## Seminar information archive

#### Algebraic Geometry Seminar

15:00-16:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Prof. Steven Zucker (Johns Hopkins University)
The RBS compactification: a real stratified space in
algebraic geometry

### 2009/05/20

#### PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)

Stability of the Burgers vortex
[ Abstract ]
The Burgers vortex is an exact vortex solution to the three dimensional stationary Navier-Stokes equations for viscous incompressible fluids in the presence of an axisymmetric background straining flow. In this talk we discuss the stability of the Burgers vortex with respect to two or three dimensional perturbation flows.

#### Mathematical Finance

17:30-19:00   Room #122 (Graduate School of Math. Sci. Bldg.)

Financial inverse problem and reconstruction of infinitely divisible distributions with Gaussian component (小谷真一氏(関西学院大)との共同研究)

#### Number Theory Seminar

16:30-17:30   Room #056 (Graduate School of Math. Sci. Bldg.)

Generalized Whittaker functions for degenerate principal series of GL(4,R)

### 2009/05/19

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Mark Hamilton (東京大学大学院数理科学研究科, JSPS)
Geometric quantization of integrable systems
[ Abstract ]
The theory of geometric quantization is one way of producing a "quantum system" from a "classical system," and has been studied a great deal over the past several decades. It also has surprising ties to representation theory. However, despite this, there still does not exist a satisfactory theory of quantization for systems with singularities.

Geometric quantization requires the choice of a polarization; when using a real polarization to quantize a regular enough manifold, a result of Sniatycki says that the quantization can be found by counting certain objects, called Bohr-Sommerfeld fibres. However, there are many types of systems to which this result does not apply. One such type is the class of completely integrable systems, which are examples coming from mechanics that have many nice properties, but which are nontheless too singular for Sniatycki's theorem to apply.

In this talk we will explore one approach to the quantization of integrable systems, and show a Sniatycki-type relationship to Bohr-Sommerfeld fibres. However, some surprising features appear, including infinite-dimensional contributions and strong dependence on the polarization.

This is joint work with Eva Miranda.

### 2009/05/18

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #126 (Graduate School of Math. Sci. Bldg.)

Conformal symmetries of self-dual hyperbolic monopole metrics (joint work with Jeff Viaclovsky)

### 2009/05/16

#### Monthly Seminar on Arithmetic of Automorphic Forms

13:30-16:00   Room #123 (Graduate School of Math. Sci. Bldg.)

3次元上半空間のスペクトル理論とエルミート保型形式
[ Abstract ]
3次元上半空間のスペクトル理論のエルミート保型形式への応用につい
て述べます。内容はジーゲル保型形式に対して2次元上半空間のスペクトル理論を応用す
るという今井氏による発見、及びその実際的応用のエルミート版への類似です。具体的に
は小嶋氏により発見されたエルミート版斉藤・黒川リフトに逆定理による解析的証明を与
えること、レベル付エルミート・アイゼンシュタイン級数のフーリエ係数の決定、それを

による記述、についてです。これらにおいて必要となる「3次元上半空間のマース形式の

ク・サルナック型の結果についても述べます。(p進エルミート・アイゼンシュタイン級

The Eisenstein series for $GL(3,Z)$ induced from cusp forms
[ Abstract ]

### 2009/04/30

#### Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)

ギーラー・マインハルト方程式に対するシャドウ系おける多重スポットの不安定性
[ Abstract ]

この系にはスポットパターンと呼ばれる定常解が存在することが知られており、この解は、その値が非常に大きい点(スポット)を持つこととその近傍の外側では急激に値が減少することにより特徴付けされる。

#### Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

Measure Equivalence Rigidity and Bi-exactness of Groups

### 2009/04/28

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

The ambient metric in conformal geometry
[ Abstract ]
In 1985, Charles Fefferman and Robin Graham gave a method for realizing a conformal manifold of dimension n as a submanifold of a Ricci-flat Lorentz metric on a manifold of dimension n+2, which is now called the ambient space. Using this correspondence, one can construct many examples of conformal invariants and conformally invariant operators. However, if n is even, their construction of the ambient space is obstructed at the jet of order n/2 and thereby the application of the ambient space was limited. In this talk, I'll recall basic ideas of the ambient space and then explain how to avoid the difficulty and go beyond the obstruction. This is a joint work with Robin Graham.

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)

### 2009/04/27

#### Algebraic Geometry Seminar

15:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
Prof. Alessandra Sarti (Universite de Poitier) 15:30-16:30
Automorphism groups of K3 surfaces
[ Abstract ]
I will present recent progress in the study of prime order automorphisms of K3 surfaces.
An automorphism is called (non-) symplectic if the induced
operation on the global nowhere vanishing holomorphic two form
is (non-) trivial. After a short survey on the topic, I will
describe the topological structure of the fixed locus, the
geometry of these K3 surfaces and their moduli spaces.

Prof. Samuel Boissier (Universite de Nice
) 17:00-18:00
The cohomological crepant resolution conjecture

[ Abstract ]
The cohomological crepant resolution conjecture is one
form of Ruan's conjecture concerning the relation between the
geometry of a quotient singularity X/G - where X is a smooth
complex variety and G a finite group of automorphisms - and the
geometry of a crepant resolution of singularities of X/G ; it
generalizes the classical McKay correspondence. Following the
examples of the Hilbert schemes of points on surfaces and the
weighted projective spaces, I will present some of the recents
developments of the subject.

### 2009/04/23

#### Operator Algebra Seminars

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)

Entire Cyclic Cohomology of Noncommutative 2-Tori

### 2009/04/22

#### PDE Real Analysis Seminar

10:30-11:30   Room #128 (Graduate School of Math. Sci. Bldg.)
Wilhelm Klingenberg (University of Durham)
From Codazzi-Mainardi to Cauchy-Riemann
[ Abstract ]
In joint work with Brendan Guilfoyle we established an upper bound for the winding number of the principal curvature foliation at any isolated umbilic of a surface in Euclidean three-space. In our talk, we will focus on the analytic core of the problem. Here is a model of the triaxial ellipsoid with its curvature foliation and one umbilic on the right.

#### Geometry Seminar

14:45-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)

Einstein-Weyl structures on 3-dimensional Severi varieties
[ Abstract ]
The space of nodal curves on a projective surface is called a Severi variety.In this talk, we show that any Severi variety of nodal rational curves on a non-singular projective surface is always equipped with a natural Einstein-Weyl structure, if the space is 3-dimensional. This is a generalization of the Einstein-Weyl structure on the space of smooth rational curves on a complex surface, given by N. Hitchin in the context of twistor theory. We will explain some properties of the Einstein-Weyl spaces given by this method, and we will also show some examples of such Einstein-Weyl spaces. (This is a joint work with Nobuhiro Honda.)
Tamas Hausel (Oxford University) 16:30-18:00
Toric non-Abelian Hodge theory
[ Abstract ]
First we give an overview of the geometrical and topological aspects of the spaces in the non-Abelian Hodge theory of a curve and their connection with quiver varieties. Then by concentrating on toric hyperkaehler varieties in place of quiver varieties we construct the toric Betti, De Rham and Dolbeault spaces and prove several of the expected properties of the geometry and topology of these varieties. This is joint work with Nick Proudfoot.

#### Seminar on Probability and Statistics

15:00-16:10   Room #128 (Graduate School of Math. Sci. Bldg.)
Arnaud DOUCET (統計数理研究所)
Interacting Markov chain Monte Carlo Methods for Solving Nonlinear Measure-Valued Equations
[ Abstract ]
We present a new class of interacting Markov chain Monte Carlo algorithms for solving numerically discrete-time measure-valued equations. The associated stochastic processes belong to the class of self-interacting Markov chains. In contrast to traditional Markov chains, their time evolution depend on the occupation measure of their past values. This general methodology allows us to provide a natural way to sample from a sequence of target probability measures of increasing complexity. We develop an original theoretical analysis to analyze the behaviour of these iterative algorithms. We establish a variety of convergence results including exponential estimates and a uniform convergence theorem with respect to the number of target distributions. We also illustrate these algorithms in the context of Feynman-Kac distribution flows.
(this is joint work with Professor Pierre Del Moral)
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/02.html

### 2009/04/21

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Ivan Marin (Univ. Paris VII)
Some algebraic aspects of KZ systems
[ Abstract ]
Knizhnik-Zamolodchikov (KZ) systems enables one
to construct representations of (generalized)
braid groups. While this geometric construction is
now very well understood, it still brings to
attention, or helps constructing, new algebraic objects.
In this talk, we will present some of them, including an
infinitesimal version of Iwahori-Hecke algebras and a
generalization of the Krammer representations of the usual
braid groups.