Ivonne J. Ortiz

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:

  • I finished my doctorate at SUNY Binghamton in 2003, under the guidance of Thomas Farrell.
  • I am the current chair of the Department Colloquium.
  • Spring 2014: This semester, I'm teaching MTH 691, Introduction to Algebraic Topology (MTRF 10:00am - 11:15am), and MTH 222, Introduction to Linear Algebra (MWF 2:30pm - 3:25pm).
  • Information on my upcoming travel plans and my visitors can be found Here.

    I am a coorganizer with Mike Davis and Jean-Francois Lafont, of the upcoming conference Topological Methods in Group Theory in honor of Ross Geoghegan's 70th birthday, Columbus, OH, June 16th-20th, 2014.

    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).

  • Kleinian groups: lattice retracts, accessibility, and the Farrell-Jones isomorphism conjectures, (joint with, Jean-Francois Lafont, and D. Vavrichek)). Using some of the spectacular recent work in 3-manifold theory, we show that various isomorphism conjectures known to hold for lattices in the isometry group of hyperbolic 3-space actually hold for the broader class of Kleinian groups. In previous work, I'd developed techniques with Lafont for computing the lower algebraic \(K\)-theory of lattices inside the isometry group of hyperbolic 3-space; we also show that these techniques can now be extended to the setting of Kleinian groups. [This paper still needs some work. We can currently deal with the case of Kleinian groups that are 1-ended and do not split over any 2-ended subgroup. We are working on removing the "does not split over 2-ended subgroup" hypothesis.].
  • The lower algebraic \(K\)-Theory of Hilbert Modular groups.
  • The lower algebraic \(K\)-theory of hyperbolic 4-simplex reflections groups.