## 過去の記録

### 2008年05月13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
Tamas Kalman 氏 (東京大学大学院数理科学研究科, JSPS)
The problem of maximum Thurston--Bennequin number for knots
[ 講演概要 ]
Legendrian submanifolds of contact 3-manifolds are
one-dimensional, just like knots. This coincidence'' gives rise to an
interesting and expanding intersection of contact and symplectic geometry
on the one hand and classical knot theory on the other. As an
illustration, we will survey recent results on maximizing the
Thurston--Bennequin number (which is a measure of the twisting of the
contact structure along a Legendrian) within a smooth knot type. In
particular, we will show how Kauffman's state circles can be used to solve
the maximization problem for so-called +adequate (among them, alternating

#### 解析学火曜セミナー

16:30-18:00   数理科学研究科棟(駒場) 128号室
Andr\'e Martinez 氏 (ボローニャ大学)
Resonances for non-analytic potentials (joint work with T. Ramond and J. Sj\\"ostrand)

#### Lie群論・表現論セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室

On endomorphisms of the Weyl algebra
[ 講演概要 ]
Noncommutative geometry has revived the interest in the Weyl algebras, which are basic building blocks of quantum field theories.
The Weyl algebra $A_n(\\C)$ is an associative algebra over $\\C$ generated by $p_i, q_i$ ($i=1,\\cdots,n$) with relations $[p_i, q_j]=\\delta_{ij}$. Every endomorphism of $A_n$ is injective since $A_n$ is simple.
Dixmier (1968) initiated a systematic study of the Weyl algebra $A_1$ and posed the following problem: Is every endomorphism of $A_1$ an automorphism?
We give an affirmative answer to this conjecture.
[ 講演参考URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

### 2008年05月12日(月)

#### Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 002号室
Jean-Michel Bismut 氏 (Univ. Paris-Sud, Orsay)
The hypoelliptic Laplacian
[ 講演概要 ]
Let $X$ be a compact Riemannian manifold. The Laplace Beltrami
operator $-\\Delta^{X}$, or more generally the Hodge Laplacian
$\\square^{X}$, is an elliptic second order self adjoint operator on $X$.

We will explain the construction of a deformation of the elliptic
Laplacian to a family of hypoelliptic operators acting on the total
space of the cotangent bundle $\\mathcal{X}$. These operators depend
on a parameter $b>0$, and interpolate between the Hodge Laplacian
(the limit as $b\\to 0$) and the geodesic flow (the limit as $b\\to + \\infty$).
Actually, the deformed Laplacian is associated with an exotic Hodge
theory on the total space of the cotangent bundle, in which the
standard $L_{2}$ scalar product on forms is replaced by a
symmetric bilinear form of signature $\\left( \\infty, \\infty \\right)$.

This deformation can be understood as a version of the Witten
deformation on the loop space associated with the energy functional.
From a probabilistic point of view, the deformed Laplacian
corresponds to a Langevin process.

The above considerations can also be used in complex geometry, in
which the Dolbeault cohomology is considered instead of the Rham cohomology.

Results obtained with Gilles Lebeau on the analysis of the
hypoelliptic Laplacian will also be presented, as well as
applications to analytic torsion.

#### 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

### 2008年05月08日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

Non-separable UHF algebras

### 2008年05月07日(水)

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 117号室

(東京大学大学院数理科学研究科)
On the connected components of moduli spaces of finite flat models

### 2008年05月01日(木)

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室
Rune Johansen 氏 (Copenhagen 大学)
On the structure of graph algebras of presentations of a sofic shift

### 2008年04月30日(水)

#### 東京幾何セミナー

14:40-18:00   数理科学研究科棟(駒場) 056号室

「今後の予定」欄には、東工大で行われるセミナーは表��

Morse theory for abelian hyperkahler quotients
[ 講演概要 ]
Kirwan はモーメント写像のノルムの2乗を Morse 関数として Morse 理論を展開することにより,シンプレクティック商のトポロジーを研究した.本講演では,これらの理論をトーラスによるハイパーケーラー商に拡張する.ハイパーケーラーモーメント写像のノルムの2乗はプロパーな関数でないが,ある場合には Morse 理論が展開できることを示す.さらに,Morse 理論が展開できる場合には,シンプレクティック商の場合より組織的に Betti 数やコホモロジー環が決定できることを示す.

ラグランジュはめ込みのフレアー理論について
[ 講演概要 ]

#### 代数学コロキウム

16:30-17:30   数理科学研究科棟(駒場) 117号室

Iwasawa theory of totally real fields for certain non-commutative $p$-extensions
[ 講演概要 ]
Recently, Kazuya Kato has proven the non-commutative Iwasawa main
conjecture (in the sense of Coates, Fukaya, Kato, Sujatha and Venjakob) for
non-commutative Galois extensions of "Heisenberg type" of totally real fields,
using integral logarithmic homomorphisms. In this talk, we apply Kato's method
to certain non-commutative $p$-extensions which are more complicated than those
of Heisenberg type, and prove the main conjecture for them.

### 2008年04月24日(木)

#### 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

[ 講演概要 ]

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]

・判別問題(特にクラス数が3以上の多値判別問題)
・誤り訂正符号
・ゲーム理論
・最適化理論(線形計画法、2次錐計画法)
・ネットワークフロー理論
・フォン=ノイマンのミニマックス定理
などが挙げられると思います。
[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/01.html

#### Kavli IPMU Komaba Seminar

17:00-18:30   数理科学研究科棟(駒場) 056号室
Motohico Mulase 氏 (University of California, Davis)
Recursion relations in intersection theory on the moduli spaces of Riemann surfaces
[ 講演概要 ]
In this talk I will give a survey of recent developments in the intersection theory of tautological classes on the moduli spaces of stable algebraic curves. The emphasis is placed on explaining where the Virasoro constraint conditions are originated. Recently several authors have encountered the same combinatorial recursion relation from completely different contexts, that eventually leads to the Virasoro constraint. This mysterious structure of the theory will be surveyed.

### 2008年04月22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
Sergey Yuzvinsky 氏 (University of Oregon)
Special fibers of pencils of hypersurfaces
[ 講演概要 ]
We consider pencils of hypersurfaces of degree $d>1$ in the complex
$n$-dimensional projective space subject to the condition that the
generic fiber is irreducible. We study the set of completely reducible
fibers, i.e., the unions of hyperplanes. The first surprinsing result is
that the cardinality of thie set has very strict uniformed upper bound
(not depending on $d$ or $n$). The other one gives a characterization
of this set in terms of either topology of its complement or combinatorics
of hyperplanes. We also include into consideration more general special
fibers are iimportant for characteristic varieties of the hyperplane
complements.

### 2008年04月21日(月)

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 122号室

Scorza quartics of trigonal spin curves and their varieties of power sums
[ 講演概要 ]
Our fundamental result is the construction of new subvarieties in the varieties of power sums for the Scorza quartic of any general pairs of trigonal curves and non-effective theta characteristics. This is a generalization of Mukai's description of smooth prime Fano threefolds of genus twelve as the varieties of power sums for plane quartics. Among other applications, we give an affirmative answer to the conjecture of Dolgachev and Kanev on the existence of the Scorza quartic for any general pairs of curves and non-effective theta characteristics.

#### 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

Ambient realization of conformal jets and deformation complex

### 2008年04月17日(木)

#### 統計数学セミナー

16:20-17:30   数理科学研究科棟(駒場) 126号室

[ 講演概要 ]

[ 講演参考URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/00.html

#### 作用素環セミナー

16:30-18:00   数理科学研究科棟(駒場) 056号室

On a class of II$_1$ factors with at most one Cartan subalgebra II

#### 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
WEISS Georg 氏 (東京大学大学院数理科学研究科)
Hidden dynamics and pulsating waves in self-propagating high temperature synthesis
[ 講演概要 ]
We derive the precise limit of SHS in the high activation energy scaling suggested by B.J. Matkowksy-G.I. Sivashinsky in 1978 and by A. Bayliss-B.J. Matkowksy-A.P. Aldushin in 2002. In the time-increasing case the limit coincides with the Stefan problem for supercooled water with spatially inhomogeneous coefficients. In general it is a nonlinear forward-backward parabolic equation with discontinuous hysteresis term.

In the first part we give a complete characterization of the limit problem in the case of one space dimension. In the second part we construct in any finite dimension a rather large family of pulsating waves for the limit problem. In the third part, we prove that for constant coefficients the limit problem in any finite dimension does not admit non-trivial pulsating waves.
This is a joint work with Regis MONNEAU (CERMICS, France).

### 2008年04月15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

On the invariants of knots and 3-manifolds related to the restricted quantum group
[ 講演概要 ]
I would like to talk about the colored Alexander invariant and the logarithmic
invariant of knots and links. They are constructed from the universal R-matrices
of the semi-resetricted and restricted quantum groups of sl(2) respectively,
and they are related to the hyperbolic volumes of the cone manifolds along
the knot. I also would like to explain an attempt to generalize these invariants to
a three manifold invariant which relates to the volume of the manifold actually.

### 2008年04月14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

トーリック・ファノ多様体のマルチプライア・イデアル層と二木不変量の関係について

### 2008年04月08日(火)

#### Kavli IPMU Komaba Seminar

10:30-12:00   数理科学研究科棟(駒場) 002号室
Akihiro Tsuchiya 氏 (IPMU, The University of Tokyo)
IPMU Komaba Lectures,Homotopy Theory (before 1970)

[ 講演概要 ]
Tuesday, April -- July, 2008
First Lecture Aprl 8

Recently the notion of homotopy theory has been widely used in many areas of
contemporary mathematics including mathematical physics.
The purpose of the lectures is to present an overview of the developments
of homotopy theory mainly from 1940's through 1960's, partly in view of
more recent progress in other areas.

(1) Prehistory of homotopy theory
-- Hurewicz theorem, Hopf theorem, Freudentahl suspension theorem
(2) Eilenberg-MacLane space and Postnikov system
(3) Steenrod algebras
(4) Serre's theorem on the homotopy groups of spheres
(5) Rational homotopy theory
(6) Stable homotopy category and Adams spectral sequence
(7) Vector bundles and characteristic classes
(8) Complex cobordism and Quillen's theorem
(9) Miscellaneous topics
Rereferences :
(1) J.P.May, A Concise Course in Algebraic Topology,
The University of Chicago Press
http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf
(2) Douglas Ravenel, Complex cobordism and stable homotopy groups of spheres

The second edition, AMS Chelsea Series
http://www.math.rochester.edu/u/faculty/doug/mu.html
(3) Mark Hovey, Model Category, AMS
(4) Gelfand and Manin, Homology Algebra

### 2008年03月19日(水)

#### PDE実解析研究会

10:30-11:30   数理科学研究科棟(駒場) 056号室
Juergen Saal 氏 (Department of Mathematics and Statistics, University of Konstanz)
Maximal Regularity for Mixed Order Systems
[ 講演概要 ]
In classical boundary value problems the related symbols are homogeneous in space and time. This allows for the application of a standard compactness argument in order to obtain the important maximal regularity. However, quasilinear systems arising e.g. from free boundary problems are in general of mixed order. In other words the related symbols are of intricate structure and in particular highly inhomogeneous. Therefore, the standard compactness argument fails. The purpose of this talk is to introduce the Newton polygon method, which gives a systematic approach to such mixed order systems and to demonstrate its strength by applications to the Stefan problem and a free boundary problem for the Navier-Stokes equations.

### 2008年03月14日(金)

#### 代数幾何学セミナー

16:30-18:00   数理科学研究科棟(駒場) 126号室
David Morrison 氏 (UC Santa Barbara)
Understanding singular algebraic varieties via string theory
[ 講演概要 ]
String theory has helped to formulate two major new insights in the study of singular algebraic varieties. The first -- which also arose from symplectic geometry -- is that families of Kaehler metrics are an important tool in uncovering the structure of singular algebraic varieties. The second, more recent insight -- related to independent work in the representation theory of associative algebras -- is that one's understanding of a singular (affine) algebraic variety is enhanced if one can find a non-commutative ring whose center is the coordinate ring of the variety. We will describe both of these insights, and explain how they are related to string theory.

### 2008年03月13日(木)

#### 解析学火曜セミナー

15:00-17:30   数理科学研究科棟(駒場) 117号室
「解析学(臨時)セミナー」と名称変更し,曜日,部屋も臨時に変更.

Schr/"odinger equations on scattering manifolds and microlocal singularities
Maciej ZWORSKI 氏 (カリフォルニア大学バークレイ校) 16:30-17:30
Local smoothing in the presence of lots of trapping
[ 講演参考URL ]
http://agusta.ms.u-tokyo.ac.jp/seminerphotos2/Zworski-abstract.pdf