Starting with a cardinal which is both subcompact and measurable, we produce a model in which \square_{\kappa,2} holds but \square_\kappa fails at a singular cardinal \kappa.  We will discuss several of the essential tools used, and also several ways in which this result may be extended.
 

Committee:
Professor Knut Solna, Chair
Professor Abel Klein
Professor Jack Xin

In this talk, I describe the Function Field Sieve algorithm and its
application to solving the discrete log problem, highlighting Joux's
recent advancements that reduce the heuristic work factor to L(1/4 + o(1)).

In this talk we aim at emphasizing the role of information in financial markets (public information versus insider information). In particular, if the information about a particular event (as for instance the default event of a company) is incorporated into a pricing model, then by a change of the underlying filtration, one can compute risk premiums attached to particular events. We also show that modeling of the information leads eventually to modeling of dependencies.