**Associate Professor
Department of Mathematics
Miami University
Room 123 Bachelor Hall
Oxford, OH 45056, USA
E-mail: ortizi@muohio.edu
Phone: (513)-529-5834
Fax: (513)-529-1493**

**OTHER INFORMATION:**

My CV, Fall 2013.

**RESEARCH INTERESTS:**

My research focuses on the interplay between geometry, topology, and algebraic \(K\)-theory. Here are all my completed projects. All my work presented here is partly supported by the National Science Foundation under the grant DMS-0805605 (2008-2012) and DMS-1207712 (2012-2015).

**ACCEPTED PAPERS:**

**The lower algebraic \(K\)-Theory of three-dimensional
crystallographic groups.**

PDF 116 pages as a preprint. To appear in the Lecture Notes Series of Mathematics, Springer.

In this joint work with Dan Farley, we compute \(K_{-1}\), \(\tilde{K}_{0}\), and the Whitehead groups of all three-dimensional crystallographic groups \(\Gamma\) which fit into a \emph{split} extension \( \mathbb{Z}^{3} \rightarrowtail \Gamma \twoheadrightarrow H,\) where \(H\) is a finite group acting effectively on \(\mathbb{Z}^{3}\). Such groups \(\Gamma\) account for \(73\) isomorphism types of three-dimensional crystallographic groups, out of \(219\) types in all. We also prove a general splitting formula for the lower algebraic \(K\)-theory of all three-dimensional crystallographic groups, which generalizes the one for the Whitehead group obtained by Alves and Ontaneda.

**WORKS IN PROGRESS:**

The following projects are in various stages of typing. Preprints will be available as soon as they get completed. The descriptions below reflect, to the best of my knowledge, the results that will be appearing in the completed papers. The projects are organized roughly according to proximity to completion (closest to finished are at the top of the list).