Previous Special Year Seminar

We start by stating the general form of the Minimal Model Conjecture and explain the relevance of some recent work of Bouksom-Demailly-Paun-Peternell. After that we describe the general picture of the proof of Hacon et al for the general type case.

First we define, for any analytic manifold $X$ of dimension $n$, locally residual currents; $C^{q,p}$ denotes the sheaf of locally residual currents of bidegree $(q,p)$. Then, we have a fundamental resolution of the sheaf of holomorphic $q-$forms $...

This will be an informal working seminar, trying to understand the recent paper of Birkar, Cascini, Hacon and McKernan on the finite generation of canonical rings.

On a topological space, algebraic topology and homological algebra endow cohomology groups with various filtrations. In the case of algebraic varieties, one may wonder if such filtrations, e.g. the Grothendieck filtration, the Leray filtration, the...

The method of multiplier ideals is one of the most versatile tools to study singularities of varieties. For the local theory, we present a connection between multiplier ideals and D-modules based on joint work with M. Mustata and M. Saito which has...

Main conjectures of (log) MMP are: A) existence of flips, B) termination of flips, and C) finite generation, all of which were settled by 1992 in dim 3 by Mori, Shokurov, Kawamata, Koll\'ar et al. In dim 4, A was done by 2005 due to Shokurov and...

In this talk, we have two subjects. I. Partial toroidal compactifications and moduli of PLH. II. The eight enlargements of Griffiths domain D and the fundamental diagram. For I, we have Theorem. For a given pair of global monodromy and fan, there...

In joint work with Yehuda Shalom, we have proved Margulis' Normal Subgroup Theorem for any discrete subgroup $\Gamma$ of the automorphism group of a locally finite $A_2$-tilde building, $B$, provided that the quotient of $B$ by $\Gamma$ is compact...

We consider maps between smooth projective curves and some arithmetic and geometric properties of such maps. In particular, we will discuss the case of maps from the generic Riemann surface of genus g -- a problem first seriously looked at by...