Characterization of branched covers with simplicial branch sets
Abstract:
Seminar
Manifold Approximation via Transported Subspaces (MATS)
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.
From lower measure bound to Sobolev embedding and back again
Proving $H(a,b) = \hat{H}(a,b)$ using rational zeta series
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 $a,b$.
Rational zeta series for zeta(2n) and zeta(2n+1)
Abstract:
The problem of equal parts
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
From Fluids to Geometry and Back