複素幾何セミナーの記録

１月１１日（水）　１６：３０〜１７：３０
池田　京司氏（東京電機大）
ヘッシアンを分岐因子とする３次曲面の２重被覆


１２月９日（金）　１４：３０〜１５：３０時間がいつもと違います
大橋　久範氏（名古屋大学多元数理研究科）
エンリケス曲面上の対合の分類


１２月７日（水）　１６：３０〜
修論中間発表会


１０月４日（火）　１６：００〜１７：００ 時間がいつもと違います
Alan Huckleberry (Ruhr Univ./ Jacobs Univ.)
Random matrix models of disordered bosons 

Abstract: 
The mathematics in the talk involves the study of a concrete complex analytic setting 
from symplectic geometric and probabalistic view-points. 
The motivation comes from a question relatated to the quantum mechanics of disordered bosons. 
Unlike the fermionic side where the underlying Lie groups of the classical ensembles are compact, 
the symmetry groups for ensembles of disordered bosons are typically noncompact. 
In the bosonic case the basic random matrix models consist of matrices in the Lie algebra g = sp_n (R). 
Assuming dynamical stability, their eigenvalues are required to be purely imaginary. 
In the lecture we will sketch our recent work with K. Schaffert (J.Phys.A.Math. 44 (2011) 335207) 
where a method is proposed for constructing ensembles (E, P) of G-invariant sets E of such matrices with probability measures P. 
These arise as moment map direct images from phase spaces X which play an important role in complex geometry and representation theory. 
We will discuss in detail the toy-model case of n = 1, 
where X is the complex bidisk and P is the direct image of the uniform measure.


９月８日（木）　１１：３０〜１２：３０ 時間がいつもと違います
Jochen Bruening (Humboldt Universitaet zu Berlin)
Multiplicities of compact group representations and invariant indices

Abstract: 
This is joint work with Ken Richardson and Franz Kamber. 
We give an explicit formula for the multiplicitiy of an irreducible representation in the graded kernel of a G-equivariant elliptic operator on a compact manifold, with G also compact. 
Such formulas have been sought for a long time and were available so far only in very special cases.


６月１日（水）　１６：３０〜１７：３０
Alvaro Nolla de Celis (名大）
G-Hilb via G-graphs and representations of the McKay quiver

Abstract: 
If we have an abelian group G, since I. Nakamura around 2000 the use of G-graphs has been proved to be a useful tool to describe the G-equivariant Hilbert scheme so called G-Hilb. 
The notion of G-graph can be can be extended to non-abelian groups, although in most of the cases it becomes a difficult explicit problem to recover G-Hilb from them. 

In this talk I will explain how, by assigning to every G-graph a distinguished representation of the McKay quiver, we can easily construct an open cover of G-Hilb as the moduli space of stable representations of Q. 
To show this method I will explain the case when G is a binary dihedral subgroup of GL(2,C), giving the relation with the Special McKay Correspondence, and also some examples in dimension 3.