### Recent Submissions

• #### Homological stability for moduli spaces of high dimensional manifolds. I ﻿

We prove a homological stability theorem for moduli spaces of simply connected manifolds of dimension 2n > 4, with respect to forming connected sum with S$^{n}$ x S$^{n}$ . This is analogous to Harer's stability theorem ...
• #### High-dimensional change point estimation via sparse projection ﻿

Changepoints are a very common feature of Big Data that arrive in the form of a data stream. In this paper, we study high-dimensional time series in which, at certain time points, the mean structure changes in a sparse ...

• #### Critical surface of the 1-2 model ﻿

The 1-2 model on the hexagonal lattice is a model of statistical mechanics in which each vertex is constrained to have degree either 1 or 2. There are three edge directions, and three corresponding parameters a, b, c. It ...