Fri, 24 Jan 2025
15:00
L4

Efficient computation of the persistent homology of Rips complexes

Katharine Turner
(Australian National University)

Note: we would recommend to join the meeting using the Teams client for best user experience.

Abstract

Given a point cloud in Euclidean space and a fixed length scale, we can create simplicial complexes (called Rips complexes) to represent that point cloud using the pairwise distances between the points. By tracking how the homology classes evolve as we increase that length scale, we summarise the topology and the geometry of the “shape” of the point cloud in what is called the persistent homology of its Rips filtration. A major obstacle to more widespread take up of persistent homology as a data analysis tool is the long computation time and, more importantly, the large memory requirements needed to store the filtrations of Rips complexes and compute its persistent homology. We bypass these issues by finding a “Reduced Rips Filtration” which has the same degree-1 persistent homology but with dramatically fewer simplices.

The talk is based off joint work is with Musashi Koyama, Facundo Memoli and Vanessa Robins.

Join virtual meeting
Tue, 14 Mar 2023
16:00
C3

Linking vertex algebras and Wightman QFTs

Christopher Raymond
(Australian National University)
Abstract

There has been a great deal of interest in understanding the link between the axiomatic descriptions of conformal field theory given by vertex operator algebras and conformal nets. In recent work, we establish an equivalence between certain vertex algebras and conformally-symmetric quantum field theories in the sense of Wightman. In this talk I will give an overview of these results and discuss some of the difficulties that arise, the functional analytic properties of vertex algebras, and some of the ideas for future work in this area.

This is joint work with James Tener and Yoh Tanimoto.

Fri, 04 Feb 2022

11:00 - 12:00
L6

Computing the Extended Persistent Homology Transform of binary images

Katharine Turner
(Australian National University)
Abstract

The Persistent Homology Transform, and the Euler Characteristic Transform are topological analogs of the Radon transform that can be used in statsistical shape analysis. In this talk I will consider an interesting variant called the Extended Persistent Homology Transform (XPHT) which replaces the normal persistent homology with extended persistent homology. We are particularly interested in the application of the XPHT to binary images. This paper outlines an algorithm for efficient calculation of the XPHT exploting relationships between the PHT of the boundary curves to the XPHT of the foreground.

Further Information

PLEASE NOTE this seminar will be at 11am instead of 3pm.

Fri, 18 Jul 2008

13:30 - 14:30
Gibson 1st Floor SR

On Monge-Ampere type equations with supplementary ellipticity

Neil Trudinger
(Australian National University)
Abstract

We present a selection of recent results pertaining to Hessian

and Monge-Ampere equations, where the Hessian matrix is augmented by a

matrix valued lower order operator. Equations of this type arise in

conformal geometry, geometric optics and optimal transportation.In

particular we will discuss structure conditions, due to Ma,Wang and

myself, which imply the regularity of solutions.These conditions are a

refinement of a condition used originally by Pogorelev for general

equations of Monge-Ampere type in two variables and called strong

ellipticity by him.

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