Seminar information archive

Seminar information archive ~08/18Today's seminar 08/19 | Future seminars 08/20~

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.)
加藤晃史 (東京大学)
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 ]


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.)
藤川 英華 (千葉大理)


Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
勝良健史 (慶應大学)
Non-separable UHF algebras


Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
今井 直毅
On the connected components of moduli spaces of finite flat models


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


Geometry Seminar

14:40-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
今野宏 (東京大学大学院数理科学研究科) 14:40-16:10
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.
赤穂まなぶ (首都大学東京 都市教養学部理工学系) 16:30-18:00
[ Abstract ]
深谷・Oh・太田・小野は,シンプレクティック多様体 M の中のラグランジュ部分多様体 L に対して,種数 0 の prestable な境界付きリーマン面から M への安定写像で,境界値が L に含まれるようなものを考えることにより,L の鎖複体(の部分複体)上にギャップ・フィルター付き A 無限大代数の構造を定義した.本講演では,上の結果をラグランジュ部分多様体から(横断的な自己交叉をもつ)ラグランジュはめ込みへと拡張する.これにより,(横断的に交わる)有限個のラグランジュ部分多様体の和集合を一つのラグランジュはめ込みと見なすことができるなど,新しい視点が得られることを説明する.

Number Theory Seminar

16:30-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
原 隆 (東京大学大学院数理科学研究科)
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.


Applied Analysis

16:00-17:30   Room #002 (Graduate School of Math. Sci. Bldg.)
宮本 安人 (東京工業大学 大学院理工学研究科)
[ Abstract ]
円盤領域(2次元球領域)におけるNeumann問題 Δu+\\lambda f(u)=0 を考える.広いクラスの非線形項 f に対して,第2固有値と第3固有値から非球対称解からなる大域的な枝(シート)が分岐することを示し,第2固有値からの分岐の枝は,分岐直後は一意的であることを示す.

Seminar on Probability and Statistics

16:20-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
白石 友一 (統計数理研究所)
[ Abstract ]
[ Reference URL ]

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.


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


Algebraic Geometry Seminar

16:30-18:00   Room #122 (Graduate School of Math. Sci. Bldg.)
高木寛通 (東大数理)
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.)
平地 健吾 (東大数理)
Ambient realization of conformal jets and deformation complex


Seminar on Probability and Statistics

16:20-17:30   Room #126 (Graduate School of Math. Sci. Bldg.)
中野 張 (科学技術振興機構)
[ Abstract ]
[ Reference URL ]

Operator Algebra Seminars

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
小沢登高 (東大数理)
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).


Tuesday Seminar on Topology

16:30-18:00   Room #056 (Graduate School of Math. Sci. Bldg.)
村上 順 (早稲田大学理工)
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.


Seminar on Geometric Complex Analysis

10:30-12:00   Room #128 (Graduate School of Math. Sci. Bldg.)
佐野 友二 (東大IPMU)


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
(2) Douglas Ravenel, Complex cobordism and stable homotopy groups of spheres

The second edition, AMS Chelsea Series
(3) Mark Hovey, Model Category, AMS
(4) Gelfand and Manin, Homology Algebra


PDE Real Analysis Seminar

10:30-11:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Juergen Saal (Department of Mathematics and Statistics, University of Konstanz)
Maximal Regularity for Mixed Order Systems
[ Abstract ]
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.


Algebraic Geometry Seminar

16:30-18:00   Room #126 (Graduate School of Math. Sci. Bldg.)
David Morrison (UC Santa Barbara)
Understanding singular algebraic varieties via string theory
[ Abstract ]
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.


Tuesday Seminar of Analysis

15:00-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)
伊藤健一 (東京大学大学院数理科学研究科) 15:00-16:00
Schr/"odinger equations on scattering manifolds and microlocal singularities
Maciej ZWORSKI (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
[ Reference URL ]


Infinite Analysis Seminar Tokyo

13:00-16:30   Room #270 (Graduate School of Math. Sci. Bldg.)
岩尾慎介 (東大数理) 13:00-14:30
Solutions of hungry periodic discrete Toda equation and its ultradiscretization
[ Abstract ]
The hungry discrete Toda equation is a generalization of the discrete Toda
equation. Through the method of ultradiscretization, the generalized
Box-ball system (gBBS) with finitely many kinds of balls is obtained from
hungry discrete Toda eq.. It is to be expected that the general solution of
gBBS should be obtained from the solution of hungry discrete Toda eq.
through ultradiscretization. In this talk, we derive the solutions of hungry
periodic discrete Toda eq. (hpd Toda eq.), by using inverse scattering
method. Although the hpd Toda equation does not linearlized in the usual
sense on the Picard group of the spectral curve, it is possible to determine
its behavior on the Picard group.
竹縄知之 (東京海洋大・海洋工) 15:00-16:30
A tropical analogue of Fay's trisecant identity and its application to the ultra-discrete periodic Toda equation.
[ Abstract ]
The ultra-discrete Toda equation is essentially equivalent to the integrable
Box and Ball system, and considered to be a fundamental object in
ultra-discrete integrable systems. In this talk, we construct the general
solution of ultra-discrete Toda equation with periodic boundary condition,
by using the tropical theta function and the bilinear form. The tropical
theta function is associated with the tropical curve defined through the Lax
matrix of (not ultra-) discrete periodic Toda equation. For the proof, we
introduce a tropical analogue of Fay's trisecant identity. (This talk is
based on the joint work with R. Inoue.)

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