## David Lorch

I am a Ph.D. student in the DFG research training group "Experimental and Constructive Algebra".

### Where to find me

### Ph.D. thesis

*Einklassige Geschlechter orthogonaler Gruppen* / *Single-class genera of orthogonal groups* (in preparation).

### Publications

(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

### Diploma thesis

*Einklassige Geschlechter positiv definiter dreidimensionaler Gitter*, 2011.

A talk held on October 18, 2011.

### Research

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.

### Teaching

current:
- Winter 2015: Begleitpraktikum I (for Prof. Alice Niemeyer)
- Summer 2015: Begleitpraktikum II (for Prof. Wilhelm Plesken)
- Winter 2014: Begleitpraktikum I (for Prof. Wilhelm Plesken)
- Summer 2013: Quadratic Forms (for Prof. Gabriele Nebe)

as a student assistant:
- Summer 2011: Algebraic Number Theory (for Prof. Gabriele Nebe)
- Summer 2010: Computational Algebra (for Prof. Gabriele Nebe)
- Spring 2010: C++ programming for math students (for PD Dr. Helmut Jarausch)
- Winter 2009: Algebra (for Prof. Julia Hartmann)
- Summer 2009: Coding Theory (for Prof. Wolfgang Willems)
- Summer 2009: Computational Algebra (for Prof. Wilhelm Plesken)
- Spring 2009: C++ programming for math students (for PD Dr. Helmut Jarausch)
- Winter 2008: Linear Algebra II (for Prof. Wilhelm Plesken)
- Summer 2008: Linear Algebra I (for Prof. Wilhelm Plesken)
- Spring 2008: C++ programming for math students (for PD Dr. Helmut Jarausch)