## Seminar information archive

### 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 ]
https://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 ]
https://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

### 2008/03/19

#### 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.

### 2008/03/14

#### 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.

### 2008/03/13

#### Tuesday Seminar of Analysis

15:00-17:30   Room #117 (Graduate School of Math. Sci. Bldg.)

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 ]
http://agusta.ms.u-tokyo.ac.jp/seminerphotos2/Zworski-abstract.pdf

### 2008/02/23

#### Infinite Analysis Seminar Tokyo

13:00-16:30   Room #270 (Graduate School of Math. Sci. Bldg.)

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.

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.)

### 2008/02/20

#### Seminar on Probability and Statistics

16:20-17:30   Room #122 (Graduate School of Math. Sci. Bldg.)

A Test for Cross-sectional Dependence of Microstructure Noises and their Cross-Covariance Estimator
[ Abstract ]

[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/21.html

#### Lectures

13:30-17:45   Room #123 (Graduate School of Math. Sci. Bldg.)

Divergence formulae on the space of continuous functions and Malliavin calculus

Ginibre random point field and a notion of convergence of Dirichlet forms
Lorenzo Zambotti (パリ第6大学) 15:30-16:30
Stochastic PDEs and infinite dimensional integration by parts formulae

ランダム環境下の確率モデルに関連する問題
(A problem arising in stochastic models in random environments)

### 2008/02/19

#### Lectures

16:30-17:30   Room #118 (Graduate School of Math. Sci. Bldg.)
An overview on archimedean L-factors for G_1xG_2
[ Abstract ]
When G_1xG_2 is one of pairs GL(n)xGL(n), GL(n)xGL(n+1), GL(n)xSO(2n+1), and GL(n+1)xSO(2n+1), we have evaluation of the archimedian L-factors of automorphic L-functions obtained by Rankin-Selberg convolution.
The last two cases are joint works with Taku Ishii (Chiba Inst. of Tech) which are in progress.

### 2008/02/13

#### Seminar on Probability and Statistics

16:20-17:30   Room #123 (Graduate School of Math. Sci. Bldg.)

Realized multipower variationの統計推測への応用について
[ Abstract ]

[ Reference URL ]
https://www.ms.u-tokyo.ac.jp/~kengok/statseminar/2007/20.html

### 2008/02/12

#### Kavli IPMU Komaba Seminar

17:00-18:30   Room #056 (Graduate School of Math. Sci. Bldg.)
Katrin Wendland (University of Augrburg)
How to lift a construction by Hiroshi Inose to conformal field theory
[ Abstract ]
The moduli space of Einstein metrics is well known to algebraic and differential geometers. Physicists have introduced the notion of conformal field theories (CFTs) associated to K3, and the moduli space of these objects is well understood as well. It can be interpreted as a generalisation of the moduli space of Einstein metrics on K3, which allows us to introduce this space without having to use background knowledge from conformal field theory. However, just as no smooth Einstein metrics on K3 are known explicitly, the explicit construction of CFTs associated to K3 in general remains an open problem. The only known constructions which allow to deal with families of CFTs give CFTs associated to K3 surfaces with orbifold singularities.

We use a classical construction by Hiroshi Inose to explicitly construct a family of CFTs which are associated to a family of smooth algebraic K3 surfaces. Although these CFTs were known before, it is remarkable that they allow a description in terms of a family of smooth surfaces whose complex structure is deformed while all other geometric data remain fixed.

We also discuss possible extensions of this result to higher dimensional Calabi-Yau threefolds.

### 2008/02/07

#### Lectures

16:30-18:00   Room #002 (Graduate School of Math. Sci. Bldg.)
Luc Illusie (パリ南大学)
On Gabber's refined uniformization theorem and applications
[ Abstract ]
Gabber has announced the following theorem : if X is a noetherian quasi-excellent scheme, Z a nowhere dense closed subset, and l a prime number invertible on X, then, locally for the topology on schemes of finite type over X generated, up to thickenings, by proper surjective maps which are generically finite of degree prime to l and by Nisnevich covers, the pair (X,Z) can be uniformized, i. e. replaced by a pair (Y,D), where Y is regular and D a strict normal crossings divisor. The whole proof is not yet written. I will give an overview. The plan is :
1. Statement and reduction to the complete local case (techniques of approximation)
2. Refined partial algebraization of complete local noetherian rings
3. Reduction to the equivariant log regular case (de Jong's techniques)
4. Making actions very tame, end of proof.
If time permits, I will show how the above theorem provides a short proof of Gabber's finiteness theorem for higher direct images of constructible sheaves of torsion prime to the characteristics by morphisms of finite type between quasi-excellent noetherian schemes.