other Handouts |
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 PolygonsConstructions and nonexistence results for generalised polygons, particularly finite projective planes with specified properties (such as order and/or collineation group) |
Double Covers of GraphsStudy, 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 |
LoopsConstructions 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 TheoryDistance regular graphs and association schemes; algebraic methods for determining chromatic numbers of graphs |
other Handouts |