This lecture will describe the historical context and some key properties of o-minimality. It will then describe certain results in functional transcendence, generalizing the classical results on exponentiation due to Ax, and sketch how they can be proved.
School of Mathematics
This talk is mainly concerned with the investigation of small set expansion on the Grassmann Graphs, a study that was motivated by recent applications to Probabilistically Checkable Proofs and hardness of approximation.
This introductory lecture will describe results about counting rational points on certain non-algebraic sets and sketch how they can be used to attack certain problems in diophantine geometry and functional transcendence.
Matrix rank is well-known to be multiplicative under the Kronecker product, additive under the direct sum, normalized on identity matrices and non-increasing under multiplying from the left and from the right by any matrices. In fact, matrix rank is the only real matrix parameter with these four properties.