Previous Special Year Seminar
The Syntomic Regulator for K_1 of Surfaces
We give an explicit formula for the syntomic regulator of
certain elements in the first algebraic K-theory group of a smooth
complete surface over the ring of integers of a p-adic field. The
formula uses the theory of Coleman integration and the...
An Approach to the Conservation of the Nearby Motive Functor
We present a program to prove the following conjecture: Let $S$
be the spectrum of a DVR of equi-characteristic zero with field of
fraction $K$ and residue field $k$. The functor (associated to the
choice of a uniformizing) $\Psi:DM_{gm}(K) \to DM_...
Finite Generation VI: Moduli Spaces
We will finish the sketch of the proof of existence of a
geometrically meaningful compactification of the moduli space of
canonically polarized smooth varieties.
Rost's Basic Corespondences
Parabolic Chern Character of the de Rham Bundles
Characteristic classes of Flat bundles on smooth algebraic
varieties are defined in various cohomology theories. We consider
the de Rham cohomology, the Deligne cohomology and the rational
Chow groups and study the classes. We focus on the special...
Witten Equation and Singularity Theory
Yongbin Ruan
In 1991, Witten proposed a famous conjecture (solved by
Kontsevich) related the intersection theory of Deligne-Mumford
moduli space to KDV-integrable hierearchy. To generalize his
conjecture, Witten proposed a remarkable PDE based any...
Using Rost Motives to Prove Bloch-Kato
Moduli Spaces via Minimal Models (cont'd)
Singularities and Spaces of Jets
I will give an introduction to spaces of jets of algebraic
varieties, explining their relevance for birational geometry. In
particular, I will explain why these spaces are useful in the study
of singularities.
