Departmental Colloquium
Navin Singhi
TATA Institute of Fundamental Research, Mumbai, India
Projective Planes
Abstract: A new class of ternary rings -- semiadditive rings -- is defined. A free
semiadditive ring plays a similar role in studying planar ternary rings as
the ring of integers or polynomial rings over integers play in studying
fields. Methods developed recently to study free semiadditive rings will
be discussed. A well known result of G. Higman on loops and its
generalization to semiadditive rings will be discussed.
Two well known conjectures on projective planes state that the order of
every finite projective plane is a power of a prime number and that a
finite projective plane with no proper subplanes is isomorphic to a plane
coordinatized by a prime field. Application of the above mentioned
results to these problems will be discussed.
Monday October 15, 2007 at 4:00 PM in SEO 636