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Department of Mathematics

Geometry and Topology Seminars

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See below for upcoming seminars or access the seminar archive.

Organizers

Bill Bogley, Christine Escher and Ren Guo

Contact

escher@math.oregonstate.edu

Meeting time

M 1200-1250

Maximal boundary rigidity for Alexandrov spaces

111 STAG

Speaker: Qin Deng

Given an Alexandrov space with curvature bounded below by $K$, dimension $m$ and radius $r$, one may ask how large the boundary of X can be. In the case where $K=1$ and $r = \pi/2$, this is known as Lytchak’s problem and was answered by Petrunin, who showed the sharp upper bound $\mathcal{H}^{m-1}(\partial X) \leq \mathcal{H}^{m-1}(\mathbb{S}^{m-1})$. Rigidity was later analyzed by Grove-Petersen, who showed that in the case of equality $X$ must be a hemisphere or the intersection of two hemispheres. In this talk, I will address both the bound and rigidity for arbitrary $K$ and $r$ Read more.

Geometric inference and estimating the reach

111 STAG

Speaker: John Harvey

In topological data analysis, the "manifold hypothesis" is that a dataset lying in Euclidean space in fact lies on, or near, some submanifold of that space. The submanifold is understood to provide information about the non-linear relationships between different variables.The goal of statistical inference is to use some set of sample data to understand aspects of an entire population and express a mathematically justifiable level of confidence in the statements made. In this talk I will introduce geometric inference, which aims to understand the geometry of a submanifold of Euclidean space using a finite sample of points drawn from the submanifold.I will introduce some of the philosophy and tools of inference which are probably not familiar to most practicing geometers and survey some results in this field. I will have a particular focus on the reach, where I proved new bounds with Clément Berenfeld, Marc Hoffmann and Krishnan Shankar, which Berenfeld and others recently showed were… Read more.