For A an associative algebra we will introduce a scheme attached to A that parametrizes finite dimensional representations of A called the representation scheme. We will then discuss a theorem of V. Ginzburg which relates non-commutative symplectic geometry to commutative symplectic geometry on the representation scheme. If time permits we will present a  "higher dimensional" version of this construction for Calabi-Yau algebras.

One-Frequency Schrödinger operators give one of the simplest models where fast transport and localization phenomena are possible. From a dynamical perspective, they can be studied in terms of certain one-parameter families of quasi-periodic co-cycles, which are similarly distinguished as simplest classes of dynamical systems compatible with both KAM phenomena and non-uniform hyperbolicity (NUH). While much studied since the 1970's, until recently the analysis was mostly confined to ''local theories'' describing the KAM and the NUH regimes in detail. In this talk we will describe some of the main aspects of the global theory that has been developed in the last few years.

Under the Axiom of Determinacy, the least uncountable cardinal omega_1 behaves like a large cardinal. We will present a theorem due to Woodin saying that from a strong form of determinacy, namely AD_R + "Theta is regular," one can force the Axiom of Choice together with the statement "there is an omega_1-dense ideal on omega_1." In essence, omega_1 retains a trace of its "large cardinal" nature that is consistent with AC.
 

This is a joint seminar with Number theory seminar.
A classical result of Fontaine-Colmez in p-adic Hodge theory says that one can classify crystalline representations of Galois groups of p-adic fields using certain semi-linear objects, namely the weakly admissible (filtered, phi)-modules. In this talk we propose a notion of (filtered, phi)-modules over smooth adic spaces over p-adic fields, and give a characterization of their admissible locus. That is the part of the base where one can convert the (filtered, phi)-modules to crystalline local systems. This generalizes the works of Fontaine-Colmez, Berger andBrinon, and the work of Hartl on admissible locus of period domains.

Subspace codes were introduced by Koetter and Kschischang in 2007 as network error- correcting codes. Constant dimension codes is an important class of subspace codes. In this talk, we review and survey some bounds, constructions, decoding algorithm and application background for subspace codes and constant dimension codes.