### Recent Submissions

• #### On the Structure and Regularity of Stable Branched Minimal Hypersurfaces ﻿

We study the structure of large classes of stable codimension one stationary integral varifolds 𝑉 near higher multiplicity hyperplanes and classical cones, i.e. cones supported on half-hyperplanes which have a common ...
• #### High-dimensional Online Changepoint Detection ﻿

The problem of changepoint detection and estimation has a long history, dating back to at least Page (1954, 1955). As modern technological advances, data sets of unprecedented size can be collected at high frequency. This ...
• #### The Gregory--Laflamme Instability and Conservation Laws for Linearised Gravity ﻿

This thesis is concerned with the black hole stability problem in general relativity. In particular, it presents stability and instability results associated to the linearised vacuum Einstein equation on black hole ...
• #### New techniques in calculation of sutured instanton Floer homology: by Heegaard diagrams, Euler characteristics, and Dehn surgery formulae ﻿

Kronheimer-Mrowka conjectured that sutured instanton Floer homology $SHI(M,\gamma)$ has the same dimension as the sutured Floer homology $SFH(M,\gamma)$ constructed by Juh\'{a}sz for any balanced sutured manifold $(M,\gamma)$. ...