## 過去の記録

### 2009年11月09日(月)

#### Kavli IPMU Komaba Seminar

16:30-18:00   数理科学研究科棟(駒場) 002号室
Makoto Sakurai 氏 (東京大学大学院数理科学研究科)
Differential Graded Categories and heterotic string theory
[ 講演概要 ]
The saying "category theory is an abstract nonsense" is even physically not true.
The schematic language of triangulated category presents a new stage of string theory.

To illuminate this idea, I will draw your attention to the blow-up minimal model
of complex algebraic surfaces. This is done under the hypothetical assumptions
of "generalized complex structure" of cotangent bundle due to Hitchin school.
The coordinate transformation Jacobian matrices of the measure of sigma model
with spin structures cause one part of the gravitational "anomaly cancellation"
of smooth Kahler manifold $X$ and Weyl anomaly of compact Riemann surface $\\Sigma$.

$Anom = c_1 (X) c_1 (\\Sigma) \\oplus ch_2 (X)$,

in terms of 1st and 2nd Chern characters. Note that when $\\Sigma$ is a puctured disk
with flat metric, the chiral algebra is nothing but the ordinary vertex algebra.

Note that I do not explain the complex differential geometry,
but essentially more recent works with the category of DGA (Diffenreial Graded Algebra),
which is behind the super conformal field theory of chiral algebras.

My result of "vanishing tachyon" (nil-radical part of vertex algebras)
and "causality resortation" in compactified non-critical heterotic sigma model
is physically a promising idea of new solution to unitary representation of operator algebras.
This idea is realized in the formalism of BRST cohomology and its generalization
in $\\mathcal{N} = (0,2)$ supersymmetry, that is, non-commutative geometry
with non-linear constraint condition of pure spinors for covariant quantization.

### 2009年11月07日(土)

#### 東京無限可積分系セミナー

13:30-16:00   数理科学研究科棟(駒場) 117号室
Andrei Marshakov 氏 (Lebedev Physical Institute) 13:30-14:30
Tau-functions of Toda theories, partitions and conformal blocks
[ 講演概要 ]
I discuss the class of tau-functions,
corresponding to special solutions of integrable systems,
related to Hurwitz numbers and supersymmetric Yang-Mills
theories. Their natural generalization turn to coincide with
the conformal blocks of two-dimensional conformal
field theories. In special case these conformal
blocks turn into the scalar products of certain coherent
states'' in the highest-weight module of the Virasoro
algebra, generalizing the matrix elements
for the well-known coherent states in Fock spaces.
TBA 氏 (TBA) 15:00-16:00
TBA
[ 講演概要 ]
TBA

### 2009年11月05日(木)

#### GCOE社会数理講演シリーズ

16:20-17:50   数理科学研究科棟(駒場) 056号室

#### 応用解析セミナー

16:00-17:30   数理科学研究科棟(駒場) 002号室

A Mathematical Aspect of the One-Dimensional Keller and Rubinow Model for Liesegang Bands
[ 講演概要 ]
In 1896, colloid-chemist R.E. Liesegang [4] observed strikingly
regular patterns in precipitation-reaction processes, which are referred to as Liesegang bands or rings, according to their shape. In this talk I introduce an attempt to understand from a mathematical viewpoint the experiments in which regularized structures with spatially distinct bands of precipitated material are exhibited, with clearly visible scaling properties. This study is a result [1] of a collaboration with Professors D. Hilhorst, R. van der Hout, and M. Mimura.

References:

[1] Hilhorst, D., van der Hout, R., Mimura, M., and Ohnishi, I.: A Mathematical Study of the One-Dimensional Keller and Rubinow Model for Liesegang Bands. J. Stat Phys 135: 107-132 (2009)
[2] Kai, S., Muller, S.C.: Spatial and temporal macroscopic structures in chemical reaction system: precipitation patterns and interfacial motion. Sci. Form 1, 8-38 (1985)
[3] Keller, J.B., Rubinow, S.I.: Recurrent precipitation and Liesegang rings. J. Chem. Phys. 74, 5000-5007 (1981)
[4] Liesegang, R.E.: Chemische Fernwirkung. Photo. Archiv 800, 305-309 (1896)
[5] Mimura, M., Ohnishi, I., Ueyama, D.: A mathematical aspect of Liesegang phenomena in two space dimensions. Res. Rep. Res. Inst. Math. Sci. 1499, 185-201 (2006)
[6] Ohnishi, I.,Mimura, M.: A mathematical aspect of Liesegang phenomena. In: Proceedings of Equadiff-11, pp. 343-352 (2005).

### 2009年11月04日(水)

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室

Gert Heckman 氏 (IMAPP, Faculty of Science, Radboud University Nijmegen)
Birational Hyperbolic Geometry
[ 講演概要 ]
We study compactifications for complex ball quotients.
We first recall the Satake-Bailey-Borel compactification and the Mumford resolution.
Then we discuss compactifications of ball quotients minus a totally geodesic divisor.
These compactifications turn up for a suitable class of period maps.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~toshi/seminar/ut-seminar.html

### 2009年11月02日(月)

#### 代数幾何学セミナー

16:40-18:10   数理科学研究科棟(駒場) 126号室
Gerard van der Geer 氏 (Universiteit van Amsterdam)
Cohomology of moduli spaces of curves and modular forms
[ 講演概要 ]
The Eichler-Shimura theorem expresses cohomology of local systems
on the moduli of elliptic curves in terms of modular forms. The
cohomology of local systems can be succesfully explored by counting
points over finite fields. We show how this can be applied to
obtain a lot of information about the cohomology of other moduli spaces
of low genera and also about Siegel modular forms of genus 2 and 3.
This is joint work with Jonas Bergstroem and Carel Faber.

### 2009年10月30日(金)

#### GCOE社会数理講演シリーズ

16:20-17:50   数理科学研究科棟(駒場) 117号室

アクチュアリーの役割Ⅱ

#### GCOEセミナー

15:00-16:00   数理科学研究科棟(駒場) 370号室
Shuai Lu 氏 (Johann Radon Institute)
Regularized total least squares: computational aspects and error bounds
[ 講演概要 ]
For solving linear ill-posed problems, regularization methods are required when the right hand side and/or the operator are corrupted by some noise. In the present talk, regularized solutions are constructed using regularized total least squares and dual regularized total least squares. We discuss computational aspects and provide order optimal error bounds that characterize the accuracy of the regularized solutions. The results extend earlier results where the operator is exactly given. We also present some numerical experiments, which shed light on the relationship between RTLS, dual RTLS and the standard Tikhonov regularization.

### 2009年10月29日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
Robert Coquereaux 氏 (CNRS/CPT, Marseille)
Fusion graphs for Lie groups at level k and quantum symmetries

#### 講演会

16:30-17:30   数理科学研究科棟(駒場) 270号室
Michael I. Tribelsky 氏 (MIREA (Technical University), Moscow, Russia)
Spectral properties of Nikolaevskiy chaos

### 2009年10月28日(水)

#### 講演会

16:30-17:30   数理科学研究科棟(駒場) 370号室
Michael Ruzhansky 氏 (Imperial College, London)
Dispersive and Strichartz estimates for hyperbolic equations of general form

### 2009年10月27日(火)

#### トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム
Alex Bene 氏 (IPMU)
A new appearance of the Morita-Penner cocycle
[ 講演概要 ]
In this talk, I will recall the Morita-Penner cocycle on the dual fatgraph complex for a surface with one boundary component. This cocycle, when restricted to paths representing elements of the mapping class group, represents the extended first Johnson homomorphism \\tau_1, thus can be viewed as a (in some specific sense canonical) "groupoid extension" of \\tau_1. There are now several different contexts in which this cocycle can be constructed, and in this talk I will briefly review several of them, including one discovered in the context of finite type invariants of homology cylinders in joint work with J.E. Andersen, J-B. Meilhan, and R.C. Penner.

### 2009年10月26日(月)

#### 複素解析幾何セミナー

10:30-12:00   数理科学研究科棟(駒場) 128号室
Pietro Corvaja 氏 (Università di Udine)
On Vojta's conjecture in the split function field case

### 2009年10月23日(金)

#### GCOE社会数理講演シリーズ

16:20-17:50   数理科学研究科棟(駒場) 117号室

アクチュアリーの役割Ⅰ

#### 談話会・数理科学講演会

16:30-17:30   数理科学研究科棟(駒場) 002号室
お茶&Coffee&お菓子: 16:00～16:30 (コモンルーム)

p進エタール層のp進Hodge理論
[ 講演概要 ]

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 128号室
Vladimir Bogachev 氏 (Moscow State University)
On invariant measures of diffusion processes with unbounded drifts
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/08.html

### 2009年10月22日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
On some questions related to Voiculescu's noncommutative topological entropy

#### 講演会

10:40-12:10   数理科学研究科棟(駒場) 128号室

#### 統計数学セミナー

16:30-17:40   数理科学研究科棟(駒場) 122号室

ASYMPTOTICALLY EFFICIENT DISCRETE HEDGING
[ 講演概要 ]
The notion of asymptotic efficiency for discrete hedging is introduced and a discretizing strategy which is asymptotically efficient is given explicitly. A lower bound for asymptotic risk of discrete hedging is given, which is attained by a simple discretization scheme. Numerical results for delta hedging in the Black-Scholes model are also presented.
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/07.html

#### 博士論文発表会

13:00-14:15   数理科学研究科棟(駒場) 122号室

Asymptotic Analysis for Stochastic Volatility (確率的ボラティティの漸近解析)

### 2009年10月21日(水)

#### GCOEレクチャーズ

15:30-17:00   数理科学研究科棟(駒場) 122号室
Jean-Dominique Deuschel 氏 (TU Berlin)
Mini course on the gradient models, Ⅲ: Non convex potentials at high temperature
[ 講演概要 ]
In the non convex case, the situation is much more complicated. In fact Biskup and Kotecky describe a non convex model with several ergodic components. We investigate a model with non convex interaction for which unicity of the ergodic component, scaling limits and large deviations can be proved at sufficiently high temperature. We show how integration can generate strictly convex potential, more precisely that marginal measure of the even sites satisfies the random walk representation. This is a joint work with Codina Cotar and Nicolas Petrelis.

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 056号室
Bernard Le Stum 氏 (Université de Rennes 1)
The local Simpson correspondence in positive characteristic
[ 講演概要 ]
A Simpson correspondance should relate Higgs bundles to differential modules (or local systems). We stick here to positive characteristic and recall some old and recent results : Cartier isomorphism, Van der Put's classification, Kaneda's theorem and Ogus-Vologodsky local theory. We'll try to explain how the notion of Azumaya algebra is a convenient tool to unify these results. Our main theorem is the equivalence between quasi-nilpotent differential modules of level m and quasi-nilpotent Higgs Bundles (depending on a lifting of Frobenius mod p-squared). This result is a direct generalization of the previous ones. The main point is to understand the Azumaya nature of the ring of differential operators of level m. Following Berthelot, we actually use the dual theory and study the partial divided power neighborhood of the diagonal.

#### 講演会

14:40-16:10   数理科学研究科棟(駒場) 128号室

#### 統計数学セミナー

15:00-16:10   数理科学研究科棟(駒場) 002号室

AR過程の優調和事前分布と偏自己相関係数による表示
[ 講演概要 ]
Tanaka and Komaki(2008)では時系列データが2次の自己回帰過程(AR過程)に従う 時のスペクトル密度の推定を考え、優調和事前分布に基づいたベイズスペクトル 密度の方がジェフリーズ事前分布に基づいたベイズスペクトル密度よりも精度よ く推定できることを示している。高次のAR過程での優調和事前分布はTanaka( 2009)によって初めて与えられたが、特性方程式の根を用いた表示のため、数値 実験を行う上では取り扱いづらかった。本発表では高次のAR過程への応用を念頭 において偏自己相関係数(PAC)によるパラメータ表示を導入し数値実験した結 果を紹介する。 また、PACパラメータによる表示は解析的な取扱いをする上でも利点があり、AR 過程の優調和事前分布に関して新しく得られた結果も幾つか紹介したい。
[ 講演参考URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2009/06.html

### 2009年10月20日(火)

#### トポロジー火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Tea: 16:00 - 16:30 コモンルーム

Torus fibrations and localization of index
[ 講演概要 ]
I will describe a localization of index of a Dirac type operator.
We make use of a structure of torus fibration, but the mechanism
of the localization does not rely on any group action. In the case of
Lagrangian fibration, we show that the index is described as a sum of
the contributions from Bohr-Sommerfeld fibers and singular fibers.
To show the localization we introduce a deformation of a Dirac type
operator for a manifold equipped with a fiber bundle structure which
satisfies a kind of acyclic condition. The deformation allows an
interpretation as an adiabatic limit or an infinite dimensional analogue
of Witten deformation.

Joint work with Hajime Fujita and Mikio Furuta.