Deposits of clastic carbonate-dominated (calciclastic) sedimentary slope systems in the rock record have been identified mostly as linearly-consistent carbonate apron deposits, even though most ancient clastic carbonate slope deposits fit the submarine fan systems better. Calciclastic submarine fans are consequently rarely described and are poorly understood. Subsequently, very little is known especially in mud-dominated calciclastic submarine fan systems. Presented in this study are a sedimentological core and petrographic characterisation of samples from eleven boreholes from the Lower Carboniferous of Bowland Basin (Northwest England) that reveals a >250 m thick calciturbidite complex deposited in a calciclastic submarine fan setting. Seven facies are recognised from core and thin section characterisation and are grouped into three carbonate turbidite sequences. They include: 1) Calciturbidites, comprising mostly of highto low-density, wavy-laminated bioclast-rich facies; 2) low-density densite mudstones which are characterised by planar laminated and unlaminated muddominated facies; and 3) Calcidebrites which are muddy or hyper-concentrated debrisflow deposits occurring as poorly-sorted, chaotic, mud-supported floatstones. These

Phd by thesis

Combinatorial Group Theory: COMBINATORIAL GROUP THEORY

第12次 아시아ㆍ太平洋 矯政局長會議 參加記

Starting around the late 1950s, several research communities began relating the geometry of graphs to stochastic processes on these graphs. This book, twenty years in the making, ties together research in the field, encompassing work on percolation, isoperimetric inequalities, eigenvalues, transition probabilities, and random walks. Written by two leading researchers, the text emphasizes intuition, while giving complete proofs and more than 850 exercises. Many recent developments, in which the authors have played a leading role, are discussed, including percolation on trees and Cayley graphs, uniform spanning forests, the mass-transport technique, and connections on random walks on graphs to embedding in Hilbert space. This state-of-the-art account of probability on networks will be indispensable for graduate students and researchers alike.

Probability on Trees and Networks

Higher Algebraic K-Theory

In this article we study cocycles of discrete countable groups with values in � 2 G and the ring of affiliated operators UG. We clarify properties of the first cohomology of a group G with coefficients in � 2 G and answer several questions from De Cornulier et al. (Transform. Groups 13(1):125-147, 2008). Moreover, we obtain strong results about the existence of free subgroups and the subgroup structure, provided the group has a positive first � 2 -Betti num- ber. We give numerous applications and examples of groups which satisfy our assumptions.

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Group cocycles and the ring of affiliated operators

We study $\epsilon$-representations of discrete groups by unitary operators on a Hilbert space. We define the notion of Ulam stability of a group which loosely means that finite-dimensional $\epsilon$-represendations are uniformly close to unitary representations. One of our main results is that certain lattices in connected semi-simple Lie groups of higher rank are Ulam stable. For infinite-dimensional $\epsilon$-representations, the similarly defined notion of strong Ulam stability is defined and it is shown that groups with free subgroups are not strongly Ulam stable. We also study deformation rigidity of unitary representations and show that groups containing a free subgroup are not deformation rigid.

On Ulam stability

In this article we study cocycles of discrete countable groups with values in l^2(G) and the ring of affiliated operators UG. We clarify properties of the first cohomology of a group G with coefficients in l^2(G) and answer several questions from [CTV]. Moreover, we obtain strong results about the existence of free subgroups and the subgroup structure, provided the group has a positive first l^2-Betti number. We give numerous applications and examples of groups which satisfy our assumptions.

We show that for any amenable group and any Z-module M of type FL with vanishing Euler characteristic, the entropy of the natural -action on the Pontryagin dual of M is equal to the L 2 -torsion of M. As a particular case, the entropy of the principal algebraic action associated with the module Z =Z f is equal to the logarithm of the Fuglede-Kadison determinant of f whenever f is a non-zero-divisor in Z. This conrms a conjecture of Deninger. As a key step in the proof we provide a general Szeg} o-type approximation theorem for the Fuglede-Kadison determinant on the group von Neumann algebra of an amenable group. As a consequence of the equality between L 2 -torsion and entropy, we show that the L 2 -torsion of a non-trivial amenable group with nite classifying space vanishes. This was conjectured by Luck. Finally, we establish a Milnor-Turaev formula for the L 2 -torsion of a nite -acyclic chain complex.

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Entropy, determinants, and l 2 -torsion

We prove the algebraic eigenvalue conjecture of J. Dodziuk, P. Linnell, V. Mathai, T. Schick, and S. Yates (see [2]) for sofic groups. Moreover, we give restrictions on the spectral measure of elements in the integral group ring. Finally, we define integer operators and prove a quantization of the operator norm below 2. To the knowledge of the author, there is no group known that is not sofic.

Andreas Thom

Papers

Group cocycles and the ring of affiliated operators

On Ulam stability

Group cocycles and the ring of affiliated operators

Entropy, determinants, and l 2 -torsion

Sofic Groups and Diophantine Approximation