# Publications

## Phylogenetics

- Estimating Species Trees from Quartet Gene Tree Distributions under the Coalescent Model, Preprint, arXiv (2011)
- Note on expected internode distances for gene trees in species trees, Preprint, arXiv (2011)

## Algebraic geometry

- Demazure resolutions as varieties of lattices with infinitesimal structure, Journal of Algebra 324 (2010).

- A short note on vector bundles on curves, ArXiv (2010).
- On p-adic loop groups and Grassmannians, ArXiv (2010), submitted to Advances in Mathematics.

## Thesis: Spaces of lattices in equal and mixed characteristics

pdf: Spaces of lattices in equal and mixed characteristics

Summary: First, Schubert varieties in affine Grassmannians and their Demazure resolutions are studied. One finds that, over fields of positive characteristics, Demazure resolutions (which are traditionally interpreted as varieties of lattice chains) have an alternative interpretation as parameter spaces of certain affine schemes (“lattice schemes”). As such, Demazure resolutions get, up to a Frobenius twist, identified with cerain closed subvarieties of a multigraded Hilbert scheme (after Haiman and Sturmfels 2004). Second, an analogous construction is carried out in the situation of mixed characteristics. Thus one obtains an analogon of Demazure varieties for the p-adic affine Grassmannian.