A cubic surface is a surface in the 3-dimensional space defined by a polynomial equation of degree 3. It is a remarkable, classical fact in algebraic geometry that every cubic surface contains exactly 27 lines. In this talk, I will explain this fact and its generalization to higher dimensions.
Room: Thack 703
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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.
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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.
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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 $a,b$.
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