I am a Ph.D. student in the DFG research training group "Experimental and Constructive Algebra".
Einklassige Geschlechter orthogonaler Gruppen / Single-class genera of orthogonal groups (in preparation).
(with Markus Kirschmer) Single-class Genera of Positive Integral Lattices, DOI PDF List of genera
(with Markus Kirschmer) One class genera of ternary quadratic forms over number fields, Journal of Number Theory. DOI PDF
Einklassige Geschlechter positiv definiter dreidimensionaler Gitter, 2011.
A talk held on October 18, 2011.
My current research interest is genera of definite lattices over totally real number fields. My Ph.D. thesis (in preparation) focuses on a classification of those genera which consist of a single isometry class. I am working with Dr. Markus Kirschmer to incorporate relevant algorithms into the MAGMA computer algebra system.
My diploma thesis focused on single-class genera over the rational integers Z. For these genera, the Conway-Sloane genus symbol proved very helpful. I have an implementation in MAGMA of the most important algorithms relating to the Conway-Sloane genus symbol (available on request). These include creating and manipulating the genus symbol of a lattice, and constructing a lattice with a given genus symbol.