## Seminar information archive

#### Lectures

16:00-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
Jean-Pierre Puel 氏
(ヴェルサイユ大学 (Universite de Versailles St Quentin)
)
A non standard unique continuation property related to Schiffer conjecture
[ Abstract ]
Coming from a control problem for a coupled fluid-structure system, we are confronted to the following problem in dimension 2:
\\Delta^2 w = -\\lambda \\Delta w in \\Omega w = {\\partial w}/{\\partial n} = 0 on \\Gamma {\\partial\\Delta w}/{\\partial n}=0 on \\Gamma_0 \\subset \\Gamma.
The question is : do we have w=0?
There is a counterexample when \\Omega is a disc. The analogous of (local) Schiffer's conjecture is : is the disc the only domain for which we can have a non zero solution?
Notice that the term local means that the additional boundary condition occurs only on a part of the boundary and when this boundary is not analytic, this is a major difference. A sub-conjecture would be : when the boundary is not analytic, do we have w=0?
Here we show that when \\Omega has a corner of angle \\theta_{0} with \\theta_{0} \\neq \\pi, 3\\pi/2 and when $\\Gamma_{0}$ is (locally) one edge of this angle then the only solution is w=0.
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/top/general-access.html

### 2008/05/15

#### Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Mikael Pichot (東大数理)
Property RD and CAT(0) geometry

#### Applied Analysis

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

( Stability and uniqueness for surfaces with constant anisotropic mean curvature)
[ Abstract ]

を保つ変分に対する非等方的表面エネルギーの臨界点を非等方的平均曲率一定曲

あるときをいう.したがって,エネルギー極小解は安定である.

### 2008/05/13

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Tamas Kalman (東京大学大学院数理科学研究科, JSPS)
The problem of maximum Thurston--Bennequin number for knots
[ Abstract ]
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
and positive) knots and links.

#### Tuesday Seminar of Analysis

16:30-18:00   Room #128 (Graduate School of Math. Sci. Bldg.)
Andr\'e Martinez (ボローニャ大学)
Resonances for non-analytic potentials (joint work with T. Ramond and J. Sj\\"ostrand)

#### Lie Groups and Representation Theory

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)

On endomorphisms of the Weyl algebra
[ Abstract ]
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.
[ Reference URL ]
http://akagi.ms.u-tokyo.ac.jp/seminar.html

### 2008/05/12

#### Kavli IPMU Komaba Seminar

17:00-18:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Jean-Michel Bismut (Univ. Paris-Sud, Orsay)
The hypoelliptic Laplacian
[ Abstract ]
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.

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)

### 2008/05/08

#### Operator Algebra Seminars

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

Non-separable UHF algebras

### 2008/05/07

#### Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)

(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

### 2008/05/01

#### Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Rune Johansen (Copenhagen 大学)
On the structure of graph algebras of presentations of a sofic shift

### 2008/04/30

#### Geometry Seminar

14:40-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)

Morse theory for abelian hyperkahler quotients
[ Abstract ]
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
[ Abstract ]

#### Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)

Iwasawa theory of totally real fields for certain non-commutative $p$-extensions
[ Abstract ]
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.

### 2008/04/24

#### Applied Analysis

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

[ Abstract ]

#### Seminar on Probability and Statistics

16:20-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

・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。
[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/01.html

#### Kavli IPMU Komaba Seminar

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Motohico Mulase (University of California, Davis)
Recursion relations in intersection theory on the moduli spaces of Riemann surfaces
[ Abstract ]
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.

### 2008/04/22

#### Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
Sergey Yuzvinsky (University of Oregon)
Special fibers of pencils of hypersurfaces
[ Abstract ]
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.

### 2008/04/21

#### Algebraic Geometry Seminar

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)

Scorza quartics of trigonal spin curves and their varieties of power sums
[ Abstract ]
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.

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)

Ambient realization of conformal jets and deformation complex

### 2008/04/17

#### Seminar on Probability and Statistics

16:20-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)

[ Abstract ]

[ Reference URL ]
http://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2008/00.html

#### Operator Algebra Seminars

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

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

#### Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
WEISS Georg (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
[ Abstract ]
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).

### 2008/04/15

#### Tuesday Seminar on Topology

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

On the invariants of knots and 3-manifolds related to the restricted quantum group
[ Abstract ]
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.

### 2008/04/14

#### Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)

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

### 2008/04/08

#### Kavli IPMU Komaba Seminar

10:30-12:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Akihiro Tsuchiya (IPMU, The University of Tokyo)
IPMU Komaba Lectures,Homotopy Theory (before 1970)

[ Abstract ]
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