of the mapping cylinder of the induced map fA on the torus T n. The standard actions p), of FA on the circle RP 1 are generated by maps f(x) = Ax and gi(x) = x + bi, where A is a realvalued eigenvalue for A, and (01, ..., 0n) is the associated eigenvector. It is known that any analytic action of FA on the circle is a ramified lift of one of the standard actions p),. This thesis shows that for each analytic action, p, there exists R > 2 such that p is Cr locally rigid for all r > R.
We then consider actions of the groups FA on compact manifolds of higher dimension that are generated by C1 diffeomorphisms clos...

 Thesis
Authors: Ahmadov, Anar (2006)  We investigate the exotic smooth structures on 4manifolds with small Euler characteristic. Using the surgical techniques of knot surgery and fiber sum, we construct new symplectic 4manifolds with zero signature and cohomology equivalent to S2 x S2. In fact, a more general construction provides exotic manifolds with zero signature and cohomology equivalent to #(29_1)(S2 x S2) for any g. Applying the surgical methods of FintushelStern [FS4], we also construct simply connected nonsymplectic 4manifolds starting from the elliptic surfaces E(n) for n > 3. SeibergWitten invariants are used to distinguish their smooth structures. «'e also give a uniform technique that yields nonsymplectic manifolds homeomorphic CP 2#k CP 2 for k = 5, 6 and also 3CP 2#8 CP 2. The main construction used...

 Thesis
Authors: Takeda, Shuichiro (2006)  We, firstly, improve a theorem of B. Roberts which characterizes nonvanishing of a global theta lift from 0(X) to Sp(n) in terms of nonvanishing of local theta lifts. In particular, we will remove all the archimedean conditions imposed upon his theorem. Secondly, we will apply our theorem to theta lifting of low rank similitude groups as Roberts did so. Namely we characterize the nonvanishing condition of a global theta lift from GO(4) to GSp(2) in our improved setting. Also we consider nonvanishing conditions of a global theta lift from GO(4) to GSp(1) and explicitly compute the lift when it exists.
