Abstract:
In this fourth and final part, we discuss the Bloch group. Moreover, we introduce Dedekind zeta function and we show how to compute values of $\zeta_{F}(2)$, where $F$ is a certain number field. The computation of these values will involve volumes of hyperbolic 3-manifolds.
Abstract:
In this third part, we explore more the connections of the Bloch-Wigner dilogarithm with volumes of hyperbolic 3-manifolds. Specifically, we will express the volume of a hyperbolic 3-manifold as a finite sum of Bloch-Wigner dilogarithms. If time allows, we also discuss the Bloch group.
Abstract:
In this second talk, we explore the Bloch-Wigner dilogarithm which is very important in connections with volumes of hyperbolic 3-manifolds and K-theory.
Abstract:
We introduce a model reduction approach for time-dependent nonlinear scalar conservation laws. Our approach, Manifold Approximation via Transported Subspaces (MATS), exploits structure via a nonlinear approximation by transporting reduced subspaces along characteristic curves. The notion of Kolmogorov N-width is extended to account for this new nonlinear approximation. We also present an online efficient time-stepping algorithm based on MATS with costs independent of the dimension of the full model.
The outline of Cezar's and my work will be to show (1) $\hat{H}(a,b)$ is equal to a certain rational zeta series, and (2) $H(a,b)$ is equal to that same raitonal zeta series. Thus $H(a,b) = \hat{H}(a,b)$ independent of Don Zagier's proof. Cezar has proven (2) for $b=0$. In this talk, I will prove (1) for all $a,b$.
Abstract:
A topological group is extremely amenable if it has a fixed
point under every continuous action on a compact Hausdorff space. The
group of measure preserving transformations of the standard
probability space is extremely amenable by a result of Giordano and
Pestov applying analytical techniques. This in turn implies that the
class of finite measure algebras posseses the approximate Ramsey
property. Via discretization, Giordano and Pestov's result would
follow from (an exact) Ramsey property for finite measure algebras