Previous Special Year Seminar
Locally Residual Currents and Dolbeault Cohomology on Projective Manifolds
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 $...
Micea Mustata
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.
Filtrations in Cohomlogy and Geometry
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...
Multiplier Ideals and Singularities
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...
Minimal Model Program in Dimensions 4 and 5
Valery Alexeev
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...
Polarized Logarithmic Hodge Structures and Enlargements of Griffiths Domain
Sampei Usui
2:00pm|Simonyi Hall Classroom - (S-114)
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...
On Margulis' Normal Subgroup Theorem
2:00pm|West Building Lecture Theatre
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...
Almost Normal Subgroups of Lattices
George Willis
Let $G$ be a simple $G(\mathbf Q)$-group of $G(\mathbf Q)$-rank
at least 2. In 1987 T. N. Venkataramana showed that if $\Gamma
\subset G(\mathbf Z)$ is an infinite subgroup whose commensurator
is a subgroup of finite index in $G(\mathbf Z)$, then $...