Çankaya University, 2010 (seminar in the Department of
Mathematics and Computer Science, March 26): “Model theory and
linear algebra”
Abstract: Like set theory or category theory, model theory
provides ways of organizing and thinking about (parts of)
mathematics, and
is itself a branch of mathematics like any other, which raises its own
questions and (sometimes!) answers them.
I shall discuss some of the basic concepts and examples in model theory,
especially involving vector spaces. Some of the results are quite recent,
although they are directly inspired by the _Geometry_ of Descartes.
Ankara, 2009 (algebra seminar at METU, November 20): “One
amateur's approach to elliptic curves.”
Abstract: Every curve has a function field. If two such
function fields are isomorphic, then they have the same first-order
logical theories. The converse holds as well, unless one of the curves is
an elliptic curve with complex multiplication. In this case, the
endomorphism ring of the curve turns out to be important. I shall discuss
these matters, mainly working over the complex numbers. In particular, I
shall use the understanding of an elliptic curve as the complex field
modulo a lattice. However, some of the results can be proved over
arbitrary fields of arbitrary characteristic.
