G. Eric Moorhouse: Research Interests

p-ranks

Determination of the rank (over fields of prime characteristic p) of incidence matrices arising in finite geometries. Techniques include methods from algebraic geometry and group representation theory

Ovoids and Spreads

Constructions and nonexistence results for ovoids in finite classical polar spaces. Techniques include the use of integral lattices and theta series

Projective Planes and Generalised Polygons

Constructions and nonexistence results for generalised polygons, particularly finite projective planes with specified properties (such as order and/or collineation group)

Double Covers of Graphs

Study, including construction and classification, of various combinatorial objects which may be described as double covers of graphs, especially two-graphs, Hadamard matrices and semibiplanes. Techniques include the use of representation theory and cohomology

Loops

Constructions and stucture theorems for nonassociative systems including loops and their rings

Quantum Information and Computation

Quantum algorithms, quantum codes, and quantum complexity theory

Nets and Webs

The main open problems concerning finite projective planes are reducible to questions about nets. Such questions are discrete analogues of questions in the theory of webs, and are amenable to a variety of algebraic techniques, particularly exponential sums

Algebraic Graph Theory

Distance regular graphs and association schemes; algebraic methods for determining chromatic numbers of graphs

Research Interests

my Publications/ Errata

my Seminar Slides

other Handouts

Open Problems

video

/ revised August, 2005